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3 Abstract This thesis focuses on various problems of the operation of a WDM optical packet ring: design, packet scheduling, delivered QoS and efficiency of optical transport. The relationship between these issues is shown and a range of tools for dimensioning and network control is proposed. This synchronous optical packet ring with multiple data channels and a single control channel has been studied by the ANR ECOFRAME ( ). The stations of the ring have tunable transmitters and WDM fixed receivers. Using information from control channel, a station extracts, at each slot, all packets that are destined to it and lets the transit traffic pass transparently and can insert at most one packet per slot, into a data channel. The study is limited to the most plausible scenarios on the operational plan: transportation of guaranteed traffic only and absence of slot reservation mechanisms. The ring may authorize or not a direct traffic between stations. Indeed, metropolitan networks often have a function of concentration and distribution but the direct transit between stations seems to be more efficient. The first results relate to the design. For a given traffic matrix, we minimize a cost of configuration incorporating costs of using wavelengths (data channels) and receivers. Under different flow allocation constraints, complexity results have been obtained, and the optimization is obtained in Integer Linear Programming (ILP) form. An optimal solution has been obtained for rings of up to 9 nodes, and the heuristics has been proposed for the larger sizes of rings. We have integrated the fact that a station can transmit only one packet per slot. This constraint arises if all stations cannot receive packets on all channels of data. The formulation of type MILP is valid for any process of packet scheduling of type MaxWeight. We evaluated the performance of a properly dimensioned ring with analytical models (insertion into the ring with a queue Geo/Geo/1), which were validated by simulating in ns2 a new MAC for synchronous ring. The analytical model is used to quantify the gain in efficiency due to WDM receivers. The simulator has allowed us to compare different scheduling mechanisms in terms of fairness of the process of issuing packets by a given station. This process is not work conserving (unless each station can receive packets on all channels). We have identified a simple mechanism, operating a single state per queue, with a behavior similar to that of the mechanism OPF (Oldest Packet First) that emulates, as much as possible, a FIFO packet insertion. The two main operational conclusions are given below. The special case where each station can receive traffic on all channels of data is optimal in terms of design and performance. More generally, we believe we have shown that our initial assumptions, namely not to use the slot reservation process, but find an adequate design of the ring, allow stable operation of the ECOFRAME ring, with a good performance.

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5 Résumé court Cette thèse porte sur différentes problématiques du fonctionnement d un anneau WDM de paquets optiques: dimensionnement, ordonnancement des paquets, QoS délivrée et efficacité du transport optique. Les relations entre ces problématiques sont montrées et une palette d outils pour dimensionner et contrôler ce réseau est proposée. Cet anneau synchrone de paquets optiques avec plusieurs canaux de données et un unique canal de contrôle a été étudié par le projet ANR ECOFRAME ( ). Les stations de l anneau disposent d émetteurs accordables et de récepteurs WDM fixes. A partir des informations du canal de contrôle, une station extrait, à chaque slot, tous les paquets qui lui sont destinés et laisse passer de façon transparente le trafic en transit ; elle peut insérer au plus un paquet par slot, sur un canal de données. L étude est limitée aux scénarios les plus vraisemblables au plan opérationnel : transport uniquement de trafic garanti et absence de mécanisme de réservation de slots. L anneau peut autoriser, ou non, un trafic direct entre stations. En effet, les réseaux métropolitains ont souvent une fonction de concentration et de distribution mais le transit direct entre stations semble plus performant. Les premiers résultats portent sur le dimensionnement. Pour une matrice de trafic donnée, on minimise un coût de configuration intégrant coûts d usage d une longueur d onde (canal de données) et des récepteurs. Sous différentes contraintes d allocation des flux, des résultats de complexité ont été obtenus, et l optimisation formulée en Integer Linear Programming (ILP). Une solution optimale a été obtenue pour les anneaux d au plus 9 nœuds, et des heuristiques proposées pour des tailles supérieures. Nous avons intégré le fait qu une station ne peut émettre qu un seul paquet par slot. Cette contrainte survient si toutes les stations ne peuvent recevoir des paquets sur tous les canaux de données. La formulation, de type MILP, est valide pour tout processus d ordonnancement des paquets de type MaxWeight. Nous avons évalué les performances d un anneau correctement dimensionné avec des modèles analytiques simples (insertion sur l anneau par une file d attente Geo/Geo/1), qui ont été validés en simulant sous ns2 une nouvelle MAC pour anneau synchrone. La modélisation analytique a permis de quantifier le gain en efficacité dû aux récepteurs WDM. Le simulateur nous a permis de comparer différents mécanismes d ordonnancement en terme d équité du processus d émission des paquets par une station donnée. Ce processus n est pas work conserving (sauf si chaque station peut recevoir des paquets sur tous les canaux). Nous avons identifié un mécanisme très simple, car exploitant un unique état par file d attente; son comportement est proche de celui d un mécanisme OPF (Oldest Packet First) qui émule, autant que possible, une insertion FIFO des paquets. Les deux principales conclusions opérationnelles sont données ci après. Le cas particulier où chaque station peut recevoir du trafic sur tous les canaux de données est optimal en terme de dimensionnement et de performance. Plus généralement, nous pensons avoir montré que nos hypothèses initiales, consistant à ne pas utiliser de processus de réservation, mais s appuyant sur un dimensionnement adéquat de l anneau, permettaient un fonctionnement stable de

6 iv RÉSUMÉ COURT l anneau ECOFRAME, avec une bonne performance.

7 Résumé Introduction Ce travail porte sur l étude d une nouvelle technologie pour les réseaux métropolitains (Metropolitan Area Networks, MAN). Traditionnellement, les réseaux métropolitains sont basés sur l architecture SONET/SDH. Leur topologie est typiquement composée de plusieurs anneaux. Le type de commutation utilisé dans les anneaux métropolitains traditionnels est la commutation des circuits (Optical Circuit Switching, OCS). Les contraintes que les réseaux métropolitains du futur doivent satisfaire sont 1. Scalabilité améliorée; 2. Délivrance multiservices de la bande passante; 3. Grande flexibilité et efficacité en termes de coût des services. Les solutions envisagées pour répondré à ces contraintes sont basées sur l utilisation des commutations différentes. Les commutations à granularité plus fines comme Optical Packet Switching (OPS) et Optical Burst Switching (OBS) sont prises en compte pour construire un réseau métropolitain du futur. Optical Packet Switching est la technologie de commutation à granularité la plus fine, où les unités de commutation sont les paquets optiques. Optical Burst Switching emploie la commutation de paquets de grande taille (appellés burst). Des topologies différentes sont envisagées aussi pour cette partie du réseau: le réseau métropolitain du futur devrait être en forme d anneau ou maillé. Architecture ECOFRAME Le réseau étudié dans ce travail est développé dans le cadre du projet français ECOFRAME, supporté par l Agence Nationale de Recherche. Ce projet a commencé début Sous la direction d Alcatel-Lucent France, et avec la participation de TELECOM Bretagne, TELE- COM Paris Tech, TELECOM SudParis, Université de Limoges, Université de Versailles - Saint Quentin en Yvelynes, France Télécom et Kloé. L anneau ECOFRAME est caractérisé par la topologie en anneau. Le système est synchronisé et le médium optique est accessible par les stations ECOFRAME à des intervalles à durée finie (time slots). Les anneaux optiques ECOFRAME utilisent le multiplexage WDM et les conteneurs optiques de taille fixe.

8 vi RÉSUMÉ Il existe deux types de canaux utilisés dans l anneau ECOFRAME: un canal de contrôle et approximativement 40 canaux de données. Le canal de contrôle transporte l information sur les conteneurs optiques des canaux de données. Parmi les informations transportées par le canal de contrôle, les plus importants sont le statut des time slots sur les canaux de données (un time slot peut être soit libre soit occupé), la classe de services des conteneurs optiques, les informations relatives aux mécanismes de réservation, etc. Les caractéristiques principales de l anneau ECOFRAME sont la transparence optique de trafic en transit et la commutation de type OPS. La transparence optique diminue la taille des stations en simplifiant le hardware installé à chaque location, et par conséquence, elle réduit le coût de consommation énergétique. D un autre côté, la granularité du paquet de commutation rend l utilisation de la bande passante plus efficace, ce qui est un autre avantage notable de cette technologie. Chaque station ECOFRAME est équipée d un émetteur accordable et d un certain nombre de récepteurs fixes. Il existe deux types de récepteurs utilisés dans l anneau ECOFRAME (comme présenté à la Fig. 1), les récepteurs : 1. à mono-longeur d onde (récepteurs non-wdm ) 2. à multi-longeur d onde (récepteurs WDM ). Λ i Λ i1 Λ i2 Λ in... non-wdm Rx WDM Rx 10 Gbps (a) récepteur non-wdm 10 Gbps (b) récepteur WDM Figure 1 Réprésentation fonctionnelle des récepteurs non-wdm et WDM Les stations équipées par un récepteur mono-longueur d onde peuvent recevoir le trafic sur une seule longueur d onde prédéfinie, alors que les stations équipées par des récepteurs multi-longeur d onde peuvent recevoir le trafic sur un ensemble de longeurs d onde. Si le récepteur multi-longeur d onde a une taille fixe (S), il est de type barette. Typiquement S = 2,4,8,10,... Le débit maximal reçu par un récepteur est limité à 10 Gbps, indépendamment du type de récepteur. Par conséquent, une station ECOFRAME ne peut insérer qu un paquet par time slot mais est capable d extraire plusieurs paquets par time slot. Les récepteurs qui opèrent sur la même partie de la bande passante peuvent être utilisés pour plusieurs destinations. Le protocole ECOFRAME utilise deux types d unités d information de base: Service Data Unit (SDU) et Protocole Data Unit (PDU). Un SDU est formé à partir d une trame cliente dans le processus d encapsulation. Par conséquent, les SDU n ont pas une taille fixe. Chaque

9 RÉSUMÉ vii PDU est créé à partir d un ou plusieurs SDU dans un processus dans lequel la segmentation est éventuellement utilisée. La taille du PDU est fixe. Etat de l art des technologies de paquets pour le métro Pour les réseaux métropolitains, deux types de solutions sont actuellement offertes: 1. Technologies à paquet électronique, ou les réseaux All-IP: RPR, MPLS-TP, PBB-TE. 2. Technologies à paquets optiques: Projets de recherche : HORNET, RINGO, DAVID, DBORN, FLAMINGO, Réseau commercialisé: MATISSE. Les technologies de la première catégorie appartiennent à la catégorie des réseaux opaques optiques WDM. Autrement dit, dans ces réseaux, tout le trafic en transit subit systématiquement une conversion Optical-Electrical-Optical (OEO). Par la suite, la consommation d énergie dans ces réseaux sera plus grande que dans ECOFRAME. La différence principale entre ECOFRAME et les réseaux de deuxième catégorie est le nombre et le type d émetteurs et/ou récepteurs utilisés par les stations. ECOFRAME est caractérisé par des émetteurs accordables et des récepteurs à multi-longueurs d ondes partagées. Dans ce travail, l efficacité des solutions ECOFRAME par rapport à celles de MATISSE, la technologie récemment commercialisée, en termes de coût, sont démontrées. Formulation du problème Cette thèse a essayé d aborder deux problèmes relatifs à la conception d un anneau ECOFRAME: Comment trouver une configuration optimale de l anneau ECOFRAME? Comment inclure les garanties de QoS dans la configuration optimale? Pour résoudre ces problèmes, les techniques de planification (dimensionnement) des réseaux et d ingénierie de trafic ont été utilisées. Ces deux techniques ont été utilisées ensemble et les conclusions obtenues en utilisant une de ces techniques ont été considérées en appliquant l autre technique. Les problèmes précédents ont été traités dans cette thèse pour le trafic garanti (car ECOFRAME est un réseau de transport), et pour un accès aux time-slots de type opportuniste, c est-à-dire que les mécanismes de réservation des time slots n ont pas été pris en compte. Les problèmes mentionnés ont été abordés en utilisant des matrices de trafic différentes. Une matrice de trafic donne la quantité de trafic que chaque station voudrait envoyer aux autres. Comme le but de ce travail était de dimensionner un anneau ECOFRAME, il faut d abord définir ce qu est un dimensionnement. En effet, le dimensionnement consiste à mapper chaque flux source-destination sur les longueurs d onde pour que le coût des ressources utilisées soit minimal.

10 viii RÉSUMÉ Dimensionnement TDM/WDM de l anneau à commutation des paquets optiques Dans cette partie du travail, les méthodes classiques de dimensionnement des réseaux optiques WDM ont été appliquées pour trouver une configuration à coût optimal de l anneau ECOFRAME. Une configuration de l anneau ECOFRAME est déterminée par: les longueurs d onde activées sur l anneau, les récepteurs de chaque station. Le but du dimensionnement dans cette section était de minimiser le coût total, c est-à-dire de trouver une configuration au coût optimal. Le coût total est égal à la somme des coûts des longueurs d onde et des récepteurs. Il est évident qu il existe un compromis entre le nombre de récepteurs et le nombre de longueurs d onde utilisées sur l anneau. Comme nous pouvons le voir dans la Fig. 2, pour la même matrice de trafic, les configurations pour un nombre optimal de longueur d onde et un nombre optimal de longueurs d onde ne sont pas équivalents. Le réseau à gauche (Fig. 2) a seulement 2 longueurs d onde mais utilise 4 récepteurs, alors que l anneau à droite à seulement 3 récepteurs mais utilise 3 longueurs d onde. L évaluation du compromis entre le nombre de récepteurs et le nombre de longueurs d onde est un des résultats de ce travail. transmet reçoit station 1 station 2 transmet reçoit station 1 station 2 station 4 station 3 station 4 station 3 (a) Dimensionnement à coût de longueurs d onde minimal (b) Dimensionnement à coût de récepteurs minimal Figure 2 Exemples de dimensionnement de l anneau ECOFRAME Pour trouver un dimensionnement optimal, nous avons utilisé l optimisation convexe (notamment la programmation linéaire), et quand c était nécessaire et possible, les heuristiques. Comme déjà mentionné, en cherchant la configuration optimale les coûts de l utilisation des longueurs d onde et des récepteurs multi-longueurs d onde de tailles fixes (type barettes) ont été pris en compte. Le coût des émetteurs n est pas pris en compte, chaque station étant équipée d un émetteur accordable. Le coût d une longueur d onde (C w ) peut être estimé à 1/40 du coût de location d une fibre noire. Le côut de location de cette dernière peut être estimé à 1.2 euros/m/an pour une période de location de 5 ans, par exemple. Le coût d un récepteur mono-longueur d onde (C r (1) ) est approximativement égal au coût d un émetteur relié à un port 10GigE (C r (1) ]1, 2[k$).

11 RÉSUMÉ ix On suppose qu entre le coût d un récepteur multi-longueur d onde et celui d un récepteur mono-longueur d onde existe une relation sous-linéaire: C (n) r = C (1) r n α, (1) où n est le nombre de longueurs d onde du récepteur, C r (n) est le coût du récepteur multilongueur d onde et α est une constante plus petite que 1. La même formule pour α = 0.5 est valide pour les récepteurs dans le réseau SONET/SDH. Pour résumer, une estimation approximative du coût d un récepteur non-wdm, C r (1), et du coût d une longueur d onde utlilisée dans l anneau, C w, est C (1) r 300, C w 30 D, (2) où D est la longueur de l anneau, en km. Pour la circonférence de l anneau métropolitain de 50 km, le rapport de coût est (C (1) r /C w ) 0.2. Bien que ce rapport de coût de récepteur et de longueurs d onde semble le plus réaliste, nos méthodes de dimensionnement donnent un résultat pour tous les rapports de coûts possibles. Types de dimensionnement Les 4 configurations suivantes ont été étudiées: 1. Single dedicated wavelength per destination (SDW). Dans cette configuration, une seule longueur d onde est utilisée par destination. Autrement dit, le nombre de longueur d onde utilisé dans l anneau est égal au nombre des stations. Un exemple d une telle configuration est le réseau MATISSE. 2. Single shared receiver per destination (SSR). Dans cette configuration, un récepteur de taille S est utilisé par destination mais on suppose que ces récepteurs peuvent être partagés entre les destinations. 3. Multi shared receivers per destination without flow splitting (MR-N). Dans cette configuration, plusieurs récepteurs de taille S sont permis par destination, ils peuvent être partagés entre les destinations, mais le partage de flux est interdit. On dit qu un flux est partagé s il est routé sur les longueurs d onde de plusieurs récepteurs de la même destination. 4. Multi shared receivers per destination with flow splitting (MR-S). Plusieurs récepteurs sont permis par destination et les récepteurs peuvent être partagés. Le partage de flux est permis également. L intérêt d introduire les configurations précédentes est de comparer leur coût et d examiner l impact du partage du flux sur les performances du réseau. La complexité des configurations précédentes varie. La complexité de la première configuration est basse alors que celle de SSR, MR-N et MR-S est plus élevée. Les problèmes de dimensionnement SSR, MR-N et MR-S contiennent le problème de wavelength assignement (WA), comme un sous-problème. SSR et MR-N sont formalisées en forme 0-1 Integer Linear Program (0-1 ILP). MR-S est résolu en forme de Mixed Integer Linear Program (MILP).

12 Coût de dimensionnement x RÉSUMÉ Le coût total de dimensionnement, pour les différentes configurations, versus l amplitude a du trafic offert entre chaque deux stations (trafic any-to-any), dans un anneau à 6 nœuds et pour le rapport des coûts de récepteur non-wdm et de longueur d onde C r /C w = 1, est donné à la Fig. 3. Figure 3 Coût de dimensionnement des architectures des anneaux différents, dans un anneau à 6 nœuds et pour le trafic Any-to-Any De Fig. 3, nous pouvons voir que la relation entre les coûts des configurations différentes est: coût(mr-s) coût(mr-n) coût(ssr) coût(sdw). Dans ce travail, le problème de configuration MR-S est prouvé être NP-complet. En utilisant CPLEX et LP solve, les outils pour résoudre les problèmes de programmation linéaire, la configuration optimale pour le problème MR-S peut être trouvée pour les réseaux de taille N < 9. Les résultats obtenus montrent que pour C r /C w = 0.1, l économie de la configuration est très importante, dans le cas de trafic any-to-any et une taille de l anneau de 6 nœuds. Pour les réseaux d une plus grande taille, l heuristique Minimize Receiver Cost First (MRCF) est proposée. Cette heuristique a deux étapes principales. Dans la première étape, elle essaye à optimiser le nombre de récepteurs utilisés. Elle essaye ensuite, dans la deuxième étape, qui est executé que pour C r /C w, de réacheminer le trafic pour diminuer le nombre de longueurs d onde utilisées. On montre que la précision de l heuristique est au maximum de 33% du coût optimal, pour les réseaux d une taille plus petite que 9 noeuds et le trafic any-to-any. L impact du partage de flux Les flux source-destination forme la matrice de trafic utilisée pour le dimensionnement et pour l évaluation des performances.

13 RÉSUMÉ xi Comme déjà dit, un flux est partagé, s il est routé sur plusieurs récepteurs de la même destination. Un des résultats de cette thèse est l étude de l impact du partage de flux sur la complexité des ordonnanceurs utilisé dans l anneau. Notamment, il est démontré que la configuration où le partage de flux est permis (de type MR-S), a un coût moins cher, mais demande des ordonnanceurs compliqués, par rapport à la configuration où le partage de flux est permis (de type MR-N). Les ordonnanceurs dans les anneaux MR-S doivent respecter les débits donnés par la matrice de trafic, pour éviter une performance dégradée. Dans cette thèse, il est aussi montré que le cas le plus simple, où toutes les longueurs d onde sont écoutées par toutes les destinations, a la plus grande capacité parmi toutes les configurations à nombre de longueurs d onde égal. Les méthodes différentes pour dimensionner un anneau ECOFRAME proposées jusqu à maintenant trouvent une configuration optimale en termes de coût, mais ne garantissent pas la stabilité des files d attentes dans l anneau. Le problème de stabilité a été abordé dans le Chapitre 4 de cette thèse et le résumé de Chapitre 4 est donné dans la suite. Dimensionnement stable de l anneau à commutation des paquets optiques Quand on dimensionne les réseaux à commutation des circuits (OCS), le problème de stabilité n apparaît pas, parce qu on route les flux de trafic déjà formés. Le problème de stabilité existe dans les réseaux à commutation de paquets. Par exemple, dans un anneau de paquets électroniques RPR, le multiplexage des paquets est réglé par le protocole et par conséquent, le problème de stabilité existe. De mêmes raisons, le problème de stabilité existe dans un anneau ECOFRAME. Les différences d un anneau ECOFRAME, par rapport aux anneaux RPR sont: 1. trafic en transit est prioritaire ; 2. pas de conversion OEO de trafic en transit. Notons aussi, que dans un anneau ECOFRAME, un paquet et un seul peut être émis par time slot. Dans cette thèse le problème de stabilité a été adressé par une approche approximative et une approche exacte. L approche approximative considère que les files d attente peuvent être observées indépendamment, c est-à-dire, il est considéré que le nombre de paquets pouvant être émis par une station, par time slot, n est pas limité à 1. Cette approche à conduit à un dimensionnement qui s appelle Packet Aware Design with Multiple packet insertion (PAD-M) et qui est expliqué dans la section 4.2 de cette thèse. Ici, nous présentons que l approche exacte, qui donne une formulation de dimensionnement qui s appelle Packet Aware Design with Single packet insertion (PAD-S) et qui suppose que un seul paquet peut être émis par time slot, par une station. Les paquets qui arrivent dans un nœud ECOFRAME sont classifiés dans les files d attente séparées selon leur destination ou selon les longueurs d onde sur lesquelles ils sont routés. Dans ce travail, les deux manières de classification des paquets ont été étudiées.

14 xii RÉSUMÉ Nous avons comparé les performances de plusieurs mécanismes d insertion (ordonnanceurs), qui diffèrent par le mode de sélection du paquet à insérer. Tous les ordonnanceurs considérés commencent par définir, à chaque slot, l ensemble des paquets éligibles (paquets pouvant être émis), en fonction du remplissage des files d attente et de la mode de la classifications des paquets dans les files d attente. Si l ensemble des paquets éligibles est non vide, la politique de choix du paquet à émettre définit l ordonnanceur. Les ordonnanceurs différents qui ont été étudié sont: 1. Oldest Packet First (OPF): parmi les paquets éligibles, on choisit celui qui attend depuis le plus longtemps; 2. Longest Queue First (LQF): la file servie est la plus longue parmi celles contenant des paquets éligibles; 3. Longest Virtual Waiting Time First (LVWTF): une modification de LQF qui pondère la longueur de la file d attente par un facteur inversement proportionnel au débit utilisé pour dimensionner le système et sert la file pour laquelle la valeur obtenue est maximum. 4. RADNOM (RAND): on choisit la file à servir uniformément parmi les files contenant des paquets éligibles; 5. Priority Queueing: certaines files d attente ont la priorité de service, par rapport aux autres files. Relation entre stabilité et ordonnancement Le problème de stabilité est relié au choix de la politique d ordonnancement. Considerons 2 longueurs d onde Λ 1 et Λ 2. Un slot sur Λ 1 (respectivement Λ 2 ) est libre avec la probabilité µ 1 (respectivement µ 2 ); dans notre example, µ 1 = 1 et µ 2 varient entre 0.1 et 0.9. Les débits d arrivées des paquets sont λ 1 et λ 2. La politique d ordonnancement est la suivante: aussi longtemps qu il y a des paquets dans la première file d attente, ils sont servis. Les paquets de la deuxième file sont servis seulement si la première file d attente est vide. Evidemment, la première file d attente est stable, aussi longtemps que λ 1 < 1. En revanche, la probabilité qu un time slot puisse être utilisé pour servir la deuxième file d attente est µ 2 (1 λ 1 ), ce qui est significativement plus sévère que λ 2 < 1. La Fig. 4 présente le maximum de la charge de la file d attente 2 et la charge totale versus la charge de la file d attente 1, pour priority queueing et l ordonnancement OPF, où le plus vieux paquet est selectionné pour la transmission. La Fig. 4 montre que la région de stabilité pour priority queueing est beaucoup plus petite que la région de stabilité pour OPF. Autrement dit, les conditions de stabilité sont différentes pour les deux politiques d ordonnancement comparées. Etat de l art sur les conditions de stabilité Pour étudier la stabilité, un nœud ECOFRAME est modélisé par un serveur qui comporte plusieurs files d attente avec une longueur d onde par file. Par conséquent, un nœud ECOFRAME est stable si ses files d attente sont stables.

15 RÉSUMÉ xiii 1 La charge de la file d attente 2 et la charge totale OPF, la charge totale priority queueing, la charge totale OPF, la charge de la file d attente 2 priority queueing, la charge de la file d attente λ 1 Figure 4 Les valuers maximales de λ 2 et la charge totale maximale versus λ 1 Selon Tassiulas & Ephremides [84], les conditions de stabilité nécessaires pour tous les ordonnanceurs et suffisantes pour LQF sont: i Q λ i < 1 i Q (1 µ i ), Q {1,2,..,w}, (3) où {1,2,..,w} est l ensemble des longueurs d onde dans l anneau, λ i est la probabilité que un paquet arrive dans la file d attente i, dans le slot observé et µ i est la probabilité que le slot observé est libre. Selon Stolyar [83], les conditions suffisantes pour les ordonnanceurs MaxWeight sont: ( i {1,2,...,w}) ( m)( φ mi ]0,1[) ( λ i < m π m φ mi ) w φ mi 1, (4) où il est considéré que le système se trouve dans l état m avec la probabilité π m. MaxWeight est une classe d algorithmes qui pour l émission choisit la file d attente avec l index k, selon la formule: i=1 β k arg max γ i (c Q i i Q i(t) + c W i W i (t)), (5) où γ i,c Q i,cw i et β sont des constantes, pendant que Q i (t) et W i (t), sont la taille de la file d attente i et l âge du paquet en tête de la fille d attente i, respectivement. OPF, LQF et LVWTF appartient à la classe des algorithmes d ordonnancement MaxWeight, alors que ni RAND, ni Priority Queueing, n y appartient pas. Stabilité dans ECOFRAME Dans cette thèse il est prouvé que dans le cas général, pour tout w, la condition (3) suffisant pour la stabilité avec LVWTF. Le théorème suivant est aussi donné.

16 xiv RÉSUMÉ Théorème. Les conditions (3) et (4) sont équivalentes, c est-à-dire qu un nœud ECOFRAME est stable pour toutes les politiques de MaxWeight si et seulement si: (1 µ i ), Q {1,2,..,w}. (6) i Q λ i < 1 i Q Le théorème est prouvé pour w = 2 et w = 3, mais la conjecture est que le théorème est vrai pour tous w, c est-à-dire, que l anneau ECOFRAME est stable pour tous les algorithmes de type MaxWeight. L intérêt du théorème de stabilité est d obtenir le dimensionnement PAD-S de l anneau ECOFRAME, qui garantit la stabilité dans le cas général. La contrainte originale (6) est non-linéaire, mais toutes les variables qui y participent sont binaires, alors, cette contrainte peut être linéarisée [52] et le dimensionnement stable PAD-S peut être formalisé en forme de Mixed Integer Linear Program. Donc, jusqu à maintenant, nous avons montré que nous savons dimensionner un réseau en intégrant les contraintes de stabilité. On a une condition de stabilité générale pour toute une famille de ordonnanceurs (qui n intègre pas Random, ni Priority Queueing). Cependant, la configuration stable ne garantit pas les performances en termes de QoS du réseau. Dans la suite, nous explorons comment des politiques d ordonnancement différentes affectent les performances de l anneau, c est-à-dire que nous analysons les performances de l anneau. Analyse des performances Les problèmes étudiés dans cette section et Chapitre 5 de la thèse sont la performance de l anneau ECOFRAME à une longueur d onde, le choix de l algorithme d ordonnancement et l impact de récepteurs multi-longueur d onde à la capacité de réseau. Le processus d arrivée des paquets dans la station est modélisé par un processus de Bernoulli, c est-à-dire, le nombre de slots entre deux arrivées est pris d être distribué géométriquement. Cette approximation peut être justifiée par la nature du trafic dans un réseau métropolitain, qui est constitué par un grand nombre de flux indépendants multiplexés, provenant des réseaux d accès. L approximation est validée par les simulations à l aide de ns-2. La validation est montré à la Fig. 5, qui représent le délai d insertion en fonction de trafic offert, dans un anneau à 6 nœuds, pour le trafic de type client-serveur, où chaque station envoie vers le HUB 2 fois moins de trafic de ce qu elle reçoit et pour une durée de time slot de 2 µs. Dans cette thèse il est montré que le routage par station client augmente considérablement la capacité d anneau et dégrade la performance de trafic client-serveur. Le simulateur ESOPE de l anneau ECOFRAME Pour les simulations, nous avons utilisé Network Simulator ns-2.31, amélioré avec les fonctionnes additionnelles, que nous avons développé pour étudier le comportement d un anneau ECOFRAME. Le simulateur obtenu de telle façon s appelle ESOPE, ce qui vient de Ecoframe Slotted Optical PackEt ring simulator.

17 RÉSUMÉ xv 8 7 Geo/Geo/1 simulation Délai moyen d insertion [µs] Trafic offert Figure 5 Délai d insertion en fonction de trafic offert Plus précisement, une nouvelle couche Medium Access Controle (MAC) a été codé et ajoutée à ns Le simulateur ESOPE est disponible sur Internet, à l adresse [2]. La structure anneau est codée en OTCL, pendant que les fonctionalités MAC (la nouvelle classe MAC) est codé en C++. En tout, il y a 9 nouveaux fichiers ajoutés et approximativement lignes de code écrit. Quelques fichiers existant déjà dans Network Simulator, comme packet.h, channel.h, varp.cc, etc, ont été modifiés également. Tous les résultats sont obtenus avec un niveau de confiance de 95% et une intervalle de confiance de 10%. Pour évaluer les performances en termes de QoS, nous avons mesuré par simulation la somme de délai d insertion et délai d extraction. Le choix de l algorithme d ordonnancement La problématique d équité (de fairness, en anglais) existe à l intérieur d une station et entre les différentes stations de l anneau. Le problème d équité entre les stations de l anneau est adressé en dimensionnant l anneau, parce que le dimensionnement fournit une bonne QoS aux stations. Le problème d équité à l intérieur d une station peut être résolu en cherchant l ordonnanceur optimale, ce qui est le sujet de la section actuelle. L ordonnancement de type First In First Out (FIFO) règle l équité à l intérieur d une station. L exemple d un système équitable à l intérieur est un anneau où toutes les longueurs d onde sont partagées à la réception et qui utilise un ordonnancement FIFO. Dans le cas général, le FIFO génère le problème du Head Of Line (HOL) blocking, parce que dans un anneau ECOFRAME les stations différentes peuvent recevoir le trafic sur les récepteurs (longueurs d onde) différents. Donc, pour résoudre le problème d équité à l intérieur d une station il faut trouver un algorithme d ordonnancement différent que FIFO. Les ordonnanceurs introduits avant (OPF, LQF, LVWTF, RAND), qui choisissent un paquet par slot, parmi les éligibles, peuvent régler le problème du HOL blocking, mais il faut noter

18 xvi RÉSUMÉ que ces ordonnanceurs sont du type non-work conserving, c est-à-dire qu il peut se produire qu aucun paquet ne soit envoyé dans certains time slots, même s il y a des longueurs d onde libres. Notons que OPF est un bon candidat pour régler l équité à l intérieur d une station dans le cas général, parce qu il minimise le délai. Pourtant, OPF a la plus grande complexité, parmis les politiques des ordonnancement que nous avons étudié. Regardons la complexité des ordonnanceurs proposés: 1. RAND: complexité basse. RAND demande juste un indicateur par file d attente, qui spécifie si la file est vide ou pas; 2. LQF, LVWTF: complexité moyenne. LQF et LVWTF sont plus complexe que RAND, parce qu ils demandent à savoir aussi la taille des filles d attente différentes; 3. OPF: haute complexité. OPF demande l information concernant le moment d arrivée de chaque paquet. A cause de la complexité élévée d OPF, nous avons essayé dans notre étude de vérifier si OPF peut être émulé par un algorithme plus simple (LQF, LVWTF ou RAND). Comparaison des OPF, LQF, LVWTF et RAND Les résultats de cette section sont présentés en détail dans la section 5.4 de ce document. Nous supposons d abord que les stations émettent les flux prévus dans la Fig. 6, où k = 1, ce qui correspond à une longueur d onde presque saturée entre A et B. On suppose des arrivées Bernoulli à chaque station. Dans cette expérience nous avons mesuré le temps moyen d insertion et d extraction des flux A B et A C. A B C 0.59k D F E Figure 6 Scénario pour comparaison des mécanismes d ordonnancement Nous comparons (Fig. 7), pour les 4 mécanismes étudiés, les délais moyens d insertion et d extraction pour les 2 flux, dans deux scénarios: 1. les flux A B et A C ont le même volume, A B = A C = 0.2 (Fig. 7(a)), 2. les flux A B et A C n ont pas le même volume, A B = 0.3, A C = 0.1 (Fig. 7(b)).

19 RÉSUMÉ xvii Dans le premier cas, les 4 mécanismes traitent équitablement les 2 flux. De plus, ils se comportent de manière identique puisque statistiquement, les 2 files vers B et C se comportent de la même manière. (a) A B = 0.2, A C = 0.2 et k = 1 (b) A B = 0.3, A C = 0.1 et k = 1 Figure 7 Comparaison des mécanismes d ordonnancement Dans le deuxième cas, on constate dans la Fig. 7(b) que les 4 mécanismes se comportent maintenant différemment, et traitent les flux de manière plus ou moins équitable. Notons que les 4 mécanismes délivrent le même délai moyen si celui-ci est calculé sur lâensemble des paquets émis par A, dans les deux scénarios comparés.nous voyons sur la Fig. 7(b) que: LQF favorise la plus grande file d attente; LVWTF a une performance proche d OPF; RAND a une mauvaise performance. Les résultats similaires, qui nous font espérer que LVWTF émule bien OPF, sont obtenue pour l extension des résultats précédents pour les charges des liens différents (section 5.4.6) et dans un anneau WDM (section 5.4.7).

20 xviii RÉSUMÉ L impact du nombre de longueurs d onde sur la capacité Dans ce travail, il est montré que les récepteurs multi-longueurs d onde augmentent la capacité de l anneau ECOFRAME. Pour illustrer le gain de temps de séjour dans l anneau, la Fig. 8 identifie les conditions de travail quand le délai d insertion moyen est supérieur ou inférieur de 2 time slots, pour les valeurs différentes de nombre de longueurs d onde n, sur lesquelles une station ECOFRAME insère son trafic. La Fig. 8 est calculée en modélisant le processus d insertion des paquets par une file d attente Geo/Geo/1. Pour la valeur de n donnée, la surface sur la côté droite correspond aux systèmes (caractérisés par µ et ρ = λ/µ) où le délai d insertion moyen est plus petit que 2 time slots. Cette courbe montre que si µ est au minimum de 0.5, le délai d insertion moyen est toujours plus petit que 2 time slots, aussi longtemps que n 2. Aussi, si µ est au minimum 0.2 (c est-à-dire si chaque longueur d onde est occupé 80% de temps), le délai d insertion moyen est plus petit que 2 si n ρ=λ/µ n=1 n=2 n=5 n= µ Figure 8 Zones de délai moyen d insertion supérieure et inférieure à 2 time slots Conclusions Les résultats principaux obtenus dans ce travail sont: Un cas simple, où tout le monde écoute toutes les longueurs d onde est identifié comme le cas avec la plus grande capacité, parmi toutes les configurations avec le même nombre de longueurs d onde et dans lequel l utilisation d un simple ordonnanceur FIFO règle l équité à l intérieur de la station. Par conséquent, ce cas a une configuration simple et une performance optimale. Le cas général est étudié et un dimensionnement à coût optimal garantissant la stabilité du réseau est obtenu pour une large classe d algorithmes d ordonnancement,

21 RÉSUMÉ xix en utilisant la programation linéaire et les heuristiques. Les ordonnanceurs LVWTF sont simples et proches de l idéal. Le gain en capacité apporté par les récepteurs WDM est quantifié. Nous pensons avoir montré que dans un réseau ECOFRAME bien dimensionné, le mode opportuniste délivre une bonne QoS. Perspectives Quelques directions possible pour continuer le travail présenté dans ce document sont: Relâcher les hypothèses de travail pour: 1. tenir compte de la création des PDUs, 2. introduire la prise en compte du trafic best-effort. Proposer un dimensionnement qui fournira le niveau désiré de QoS des flux de trafic des stations. Proposer des heuristiques pour tous les types de dimensionnement (actuellement les algorithmes existent pour la MR-S).

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23 Acronyms ECOFRAME MAN LAN WAN SAN VLAN RPR PON FTTx xdsl MPLS MPLS-TP PBT HFC PDH SONET/SDH ATM IP FR MAC RWA WA SDM TDM WDM TDMA CSMA/CA OCS OPS Eléments de COnvergence pour les Futurs Réseaux d Accès et MEtropolitains haut débit Metropolitan Area Network Local Area Network Wide Area Network Storage Area Network Virtual Local Area Network Resilient Packet Ring Passive Optical Network Fiber To The x Digital Subscriber Line MultiProtocol Label Switching MultiProtocol Label Switching Transport Profile Provider Backbone Transport Hybrid Fibre-Coaxial Plesiochronous Digital Hierarchy Synchronous Optical Network/Synchronous Digital Hierarchy Asynchronous Transfer Mode Internet Protocol Frame Relay Medium Access Control Routing Wavelength Assignment Wavelength Assignment Space Division Multiplexing Time Division Multiplexing Wavelength Division Multiplexing Time Division Multiple Access Carrier Sense Multiple Access/Collision Avoidance Optical Circuit Switching Optical Packet Switching

24 xxii ACRONYMS OBS HORNET DBORN DAVID FLAMINGO RINGO FIFO LP ILP MILP NLP EDFA FDL BER ADM OXC OADM FOADM ROADM POADM SDU PDU SDW SSR MR-N MR-S MRCF ISO/OSI IEEE ITU IETF PAD-M PAD-S QoS OPF LQF LVWTF P2P CS ESOPE Optical Burst Switching Hybrid Opto-electronic Ring Network Dual Bus Optical Ring Network DAta and Voice Integration over DWDM Flexible Multiwavelength Optical Local Access Network Supporting Multimedia Broadband Services Ring Optical network First In First Out Linear Program Integer Linear Program Mixed Integer Linear Program Nonlinear Program Erbium Doped Fiber Amplifier Fiber Delay Line Bit Error Rate Add/Drop Multiplexer Optical Cross-Connect Optical Add/Drop Multiplexer Fixed Optical Add/Drop Multiplexer Reconfigurable Optical Add/Drop Multiplexer Packet Optical Add/Drop Multiplexer Service Data Unit Protocol Data Unit Single Dedicated Wavelength per destination Single Shared Receiver per destination Multi Shared Receivers per destination without flow splitting Multi Shared Receivers per destination with flow splitting Minimize Receiver Cost First International Organization for Standardization/Open System Interconnection Institute of Electrical and Electronics Engineers International Telecommunication Union Internet Engineering Task Force Packet Aware Design with Multiple packet insertion Packet Aware Design with Single packet insertion Quality of Service Oldest Packet First Longest Queue First Largest Virtual Waiting Time First Peer-to-Peer Client-Server Ecoframe Slotted Optical PackEt ring simulator

25 Acknowledgements At the beginning of this thesis manuscript, I would like to express my deep gratitude to the people whose help was of great importance during my work. First, I would like to thank Professor Annie Gravey, my main supervisor, for kindly accepting me as her PhD student and for her precious help, understanding and kindness during the three years of mutual work. I thank her very much for always being there to patiently answer my numerous questions, for her valuable advice and for teaching me how to think about and to resolve a problem, and how to work with passion and patience. I am very grateful to my second supervisor, Mr Michel Morvan, for kindly accepting me as his PhD student and for his great help in the three years of mutual work. Mr Michel Morvan constantly supported me and helped me with much advice and numerous ideas, and taught me that the significance of a problem is hidden in its context, and not in the difficulties of mathematical procedures, which lead to its solution. I will always remember his kindness, for which he was always such a pleasant co-worker. I am particularly thankful to Professor Philippe Gravey. Professor Philippe Gravey was not formally my supervisor, but I was lucky to be able to work with him for many hours. I am grateful to Professor Philippe Gravey for the time he found to spend in work with me. He has taught me a lot of concepts and helped me to resolve many problems and questions. After every discussion with him, I felt closer to the solution. I would like to thank him for his precious help, for his support and kindness. I would like to express my deep gratitude to Professor Jean-Louis de Bougrenet de la Tocnaye, who agreed to be the director of this work and who provided me with the excellent working conditions at the Optics Department of TELECOM Bretagne. During a significant part of my study, I have been collaborating with Professor Isabella Cerutti, of the Scuola Superiore Sant Anna in Pisa, Italy. I am very thankful to Professor Isabella Cerutti for the time we spent in mutual work. She was a very kind co-worker and taught me many interesting and important concepts in computer science. I feel happy to have been able to work with her and to have had an opportunity to learn from her. I will always remember her kindness and the friendly atmosphere in which our collaboration took place. I would also like to thank Dr Luca Valcarenghi and Professor Pierro Castoldi of the Scuola Superiore Sant Anna in Pisa, who were, together with Professor Isabella Cerutti, my kind hosts during my stay in Italy 2 years ago. I am very grateful to Professor Dominique Barth of Laboratoire PRiSM, Université de Versailles, Paris, for his great help in resolving combinatorial optimization problems. I would like

26 xxiv ACKNOWLEDGEMENTS to thank all the colleagues participating in the ECOFRAME project, within which framework this thesis has been written. I am very thankful to Professor Bernard Cousin and Dr Philippe Chanclou who kindly agreed to be the reviewers of this work. Also, I would like to express my sincere gratitude to Professor Tülin Atmaca, Dr Dominique Chiaroni and Professor Marc Sevaux, who kindly agreed to be the members of the defence jury of my thesis. Finally, I would like to thank all the professors, students and colleagues at TELECOM Bretagne, for their kindness and support during my stay in Brest. Brest, March Bogdan Ušćumlić

27 In love and gratitude to my parents.

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29 Contents Abstract Résumé court Résumé Acronyms Acknowledgements i iii v xxi xxiii Introduction 1 1 State of the art Historical overview of development of optical networks Optical Switching in Optical WDM Networks Concurrent technologies for metropolitan rings All-IP networks Optical packet switched rings Previous Work on WDM Ring Design Linear programming Nonlinear 0-1 programming Thesis problem formulation ECOFRAME Architecture Introduction ECOFRAME Optical Packet Switched Ring Node architecture Receiver types Data and control channels Insertion and extraction mechanisms

30 xxviii CONTENTS 2.3 ECOFRAME Medium Acces Control layer Supported types of client traffic Functional structure of an ECOFRAME station Structure of SDU and PDU units Service primitives Classes of Service and Time Slot Use Methods Access protocol Conclusion Design of TDM/WDM Optical Packet Ring Introduction Designing the ECOFRAME Optical Packet Ring Modelled network properties Discussion about the cost of network equipment Design with single and multi-wavelength receivers Design with splitting and without splitting Considered ring designs The notation for linear programs SSR design MR-N design MR-S design Mixed Integer Linear Programming Formulation Bounds Problem Complexity Heuristic MRCF Results and conclusions about the ring design with splitting Cost comparison of different designs Impact of splitting on scheduler complexity Conclusion Packet-Aware Design of Optical Packet Ring Introduction Addressing the packet queueing performance Stability condition for PAD-M design PAD-M design for single-wavelength receivers PAD-M design for multi-wavelength receivers (S > 1) All-Wavelengths-Shared ring Results on PAD-M design

31 CONTENTS xxix Limitations of the PAD-M approach Addressing stability in general case Scheduling policies Impact of scheduling policy choice on stability State of the art on stability MaxWeight Scheduling in ECOFRAME Stability theorem PAD-S design for rings with S-receivers Proof of validity of constraints used Comparison of PAD-M and PAD-S designs Conclusion Performance analysis Introduction Performance Analysis of the Single-Wavelength Ring Modeling of the system by using Queuing theory Simulation model of ECOFRAME single wavelength ring ECOFRAME Routing Service Architectures Validation of the analytical and simulation models Impact of P2P traffic on ring performance Conclusions on Single-Wavelength Ring Performance Impact of WDM receivers on ring capacity First motivation example The positive impact of load balancing on ring capacity Modeling of the system by using Queuing theory Simulation model of WDM ECOFRAME ring Positive impact of WDM receivers on the delivered QoS Conclusions on WDM Ring Perfomance Analysis Impact of scheduling on ring performance An Efficient Situation: All-Wavelengths-Shared Case No-Work-Conserving General Case Considered Scheduling Policies for General Case Complexity of Scheduling Policies Scheduling Policy Efficiency Metrics Performance for Single-Wavelength Receivers Illustrating Scheduling in the rings with S-receivers Destination versus wavelength queueing Conclusions on scheduling rules Conclusion

32 xxx CONTENTS Conclusion 145 A Simulation of the ECOFRAME ring in ns A.1 Logical schema and the implemented mechanisms A.2 Simulator specifications A.3 Installation A.4 The scheduling algorithms implemented in esope MAC A.5 Node architecture in simulator esope A.6 Key parameters of the simulator B Proof of PAD stability theorem in case of w = 3 167

33 List of Figures 1 Réprésentation fonctionnelle des récepteurs non-wdm et WDM vi 2 Exemples de dimensionnement de l anneau ECOFRAME viii 3 Coût de dimensionnement des architectures des anneaux différents x 4 Les valuers maximales de λ 2 et la charge totale maximale versus λ xiii 5 Délai d insertion en fonction de trafic offert xv 6 Scénario pour comparaison des mécanismes d ordonnancement xvi 7 Comparaison des mécanismes d ordonnancement xvii 8 Zones de délai moyen d insertion supérieure et inférieure à 2 time slots.... xviii 9 Contemporary computer network structure Optical Add/Drop Multiplexer (OADM) Optical Cross-Connect (OXC) Spatial reuse Routing of packets in a node The scheduling algorithm of station in dual-queue mode The position of RPR in the stack of layers The position of MPLS-TP in the stack of layers IEEE Ethernet frames format The position of PBT in the stack of layers Schematic representation of HORNET architecture and node Schematic representation of DBORN architecture and node Optical asynchronous protocol CSMA/CA Structure of the passive DAVID node Structure of the active DAVID node Structure of the FLAMINGO node Structure of the first version of RINGO node Structure of the third version of RINGO node EtherBurst Optical Carrier Ethernet architecture

34 xxxii LIST OF FIGURES 2.1 Idea of ECOFRAME project ECOFRAME optical packet ring Structure of bidirectional ECOFRAME node A functional representation of non-wdm and WDM receivers Functional scheme of an ECOFRAME station Example of design of a four-node unidirectional ring Examples of ECOFRAME ring design Examples of ECOFRAME ring design Six node ring: design cost vs. traffic rate for C w = 0.1 and C r = Six node ring: design cost vs. traffic rate for C w = 1 and C r = Six node ring: design cost vs. traffic rate for C w = 1 and C r = Six node ring: number of receivers and wavelengths vs. cost ratio γ Design, receiver, and wavelength cost vs. N Design, receiver and wavelength cost vs. γ Design Cost of Different Ring Architectures for Client-Server traffic Design Cost of Different Ring Architectures for Any-to-Any traffic QoS degradation scenario Mean queuing time in function of packet arrival rate Mean queuing time when utilization factor γ is limited wavelength WDM receiver Minimum number of wavelengths: PAD-M versus packet-unaware approach Minimum number of wavelengths versus γ when applying PAD-M Limitations of the PAD-M design: an example Maximum values of λ 2 and total maximal load versus λ The delays induced by the congestion due to 100% load of the wavelengths State Partitioning in the case n = Design cost comparison: PAD-M vs PAD-S in 5-node ring Design cost comparison: PAD-M vs PAD-S in 6-node ring Queueing Process Modeling The new MAC layer added to NS A simulation scenario comparing single class with multiclass transport Jitter values for Flow 1 versus Flow 3 traffic load (single traffic class) Flow 3 traffic loss at station 2 (two traffic classes) ECOFRAME optical ring Optional caption for list of figures

35 LIST OF FIGURES xxxiii 5.8 Optional caption for list of figures Optional caption for list of figures Traffic received by the stations (S 1)d versus S in P2P and CS cases Three possible ways of video traffic distribution in a metro ring Supporting a given traffic matrix with optical circuits: a simple example Expected insertion time for n = Expected insertion time for n = Determining whether the mean insertion time is smaller or larger than Expected extraction time (scale limited to 2 time slots) Expected extraction time (scale limited to 5 time slots) Optical packet ring with non-wdm receivers Mean insertion time with WDM receivers vs. a An example of non-work-conserving system FIFO queues to different destinations Special case considered to compare the mechanisms Comparison of scheduling mechanisms: A B = 0.2, A C = 0.2 and k = Comparison of scheduling mechanisms: A B = 0.3, A C = 0.1 and k = Comparison of OPF and LQF: A B = 0.3, A C = Comparison of OPF and LVWTF: A B = 0.3, A C = Comparison of OPF and RAND: A B = 0.3, A C = Performance of scheduling when A B < 0.3, A C = Performance of scheduling when A B < 0.3, A C < Simulation example showing interest of the use of multi-wavelength receivers Comparison of packet latency depending on the type of receiver LVWTF versus OPF in 2-wavelength receiver ring Traffic matrix in Case Scheduling rule comparison in Case Traffic matrix in Case Scheduling rule comparison in Case Scheduling rule comparison in Case 2, per wavelength results Traffic matrix in Case Scheduling rule comparison in Case A.1 The simulated network A.2 The algorithm followed by the stations in program esope v A.3 The algorithm followed by the stations in program esope v1.0 (single class). 163 A.4 The algorithm followed by the stations in program esope v

36 xxxiv LIST OF FIGURES A.5 Derivation of the new mac class B.1 State Partitioning in the case n =

37 List of Tables 1.1 Comparison of RPR, MPLS-TP and PBT Index Notation Given Parameters Main variables Optimal design for MR-S Traffic mapping with a Design Oblivious scheduler Optimal design for MR-N Mean Queuing Latency: Example from Fig The probability p i for the SERVER, CLIENT and P2P traffic type Efficiency measure value for LQF, LVWTF and RAND Efficiency measure value for LQF and LVWTF (Case 1) Efficiency measure value for LQF and LVWTF (Case 2) Efficiency measure value for LQF and LVWTF (Case 3)

38

39 Introduction THIS work focuses on the Metropolitan Area Network (MAN). With its name, metropolitan network refers to the network of area that connects access network (for example, an instance of Local Area Network, LAN) with transport, backbone network (Wide Area Network, WAN). A typical size of the metropolitan network is about km in diameter and it connects the regions bigger than a LAN. A MAN can connect for example different buildings in a certain part of the city or in the whole city, and can sometimes include regional, i.e. metropolitan, areas that surrounds a city. There are two types of metropolitan area networks: metro-edge and metro-core. Metro-edge is part of a network that is sometimes known as the metro-access part because the nodes of this network are connected primarily with the last-mile access. Metro-edge area is from km in diameter. Metro-core network covers larger spaces than metro-edge network (Fig. 9). This name refers to the part of a network that is connected to core network nodes and which is the merging point of access and metro-edge networks on one side, and backbone network on the other side. Routing of traffic in the metropolitan network is usually done through a HUB node, ie. a station serving as a connection and exit to the backbone network. Figure 9 Contemporary computer network structure From Fig. 9 we can see that a metropolitan network traditionally has the form of a ring. The main advantages of the ring topologies, in comparison with mesh topologies are: cost,

40 2 INTRODUCTION simplified routing and simple realization of control plane functions. The number of links is smaller in the ring, which could reduce the installation and operation costs of the network. Also, routing problems are trivial in rings, because the next hop is already known. Finally, in rings it is easy to apply simple distributed protocols to perform different control plane functionalities. Because of these characteristics networks in the form of a ring are very common in metropolitan areas. The main disadvantage of unidirectional ring topology is safety, according to [72]. Ring topologies are more sensitive to link or node failure. However, different technologies for metropolitan networks are designed to minimize the communication restoration time in metropolitan ring topologies and indeed, they provide an excellent protection to ring networks, which makes them even more robust than mesh networks, for the price of some resource redundancy added to such rings. Traditionally, metro networks are based on SONET/SDH rings [64]. The network is normally covered by multi-rings, which increases its reliability [51]. In this network nodes are connected by optical fibers. SONET/SDH technology provides use of an additional ring with reserve capacity in case of connection failure between nodes (stations) in the network. This protection is automatically realized within 50 ms. SONET/SDH is the technology of physical layer, according to the OSI network model. Resilient Packet Ring [4], a technology of data link layer of OSI model, is also developed for the metropolitan ring networks, and also provides an efficient protection in the event of link or node failure. This technique is based on automatic rerouting of traffic, also within the 50 ms, while turning unidirectional network links to bidirectional. There are two different protection methods used in RPR: wrap and steer. Operation Administration and Maintenance (OAM) functions have a significant role in protection in RPR rings and are realized in a distributed manner. Besides the mentioned advantages and disadvantages of ring topology, it should be noted that this topology imposes certain specificities concerning the problem of fairness between different nodes, removing the packets from the network, etc. Metropolitan networks are usually owned by a few different operators. Their role is specific and significant. These networks connect an access networks to the core network, and the evolution of LAN and WAN networks has a direct impact on them. The influence of everincreasing Internet traffic demand is first felt in WAN networks. WAN networks are typically based on WDM point-to-point links. With the introduction of new multimedia services for residential users, the need for high capacities has increased, and consequently the necessary capacities in WAN networks have also increased. A similar process took place and is still taking place in the access networks. Lately, the arrival of new network architectures and technologies such as FTTx and Passive Optical Network (PON) in the access networks, has changed the look and increased traffic rates to the users and from the users. The evolution of access networks is moving towards replacing the existing technologies by high bandwidth optical and wireless networks. In these circumstances, the evolution of metropolitan networks in terms of increase of its capacity and improvement of its features, is oriented towards new technologies and solutions for the transport of information via optical fiber. There are three main tasks that a modern metropolitan network should meet [79]: 1. improved scalability, 2. multi-service bandwidth delivery, 3. and high service flexibility and cost-effectiveness.

41 INTRODUCTION 3 The next-generation metropolitan network, which is expected to replace the existing metro SONET/SDH ring architecture will be also based on the optical infrastructure. However, unlike the traditional SONET/SDH network, which provides circuit-switched services, ie. establishes and/or terminates lightpaths between source and destination, the new metropolitan network will likely use optical packet switching - OPS technology. In OPS technology, packet-switching functions are performed optically, and not electronically, like in IP routers or ATM switches. The main goal of optical packet switching is to move packet processing operations, as much as possible, to the optical domain [79]. Optical packet switching is expected to improve the capacities achieved by routers and help increase bandwidth utilization [73]. This work studied a new slotted optical packet switching technology for metropolitan network in form of ring, which was developed within the French ECOFRAME project. ECOFRAME project started in 2007 and its leader is Alcatel-Lucent. The other participants in the project are TELECOM Bretagne, TELECOM Paris Tech, TELECOM SudParis, Université de Limoges, Université de Versailles - Saint Quentin en Yvelynes, France Télécom and Kloé. The goal of ECOFRAME project is to design a new medium access control (MAC) protocol for unidirectional network in the form of ring, which is based on transparent WDM technology and slotted media. In other words, ECOFRAME is a modern optical packet-switched alloptical network, which is designed to substitute the traditional SONET/SDH rings in the metro area and to be competitive with the concurrent metro solutions, like RPR and Matisse [60]. The new technology relies on the use of wavelength division multiplexing (WDM) technology, which is crucial for a large capacity that can be obtained using a single optical fiber. The contribution of this thesis in selection of appropriate solutions for ECOFRAME network is in analysis and comparison of various methods of designing of optical-packet switched networks, in performance analysis of important network configurations and in proposal of efficient scheduling algorithm of low complexity. ECOFRAME network design problem in the form of ring was solved by using the method of linear programming, which has traditionally been very successfully applied in solving a number of different optimization problems in optical WDM networks [64], [73]. The aforementioned problem combines the elements of the traffic grooming problem and the wavelength assignment (WA) problem [64]. Unlike the traffic grooming problem in the classical sense, which refers to the efficiency of traffic aggregation in SONET/SDH networks with add-drop multiplexers (ADM), and to which a lot of research literature is dedicated [98], [35], [64], traffic grooming problem in ECOFRAME network is characterized by the absence of the socalled grooming factor, which describes the scalability of fixed capacity flows, or the absence of hierarchy in the capacity offered in SONET/SDH hierarchy. When designing ECOFRAME rings, the splitting of flows is arbitrary. Also, the routing and wavelength assignment (RWA) problem [64] is reduced to the WA problem, because of the ring topology. The optimization objective function includes the cost of equipment for receiving, as well as the cost of leased wavelength. These costs are estimated, in order to compare different configurations of ECOFRAME network. It was shown that the optimization problem ECOFRAME ring is very complex and that some of its instances belong to the class of NP-complete problems. Where possible, approximate algorithms are proposed for solving the optimization problems. Different approaches to the problem of dimensioning of optical packet switching networks are explored: the case with and without splitting of flows, the case with or without restrictions in the number of receivers per node, cases with one, two or more wavelengths by receiver.

42 4 INTRODUCTION The analysis was performed for the typical traffic matrices. Particular attention is paid to the problem of designing a network that takes into account the nature of packet switching and which seeks to restrict the access delay of packets in queues. This problem, so-called packet-aware design problem is resolved, and its complexity was pointed out. The second part of this work relates to the performance analysis of optical ECOFRAME ring. The tools used in system modeling are queuing theory and computer based simulation. Analytical and simulation model are compared and validated. It was pointed out the improvement in the performance in the case when the network stations are able to receive data simultaneously on all wavelengths. It was shown that use of simple techniques such as loadbalancing have a positive impact on the maximum usable capacity and the cost of network. It was also discussed how peer-to-peer traffic impacts the performance of a unidirectional optical packet switched ring. Finally, one of the contributions of this thesis is the selection of efficient scheduling algorithm of low complexity for determining priorities among packets intended for different destinations. For this purpose, the performance of several basic scheduling policies is compared and a compromise option is selected. The outline of the document is given in the following. Chapter 1 provides a brief historical overview of the development of optical telecommunication networks, with focus on optical WDM networks, and current technologies, designed for metropolitan area.the previous work on design of the WDM optical rings is highlighted and the principles of linear and nonlinear 0-1 programming are briefly explained. This Chapter also summarizes the issues that this thesis attempted to answer. Chapter 2 describes the basic characteristics of the ECOFRAME network and it details the main mechanisms of ECOFRAME MAC layer and points out its differences in respect to the MAC layers of some concurrent ring technologies. Chapter 3 deals with the design of ECOFRAME network, when the connections between different stations are observed as TDM/WDM circuits. It briefly explains the principles of linear programming and lists the set of characteristics of ECOFRAME ring that need to be modeled. Then, the cost of certain network elements is discussed, and some conclusions regarding these costs are made, which is necessary in order to properly use the optimization objective function. The interest in allowing or not of sharing of traffic flows and the impact of number of wavelengths per receiver is pointed out, too. Four different Integer Linear Programming (ILP) formulations are presented and they include cases of interest in designing ECOFRAME rings. The specificities and importance of each of them is highlighted. Particular attention is paid to explaining the impact that design has on the complexity of MAC scheduling algorithm. The design of ECOFRAME network taking into account the nondeterministic nature of the packet traffic is considered in Chapter 4. This Chapter introduces the so-called packet-aware design, which as the result gives an ECOFRAME configuration with QoS guarantees. Special attention is paid to identifying and solving the problem of stability of the configuration. The results of the analysis of ECOFRAME ring performance are given in Chapter 5. The performances of single wavelength and WDM rings are considered separately. The selection of the suitable scheduling algorithm is done next. Finally, the last Chapter concludes the document.

43 CHAPTER1 State of the art In this Chapter, first the historical overview of development of optical networks is given, with emphasis on their evolution towards optical WDM networks. Then, optical WDM networks are classified according to switching granularity and the expected advantages of optical packet switching in comparison to other switching techniques are highlighted. A brief overview of technologies that are concurrent to ECOFRAME and the previous work on WDM ring design are also discussed in this Chapter. The basic principles of linear programming and the way in which it is possible to linearize the nonlinear 0-1 terms are explained next. Finally, in the last section of this Chapter, a list of problems that occur when designing an optical packet switched ring and which were resolved in this thesis, is given.

44 6 CHAPTER 1. STATE OF THE ART 1.1 Historical overview of development of optical networks History of telecommunication development leads us to the use of optical fibre in combination with a light source, as one of the most important and most promising mediums for the transfer of information. The development of the Internet has had a dominant influence on the enormous attention paid to the development of optical fibre telecommunications in recent decades. Many books provide an overview of milestones in the development of optical communications. Here we will mention only some of them, while a more detailed review can be obtained from [11] and [31], for example: Early era. Primitive societies use light signals (fire, smoke) for transmission of digital messages Diffraction and spectral composition of light discovered by Isaac Newton French engineer Claude Chapple invented the optical telegraph system. This invention enabled the transfer of information to remote destinations (several dozen kilometers) through a specific system of signs. Physicist James Maxwell in 1800 founded the theory of electromagnetism. Maxwell s equations quantify the electromagnetic nature of light and are used to this day in Boston, USA, John Tyndall demonstrates the phenomenon of propagation of light by means of total internal reflection, by directing light through a sealed barrel filled with water. This interesting experiment is nicely illustrated in [29]. Photophone patented in 1880 by Alexander Bell. Light is modulated by speech. The maximum length of transmission of signal is 213 meters Light emitting diodes (LED) developed by Oleg Vladimirovich Losev Theodore Maiman built the first laser Glass fibres with a signal attenuation of 20 db/km are produced Signal attenuation in optical fibres reduced to 4 db/km Optical communication systems based on optical fibres become commercially available The first experiments with Erbium Doped Fibre Amplifiers (EDFA) performed by David Payne The first commercial Wavelength-Division Multiplexing (WDM) systems proposed by Ciena, Lucent and Pirelli. In the early 1980s, optical communication systems were mature enough to enter into competition with other technologies as a future network carrier. A key moment in the development of optical fibre telecommunications was the discovery of excellent performance of EDFA amplifiers. It is this discovery which enabled the penetration of WDM technology in the WAN and MAN network and its dominance established during the 1990s continues until today. Also,

45 1.1. HISTORICAL OVERVIEW OF DEVELOPMENT OF OPTICAL NETWORKS 7 many believe that WDM technology is a core transmission technology for next-generation Internet backbone networks [28], [64]. All agree that fibre is a great medium for transferring information. Its advantages are thoroughly investigated and we will only mention some of its most important advantages [69]: 1. Huge bandwidth. This is one of the most fascinating properties of optical fibre as a medium for transferring information. A single fibre offers a total bandwidth of GHz, while the total bandwidth of radio on Earth is not more than few tens of GHz [59]. In addition to such a great bandwidth, optical fibre transfer speeds are also high and go up to 40 Gbps. In the future, they are expected to reach the speed of 100 Gbps. WDM has the ability to support hundreds of wavelength channels in a single optical fibre and thus provide a huge bandwidth potential. Thanks to WDM technology, the capacity that can be transmitted by an optical fibre reaches several Tbps. 2. Better signal quality, easier deployment and maintenance. The performance of optical fibres is not affected by electromagnetic and radio frequency interference. This noise immunity of optical fibres results in lower BER ratios compared to copper and wireless mediums. Optical fibres are resistant to corrosion as well. 3. Low signal attenuation. Thanks to the low signal attenuation while propagating through the optical fibres (with high quality fibre attenuation is limited to 0.25 db/km), energy consumption is low. 4. Better security. Interception of communication is extremely difficult when using optical fibres and at this stage of technology development is practically impossible. As already noted, WDM technology has a special significance in optical fibre telecommunications. However, it is important to note that WDM is only one of the multiplexing techniques used in optical networks. Besides WDM, Time Division Multiplexing (TDM) and Space Division Multiplexing (SDM) are also used. In TDM, access to bandwidth of optical fibres is divided in time. This type of multiplexing is the basis of optical SONET/SDH point-to-point networks. SDM is the use of more than one optical fibre in parallel, in order to improve the overall available bandwidth. Optical TDM (OTDM) is a new technology, still in the initial stage, which allows sharing of the spectrum of optical fibres by means of fast optical technology, that is so-called short optical pulse technology. The problem is that in OTDM [59]: 1. nodes of the network need synchronization, 2. the network is not transparent. Optical WDM is the other interesting class of optical networks. In optical WDM networks, optical fibres carry signals on more than one wavelength. These networks can be opaque or transparent. Opaque WDM networks perform Optical-Electrical-Optical (OEO) conversion of all wavelength channels at its nodes. Transparent WDM networks use the concept of optical bypassing of transit traffic. It is a network that does not process transit traffic in the electrical domain. In other words, the traffic remains in the optical domain from source to destination. Network nodes become

46 8 CHAPTER 1. STATE OF THE ART economical, because the traffic in transit is kept in the optical domain, and expensive opticalelectrical-optical conversion is avoided, which is very important, since the energy consumption is one of the largest optical fibre network costs. This type of conversion is often referred to as OOO (Optical-Optical-Optical). Optical transparency has led to the birth of all-optical networks (AON). All-optical network is actually a transparent optical WDM network. Transparent WDM optical networks are very important, because they are installed in most of today s WANs and MANs. The main components of the optical multi-wavelength network are Optical Add/Drop Multiplexers (OADMs). Optical WDM networks also use optical cross-connect (OXC) devices. OADMs and OXCs allow WDM and SDM switching. These basic components are illustrated in Figs. 1.1 and 1.2. Most optical WDM networks that are now operational, use static or fixed OADM devices, the so-called FOADM devices [64]. There are also reconfigurable OADM (ROADM) devices, whose main purpose is to provide greater flexibility to optical WDM networks, ie. to enable networks to dynamically react to traffic fluctuations. Optical amplifier DEMUX Λ bypass MUX Optical amplifier Λ Λ 1 2 Λ M 1 x M M x 1 Λ Λ 1 2 Λ M O E O E Λ drop Λ add Figure 1.1 Optical Add/Drop Multiplexer (OADM) (according to [59]) DEMUX Space Division Switch MUX N x M M x N Figure 1.2 Optical Cross-Connect (OXC) (according to [59]) The technology studied in this work is also based on the concept of optical bypassing. ECOFRAME is a transparent WDM optical network. The ECOFRAME network would also tentatively be called an all-optical network, with the difference that the ECOFRAME network has a different switching granularity: it uses optical packet switching.

47 1.2. OPTICAL SWITCHING IN OPTICAL WDM NETWORKS 9 The main optical switching methods employed in optical WDM networks are defined next. 1.2 Optical Switching in Optical WDM Networks In the present section, the main optical switching techniques that are used in optical WDM networks are briefly described. These are: Optical Circuit Switching (OCS). This type of switching is related to switching of fibres, wavebands, wavelengths (ie. lightpaths) or sub-wavelengths (time slots, in TDM optical circuits) [59]. The optical circuits are established statically or dynamically between source and destination. In wavelength routed networks, if the nodes in the network have wavelength converters, it is possible to change the assigned wavelength within the same communication. Otherwise, the same wavelength is used on all the links along which the communication is routed. The main advantage of optical circuit switching is that it can provide connections with a high level of QoS. The main drawbacks of OCS are the insufficient use of the available bandwidth and a lack of bandwidth flexibility. These problems make OCS networks more sensitive to bursts of traffic. Optical Packet Switching (OPS). This type of optical switching offers the finest granularity. It tends to realize entire packet processing in the optical domain. It does not handle lightpaths like OCS, but rather the optical packets of fixed or variable size. OPS nodes should be able to support much higher capacities than electronic packet switching nodes, but their principle of work should not be substantially different: the idea is to provide optical packet header processing, based on which packet should be properly forwarded. In order to achieve better overall bandwidth use, some form of time division multiplexing is required. OPS networks can be slotted and unslotted. Although the main goal of OPS technology is to enable large capacity and high transparency, even after several years of development OPS networks do not seem to have fulfilled what was expected from them. The main problem in the implementation of optical packet switching rings is the lack of high-speed optical memory. Some believe that the future of OPS networks is in wise integration of optical and electronic networks and that the future of optical WDM networks is actually in Optical Burst Switching technology (OBS) [64], which is explained next. Optical Burst Switching (OBS). OBS has appeared as an alternative to OPS, as a result of a need for a compromise solution between OCS and OPS technique. It is a technology that offers a lesser degree of granularity compared to optical packet switching, but a higher granularity level in comparison to optical circuit switching. Typically, at network ingress several IP packets are gathered and a burst is formed from them. Thus, a burst is the basic switching unit in the optical-burst switching network. When forming a burst, a common header for all the packets in the burst is also formed. This header is sent prior to the burst, along the path which the burst will also use. The burst will pass the path through the network after some predetermined delay time, called offset time. After the passage of a header, all the switches and nodes on the path become informed about the imminent passage of the burst and configure themselves for burst forwarding. Since a burst is larger than the individual packets, the required switching speed in OBS is lower than the required switching speed in an OPS network. Also, by forming common headers for all packets belonging to the same burst, header overhead is lower than in

48 10 CHAPTER 1. STATE OF THE ART the case of optical packet switching. Because of these favorable characteristics, OBS is a promising candidate for next-generation optical networks, according to many. As already stated, the ECOFRAME ring, the network studied in this paper, exploits optical packet switching. In the next Chapter, the basic properties of the ECOFRAME network are described. As we are going to see, the main idea of the ECOFRAME network is the belief that by combining packet switching granularity and optical transparency, a low-cost high-capacity ring network can be created. An overview of the current technologies exploited in the metropolitan area, are presented next. We give state of the art for both electronic packet switching, ie. so-called all-ip networks, and optical packet switching networks. 1.3 Concurrent technologies for metropolitan rings In the present section we first present the current proposals for packets technologies in metro networks (RPR, MPLS-TP and PBT) and then the optical packet switching WDM ring technologies. These technologies address the same network segment as ECOFRAME, and are concurrent to ECOFRAME technology, which is why we give a short overview of their characteristics All-IP networks This section aims to give the concepts of new technologies for packet transport networks. Key technologies, whose goal is the convergence towards so-called all-ip transport networks are described here: RPR, MPLS-TP and PBT. The background and motivation for the introduction of each of these new technologies and their basic properties are explained. Resilient Packet Ring Resilient Packet Ring (RPR) is a recent transport technology, which supports the exchange of data between nodes in a network composed of two rings (ringlets). Both rings carry traffic in opposite directions and are used to carry data and control information. The RPR protocol was officially published as IEEE Standard at the end of The RPR protocol provides the definition of the second layer, according to the ISO/OSI reference model, offering: Spatial reuse; Advanced protection (lasting less than 50 ms); Equitable and efficient use of bandwidth; Three priority classes of traffic; OAM functions and performance monitoring; Inter-operability with existing transmission standards; Distributed functions;

49 1.3. CONCURRENT TECHNOLOGIES FOR METROPOLITAN RINGS 11 Support for unicast, multicast and broadcast traffic. The spatial reuse (reuse of the bandwidth) allows the simultaneous transfer of independent traffic on disjoint ring segments. The traditional data ring as Token Ring or FDDI, for example, has used the removal of the packet source (stripping) and procedures using a token to control access to the ring. The packets used to move around the ring before being deleted by the originating station. A B C D Figure 1.3 Spatial reuse In contrast, RPR provides suppression of unicast packets by the destination station. As nodes can transmit packets independently, without waiting for the shared token, there is considerable potential for exploitation of the bandwidth on other portions of the ring, as shown in Fig The multicast packets will in turn be eliminated at the source station. The fair and efficient use of available bandwidth on the ring is provided with the fairness algorithm of RPR protocol. The fairness algorithm is a dynamic and distributed algorithm that has many functions. Its main features are: The operations of the fairness algorithm are done independently for each of the ringlets; The control information of the fairness algorithm is transported by the ringlet opposite the ringlet used to transport the observed flows; This algorithm can only regulate the traffic of lower priority classes; The calculated fair rates are proportional to the weight of administrative stations; The algorithm supports two methods for managing traffic. These methods are conservative and aggressive. Scheduling algorithm is a very important element of the fairness algorithm. It is illustrated in Fig It is a part of the fairness algorithm which decides the priority of traffic in the station. The goal of the scheduling algorithm is to ensure simplicity of used hardware and to provide data transport without losses. The station can work in single-queue mode or dual-queue mode. In single-queue mode, traffic transit path consists of a single queue, which is FIFO and is called primary transit queue

50 Class B 12 CHAPTER 1. STATE OF THE ART Class A Class C Mac Client Q_TX_SS Stage Queue Selection Transit Queues Q_TX_STAGE shapers fairness Mac PTQ downstream STQ DualQueueTransmit Figure 1.4 Routing of packets in a node (PTQ). In this case, the scheduling algorithm will always give priority to transit traffic, and not to the traffic originating from the station. However, it should be noted, that in RPR, transit traffic will always be a subject of OEO conversion, unlike in ECOFRAME, where transit traffic is optically bypassed. NO YES NO PTQ empty? YES stqdepth >= stqfullthreshold? NO STAGE empty? YES NO STQ empty? Send a packet YES Figure 1.5 The scheduling algorithm of station in dual-queue mode In dual-queue mode (Fig. 1.5), the node has two types of queues for traffic in transit. They are PTQ and STQ (secondary transit queue). PTQ is reserved for Class A, while STQ is for classes B and C. In dual-queue mode, the transit traffic of Class A (traffic in PTQ) always takes precedence. Let us see how the scheduling algorithm is performed (Fig. 1.5) for a station using the dualqueue mode. The server DualQueueTransmit (DQT) will choose a frame for the transfer

51 1.3. CONCURRENT TECHNOLOGIES FOR METROPOLITAN RINGS 13 from one of the queues Q TX STAGE, Q TX PTQ or Q TX STQ in the following way: 1. The server will look first at PTQ. If this queue is not empty DQT will choose the first packet of this queue. 2. If PTQ is empty DQT server looks at STQ. If stqdepth stqfullthreshold, the server will choose the first packet of this queue. (Here stqdepth is the number of bytes in the queue STQ and stqfullthreshold is a constant reference.) 3. If stqdepth < stqfullthreshold, the server will review the queue STAGE. If this queue is not empty, the server DQT will choose the first packet from this queue. 4. If STAGE is empty DQT will look at the queue STQ. If this queue is not empty, the server DQT will choose the first packet from this queue. The basic assumption of the RPR protocol, namely that the nodes form a ring, allows it an optimization of performed operations. As all nodes know the position of the other nodes on the ring, only the basic packet operations are needed: forwarding, insertion and stripping. The ring topology also allows a node to perform fewer computations compared to nodes in a mesh topology when deciding to which output port a packet should be sent. At the same time, protection, multicasting and the partition of available bandwidth in the ring are easier. RPR technology is designed to operate over different physical layers, particularly SONET/SDH and Gigabit Ethernet (IEEE 802.3ab), and also above other physical layers at higher speeds. The minimum supported speed is 155 Mbps (Fig. 1.6). SAN PDH ATM Ethernet IP/MPLS FR RPR SONET/SDH (C/D) WDM Gigabit Ethernet (IEEE 802.3ab) Optical fiber Figure 1.6 The position of RPR in the stack of layers RPR technology is interesting because it brings a new definition of the second OSI layer, enabling effective transport on a ring. RPR provides a solution for the convergence of transport infrastructure already existing and already employed, as SONET or DWDM, giving them better ability to process data. On the other hand, the main limitations of RPR are obvious. RPR is a protocol for metro networks in the form of a ring. RPR can handle traffic on a ring metro transport, but it can not manage relationships between nodes in the entire networks. RPR will not have the role of MPLS/IP. Therefore, RPR, which provides a definition of the MAC layer, cannot serve as a complete solution for metro networks. At the same time, as previously mentioned, RPR enforces electronic processing of all traffic in its nodes, including the entire transit traffic. This redundant processing is avoided in ECOFRAME rings. MPLS Transport Profile (MPLS-TP) MPLS Transport Profile (MPLS-TP) [5] is a new connection-oriented packet switched transport network, aiming to provide a low cost layer 2 technology. It is a new formulation of

52 14 CHAPTER 1. STATE OF THE ART MPLS, which is designed for transport networks. It is based on ITU-T definition of T-MPLS (Transport MPLS), dating from The definition of T-MPLS is based on the definition of existing MPLS, but it excludes certain special features of MPLS. The most important features of MPLS, which make it a good basis for the new transport protocol for MAN networks are: The granularity - the virtual circuits established by the procedures of MPLS match the needs of clients with different sizes of MAN networks; Support for QoS - necessary for transport of voice or video over IP networks. T-MPLS is an adaptation of MPLS to transport needs. Because of this, it needs a redefinition of the OAM functionality of MPLS, so that the new protocol can meet all the needs of transport networks. SAN PDH ATM Ethernet IP/MPLS FR MPLS-TP SDN OTN Optical fiber Ethernet (PHY) Figure 1.7 The position of MPLS-TP in the stack of layers In 2006, ITU-T released the main documents that define the T-MPLS networks: G : The network architecture in T-MPLS layer; G.8112: Interfaces of the T-MPLS Hierarchy (TMH); G.8121: Characteristics of the functional blocks of equipment T-MPLS. Here are the main features of T-MPLS: The forwarding of packets in T-MPLS is the same as in MPLS; The OAM functionality (based on the protocol ITU-T Y.1711) and protection options depend on the transportation system; The control plane is empty; There is no dynamic reservation of labels, thus signaling is not independent from MPLS. The characteristics of T-MPLS that are different compared to MPLS are: The use of bi-directional LSP (point-to-point); The absence of penultimate hop popping (PHP), as this option is incompatible with ITU-T Y.1711 OAM; The lack of LSP Merging option. LSP Merging is using the same MPLS label for all traffic traversing the same path to the same destination;

53 1.3. CONCURRENT TECHNOLOGIES FOR METROPOLITAN RINGS 15 The absence of equal-cost multi-path (ECMP) routing. ECMP is a routing strategy where the next hop for forwarding a packet towards the unique destination can be chosen by using several best paths, obtained by routing matrix calculations. The creators of T-MPLS have tried to minimize the work required to develop the new standard. The definition of T-MPLS is based on documents published as RFCs of the IETF and the ITU-T Standard G.8110 (the definition of MPLS). Work on the same technology under its new name, MPLS-TP, started in February 2008 by IETF and ITU-T. Consequently, MPLS-TP technology is still in development [63]. The position of MPLS-TP (T-MPLS) in the stack of layers is shown in Fig Provider Backbone Transport (PBT) Provider Backbone Transport (PBT) [6], or under its new name Provider Backbone Bridging Traffic Engineering (PBB-TE), is a new Ethernet technology, which is the result of a strong demand today for a solution for transport networks based entirely on Ethernet. Such technology is required by companies who want to obtain a transport of Ethernet services as economically as possible (in the sense of bandwidth) and on the other hand, by the service operators, who would like to reduce the costs of infrastructure of networks and to increase the profitability of services. To be able to withstand these demands, the Ethernet technology should offer the operators: scalability, reliability, hard QoS/traffic management and support for TDM services. Until now, solutions based on MPLS (MPLS-TP, among them) were the only alternative to solutions based on SDH or RPR rings, which were able to meet all these demands. Provider Backbone Transport (PBT) offers an alternative to fulfill these requests. PBT is based on Ethernet forwarding and is designed to be simple and cheap, without any loss in functionality over Ethernet. PBT has been introduced in the standardization bodies (IEEE, ITU, IETF, etc..), which have offered only minor improvements of existing Ethernet standards. PBT does not change the definitions of Ethernet interfaces that are already defined and are already heavily exploited. The evolution of Ethernet tends towards the introduction of Ethernet tunnels, which must play a role similar to virtual circuits in MPLS. PBT creates Ethernet tunnels, which provide point-to-point communication in the network, with support for QoS and security transfer of quality. Before reaching the tunnel, the definition of Ethernet has been improved gradually with the standards IEEE 802.1Q (VLAN), IEEE 802.1ad (Q-in-Q) and IEEE 802.1ah (MACin-MAC). All these standards, before the definition of PBT, aimed at addressing the problem of lack of hierarchy in Ethernet. The concept of VLAN (Virtual LAN), was introduced by the IEEE 802.1Q standard, which provides for the first time, a hierarchy in Ethernet. The VLANs can be defined as an independent broadcast domain, within which communications can be secured. Also, communications between different VLANs can be monitored. Originally the concept of VLANs was the idea of providing companies with separate areas of Ethernet that are easier to administer. The header of the VLAN Ethernet frame is a little different from that of the conventional Ethernet frame. Fig. 1.8 shows the different levels of headers in architectures used for PBT. In the header of the VLAN Ethernet frame a field of 12 bits is called Q-tag (it is a two byte subfield VLAN ID of Tag Control Information field) and is used to specify a particular VLAN. The IEEE 802.1ad (also known as Q-in-Q or Provider Bridges) introduced a third

54 16 CHAPTER 1. STATE OF THE ART level of hierarchy. This standard provides customers with the ability to organize the multiple VLANs, within the service provider s VLAN. A new field Q-tag is added to support this new type of address. The number of client VLANs that can be defined in this way is limited to 4094, which is not large enough for the needs of transport networks. The IEEE 802.1ah (also known as Provider Backbone Bridges or MAC-in-MAC) tries to solve this problem. The standard IEEE 802.1ah provides to Ethernet true scalability of carrier-grade networks. FCS FCS FCS Payload Payload = 802.1ad frame FCS Payload EtherType C-VID I-SID Payload EtherType TPID TPID VLAN ID S-VID B-VID EtherType TPID TPID TPID SA DA SA DA IEEE IEEE 802.1Q Legend: - TPID: Tag Protocol ID - VLAN ID, VID: Virtual LAN IDentifier - S-VID: Service VLAN IDentifier - C-VID: Customer VLAN IDentifier - B-DA: Backbone Destination Address - B-SA: Backbone Sourse Address - B-VID: Backbone VLAN IDentifier - I-SID: Service Instance IDentifier SA DA IEEE 802.1ad (Q-in-Q) - : VLAN TAG - : S-TAG - : C-TAG - : B-TAG - : ES-TAG B-SA B-DA IEEE 802.1ah (MAC-in-MAC) Figure 1.8 The format of Ethernet frames according to IEEE standards 802.1, 802.1Q, 802.1ad and 802.1ah As before, the network is treated as a set of separated domains of service providers and customers. Now, the MAC client packet is encapsulated (without or with the FCS field) in the MAC service provider packet. A new service tag field of 24 bits was introduced (I-SID, Service Instance IDentifier), allowing the total distinction between customer and provider domains. The number of possible client VLANs reached 16 million, with the new protocol. In this hierarchy, B-TAG identifies VLAN domains in the operator backbone network, while ES-TAG identifies VLAN domains in client networks. The use of the Spanning Tree algorithm is implied by the definitions of standards IEEE 802.1Q, IEEE 802.1ad (Q-in-Q) and IEEE 802.1ah (PBB). By creating Ethernet point-to-point tunnels, PBT provides QoS, fault resilience and OAM to the network, with a possibility of traffic engineering. PBT is based on Ethernet technology IEEE 802.1Q, IEEE 802.1ad, and IEEE 802.1ah. PBT was standardized in 2009 by the IEEE Working Group, as the PBB-TE (Provider Backbone Bridging Traffic Engineering), by standard IEEE 802.1Qay-2009.

55 1.3. CONCURRENT TECHNOLOGIES FOR METROPOLITAN RINGS 17 For forwarding traffic, PBT uses the full address MAC + VLAN composed of 60 bits (the destination MAC address of 6 bytes, plus a 12-bit VID field of VLAN Tag). PBT allocates a range of VID field values to identify specific paths through the network to the destination defined by the destination MAC address. In this way, address VID/MAC defines a path between two points in the network, which may be a working path or a protection path. The switches in the PBT network behave in the same way as in a traditional Ethernet network: they provide forwarding according to their forwarding tables, but in the case of PBT these tables will be filled using the management plan (or optionally, the control plan of GMPLS). Table 1.1 Comparison of RPR, MPLS-TP and PBT RPR MPLS-TP PBT Standardization 2004, standard 2006, standards 2009, standard IEEE ITU-T: G , IEEE G.8112 and G Qay-2009 Client Multi-client (SAN, Multi-client (SAN, Ethernet PDH, ATM, Ethernet, PDH, ATM, Ethernet, IP, MPLS, FR) IP, MPLS, FR) Packet Encapsulation, Encapsulation, Encapsulation, treatment without without without segmentation segmentation segmentation Protection Fast (< 50 ms). Fast (< 50 ms), Fast (< 50 ms), 2 protection schemes: thanks to backup thanks to backup wrap and steer routing paths routing paths CoS 3 classes of service No MEF classes of and different service sub-classes Fairness Distributed Not an issue Not an issue fairness (meshed network) (meshed network) algorithm Virtual No Yes, typical Yes. PBT introduces circuits for MPLS Ethernet tunnels which have a role similar to MPLS virtual circuits Bandwidth Yes Yes Yes allocation Limited to Yes No No ring? Control Empty. Dimensioning Empty. MPLS label Empty. Ethernet plane? statical, performed by distribution protocols control plane the operators not supported mechanisms disabled. The traditional Ethernet technology for learning the neighborhood of a node, such as flooding and spanning tree algorithm is no longer used. This leads to the creation of fixed and predetermined paths through the network, which provides a network of predictable behavior in all cases.

56 18 CHAPTER 1. STATE OF THE ART PBT works with all service layers: Ethernet services (E-LINE, E-LAN, E-TREE) and MPLS Layer 2 (VPWS, VPLS) and Layer 3 (IP-VPN) Fig SAN PDH ATM Ethernet IP/MPLS FR PBT Physical layer Figure 1.9 The position of PBT in the stack of layers Being used simultaneously with the IEEE 802.1ah standard, which provides advanced scalability of Ethernet networks and with standards IEEE 802.3ah, IEEE 802.1g and ITU Y.1731, which introduce the OAM functions of the same level of inter-operability like in SONET/SDH and/or ATM, PBT provides a complete solution for Metro Ethernet, where all the critical needs of a Carrier Grade Transport Network are covered. Tab. 1.1 provides a comparison of key features of RPR, MPLS-TP and PBT technologies Optical packet switched rings In the past few years, several groups have proposed optical-packet ring architectures. Here, a short overview of these technologies is given. HORNET (Hybrid Opto-electronic Ring Network) HORNET [95] is a U.S. project that was supported by DARPA between 1999 and It is based on a bidirectional ring containing optical packet add/drop multiplexers. In a HORNET node (see Fig. 1.10), one or more of the wavelengths of the ring is systematically extracted by one or more passive filters. Other wavelengths pass through the node without O/E conversion. Packets are emitted by a fast tunable laser. Figure 1.10 Schematic representation of HORNET architecture and node (according to [95]) Various solutions have been tested for the HORNET MAC. The final version uses a control channel at 1310 nm, extracted and inserted at each node. The control frame includes one bit per wavelength, which indicates the occupation state of each wavelength of the next

57 1.3. CONCURRENT TECHNOLOGIES FOR METROPOLITAN RINGS 19 frame. This approach implies a synchronization between control and data frames. The MAC is adapted to take into account customers packets of varying size without systematically applying the operation of segmentation/reassembly: the transmission of packets continues until there are no packets announced to come on the used wavelength. In case of interruption, a byte is added to indicate that the packet is incomplete. The incomplete package is kept in a receiver queue pending the arrival of the following pieces. Existence of multiple queues allows to avoid head of line (HOL) blocking effect. A protocol (inspired by Distributed Queue Dual Bus (DQDB) protocol) has been developed to ensure fairness between the nodes in the ring. DBORN (Dual Bus Optical Ring Network) DBORN architecture proposed by Alcatel [49] has been studied in particular in the framework of IST projects NOBEL and DAVID. It can be seen as an extension of the PON concept to the metropolitan network. Two different groups of wavelengths are used for upstream and downstream traffic flows. The nodes of the same ring can be connected by means of the wavelength conversion within the HUB. The channels are inserted or extracted by using couplers and demultiplexers and are connected to the equipment of level 2 or 3 through interfaces allowing the encapsulation of the various size client packets (up to 1500 bytes) in optical packets. In order to minimize the network cost, DBORN technology uses passive optical nodes. On the bus carrying upstream flows, a node inserts optical packets only in the holes detected between optical packets passing in transit. This is achieved by using the optical asynchronous CSMA/CA protocol (Fig. 1.12). To detect the activity on a wavelength, the node uses a photodiode operating at low frequency (eg. 155 MHz). With an optical coupler, the transit signal is separated into two identical signals: the main signal that passes directly to the next node, and its copy that is received by the photodiode. Based on the information from the photodiode, the collision between a packet to be inserted and the packet in transit is avoided by using the delay line (FDL) with a storage capacity of approximately 1500 bytes (the maximum size of an Ethernet packet). To improve the performance of the CSMA/CA protocol, a centralized traffic control mechanism (TCARD) was initially proposed [18]. This mechanism was designed primarily to improve fairness between nodes on the upstream bus. It could not solve the problem of segmentation of bandwidth, which is fundamental in an asynchronous network. Two access mechanisms were then proposed to solve the problem of fairness and segmentation of bandwidth in DBORN. The first is Modified Packet Bursting (MPB) [67], which increases the transmission efficiency of the network (ie, utilization of resources) through the removal of unnecessary optical headers. Indeed, MPB concatenates electronic packets with the same destination and sends them with a single optical header. The second mechanism is the Dynamic Intelligent Medium Access Control (MAC-DI) protocol [68], which solves the problems identified above. DI-MAC uses a distributed algorithm to dynamically space the transmission of packets from an upstream node to avoid inefficient fragmenting of the bandwidth. Therefore, more usable bandwidth is reserved for downstream nodes. The performance evaluation of these mechanisms has shown that they significantly improve network performance (much more than OU-CSMA/CA) in terms of fairness between the nodes, resource utilization and

58 20 CHAPTER 1. STATE OF THE ART Figure 1.11 Schematic representation of DBORN architecture and node (according to [49]) Figure 1.12 Optical asynchronous protocol CSMA/CA performance parameters (eg. delay, loss). Moreover, they make the network more stable and almost insensitive to changes in traffic. DAVID (DAta and Voice Integration over DWDM) This IST project took place between 1999 and 2003 [32]. DAVID metropolitan area network has multiple rings interconnected through hubs. Each ring uses DWDM with a wavelength channel dedicated to controlling information. The operation is slotted with optical packets of fixed length.

59 1.3. CONCURRENT TECHNOLOGIES FOR METROPOLITAN RINGS 21 Two structures of optical packet insertion/extraction nodes have been proposed. The first is passive (Fig. 1.13). The control channel is extracted at the entry of the node. A 2 2 coupler allows the insertion and extraction of packets. This solution implies that combs of disjoint wavelengths are used by sent and received packets, with a conversion between these combs at the hub. A single packet at most is emitted in the duration of a frame. Figure 1.13 Structure of the passive DAVID node (from [32]) The active version of DAVID node (Fig. 1.14) introduces an additional level of multiplexing in wavelength band (typically 4 per band) by use of the fast wavelength selectors based on SOA allowing to block the transit link packets destined to the local node. The wavelength of the inserted packets is also selectable through an array of SOA. Figure 1.14 Structure of the active DAVID node (from [32]) The DAVID hub provides a function of spatial and spectral switching, without using optical buffers. The methods for finding optimal sequences of permutations have been described in reference [15]. Once defined the spectral permutation (based on a known traffic matrix or

60 22 CHAPTER 1. STATE OF THE ART reservation requests made by nodes) performed by the hub, is notified to each node by the control channel. FLAMINGO (Flexible Multiwavelength Optical Local Access Network Supporting Multimedia Broadband Services) This Netherlands project [33] is based on slotted optical WDM ring architecture, in which the headers of packets are transported over a specific wavelength. The headers of the frame N correspond to the payloads of the frame N+1. It has a label indicating which wavelengths are available for this frame N+1. Figure 1.15 Structure of the FLAMINGO node (from [33]) Emphasis was placed on the transport of IP packets. An interface encapsulates IP in all kinds of frames, eg. Ethernet or SDH. To achieve a correct filling ratio of the frames, the use of sequences of frames of different lengths (by 44, 552, 1500 bytes) was envisaged, with an appropriate proportion adapted to a typical distribution of lengths of IP packets. RINGO (Ring Optical network) This Italian project focused on different architectures of metropolitan optical packet ring. It originates from the same work as the HORNET project. Early versions are based on a unidirectional fibre ring. The ring operates in a slotted mode, with frames of fixed duration. At each node (at least) one specific wavelength is extracted. The number of nodes is at most equal to the number of wavelengths. The wavelength for packet emission is variable and defined by choice of a particular laser in a bar. A packet is sent per frame, by using a wavelength on which no incoming packet has been detected (Fig. 1.16). As in the case of HORNET, the virtual queues are used to avoid the problem of head of line blocking. Specific algorithms have also been studied to improve fairness.

61 1.3. CONCURRENT TECHNOLOGIES FOR METROPOLITAN RINGS 23 Figure 1.16 Structure of the first version of RINGO node (from [22]) The latest version of RINGO node is based on a bidirectional ring (Fig. 1.17). It allows the sharing of a reception wavelength by several nodes. Insertion and extraction are performed on two different fibres. This is not really a ring architecture as the two fibres are looped in a particular point. Figure 1.17 Structure of the third version of RINGO node (from [22])

62 24 CHAPTER 1. STATE OF THE ART MATISSE Matisse Networks [60] produces EtherBurst, a new optical packet switching technology for optical transport networks. Each node is equipped with an EtherBurst Optical Carrier Ethernet Switch that performs optical packet switching and provides optical transparency of transit traffic. Network architecture is presented in Fig Ring nodes contain fully-tunable lasers that are able to change the emitting wavelength on a packet basis and theedfa amplifiers. Figure 1.18 EtherBurst Optical Carrier Ethernet architecture (from [60]) Network bandwidth capacity is dynamically allocated, based on traffic demand. Each node has a dedicated wavelength, thus the number of wavelengths in the ring is not less than the number of nodes. In ECOFRAME ring, receiving wavelengths can be shared between several nodes, which favors the ECOFRAME solution in terms of network cost, as is shown in this work (Chapter 3). In the following, the previous work on WDM ring design is summarized. 1.4 Previous Work on WDM Ring Design The problem of designing an optical WDM unidirectional ring having optical packet add/drop multiplexing capabilities, that is considered in Chapters 3 and 4, can be formalized as a multicommodity flow problem. In addition, the same problem contains the problem of assigning the traffic streams to different wavelengths, which can be formalized as a coloring problem. The considered objective function is the minimization of the wavelength and receiver cost. Multicommodity flow problems with different link cost functions (e.g., as a function of the number of utilized wavelengths) and/or node cost functions are well studied (e.g., [62]). The wavelength assignment problem in unidirectional rings (assuming that each traffic stream has a rate equal to the wavelength capacity) is also well studied in literature [73].

63 1.4. PREVIOUS WORK ON WDM RING DESIGN 25 In telecommunication networks, multicommodity flow problems arise when the traffic can be aggregated in the intermediate nodes of the network. This operation is also known as traffic grooming. As explained in [13], [19], traffic grooming can be performed either in the electronic domain or in the optical domain, using different technologies. When traffic grooming is performed in the electronic domain, optical-electrical-optical conversion of the signals may be required in some intermediate hybrid add-drop multiplexing (ADM) nodes. Initial results on the number of wavelengths and receivers required for performing traffic grooming in different ring architectures (e.g., single hub, multi hub, all-optical, all-electronic) are available in [42]. The main objective of works that focus on electronic grooming is the minimization of the ADM electronic ports, or equivalently the receivers required at the traffic stream terminations and in the intermediate nodes [14], [27], [93]. The problem of minimizing the design cost, i.e., transmitters, receivers as well as wavelength cost, is studied in [23]. In these works, the wavelength assignment problem is, however, neglected. The wavelength assignment problem is accounted in [43], [97] that aims at minimizing the number of wavelengths and the number of electronic ports. Other works on traffic grooming in WDM ring networks consider different objective functions, such as minimizing the minimum electronic port cost [25]. Moreover, [48] considers the presence of ADM having ports with limited tunability. Cost advantage is evaluated and compared against the number of the required wavelengths. On the other hand, optical grooming avoids the need for additional electronic ADM ports (i.e., transmitters and receivers) at some intermediate nodes. However, wavelength continuity constraint is enforced in such intermediate nodes (unless wavelength converters are available). Few works focus on the problem of designing a WDM networks with optical grooming. Typically the objective function is the minimization of the number of optical connections called light-trails [46] or, equivalently, the minimum number of wavelengths [12], [57]. Into this category can also fall [53] which considers the problem of minimizing the number of wavelengths in networks with electronic grooming, as the presented concept and results could be applied also to networks with optical grooming. A stochastic optimization of the light-trail ring network to account for the time varying nature of the traffic is proposed in [56]. The problem of covering a mesh of networks with rings (also referred to as cycles) is also well-studied. Interesting results and properties were found. For instance for some classes of mesh networks, e.g., networks with a Euler and planar graph as topology [37], a ring cover can be found such as each link is covered by only one ring. The problem of covering a mesh networks with rings arises when protection resources need to be allocated. Indeed, each ring can be provisioned with resources for supporting the traffic and with additional resources to protect the traffic in case of failures. For instance, in SONET/SDH, bidirectional line-switched rings (BLSR) and unidirectional path-switched rings (UPSR) are standardized. [81] focuses on the problem of finding a ring cover. The problem of covering a WDM mesh network with rings and allocating the working and protection resources to guarantee survivability to the requested connections against any single-link failure is studied in [39], [58]. Cost comparison between multi-ring networks and mesh networks is carried out in [16], [82]. Finally, the problem of traffic grooming in multi-ring networks is considered in [74], [80]. The above cited works considered single-wavelength receivers. The network design problem with multi-wavelength receivers (i.e., receivers operating on all the wavelengths of a predefined band), which has been studied in this thesis, has not been studied so far. In the solution of this problem, the existing linear programming formulation can be used, because

64 26 CHAPTER 1. STATE OF THE ART the problem of designing an OTDM WDM ring at minimum cost is the same whether singlewavelength receivers or multi-wavelength receivers are available. The difference is only in the granularity factor, i.e., wavelength capacity versus band (multi-wavelength) capacity. The main original contribution of this thesis, concerning ring design, is in the study of the stability of WDM ring design. Due to the packet nature of the traffic, the methods of designing of the OTDM WDM rings are not completely appropriate when designing an ECOFRAME ring. In Chapter 4 it is shown which stability problems can appear when designing a packet ring with methods proper to the design of OCS rings, and how the problem of stable design is resolved. 1.5 Linear programming The techniques of linear programming [91],[30] are used in this thesis as a tool for the mathematical formalization of the conditions, that network design should satisfy, and objective functions, that should be minimized or maximized. Linear programming tries to optimize a given goal linear function, ie. to find the best outcome, when a set of constraints that variables satisfy is linear and known. Leonid Kantorovich, a Russian mathematician, was the first to formulate linear programming problems, in In 1947, George B. Dantzig presented the simplex algorithm for solving linear programming problems. These events can be considered as the beginnings of the modern linear programming theory. However, the full exploitation of linear programming optimization methods started later, with introduction of modern computers and with the increase of their computing power. Formally, the Linear Programming (LP) problem is usually expressed with a linear function and a set of linear inequalities : maximize c 1 x 1 + c 2 x c n x n subject to a 11 x 1 + a 12 x a 1n x n b 1 a 21 x 1 + a 22 x a 2n x n b 2... a m1 x 1 + a m2 x a mn x n b m x 1,x 2,...,x n 0. Variables x 1,x 2,...,x n are called decision variables, while a i,c i,b j and a ij are real constants. Function F = c 1 x 1 +c 2 x c n x n is called objective function, while inequalities i a ijx i b j are called constraints. A set of decision variables (x 1,x 2,...,x n ) is called solution. A solution that satisfies all the constraints is called feasible solution. A feasible solution that maximizes the objective function is called optimal solution. An analytical formula for resolving the linear programming problems does not exist.

65 1.6. NONLINEAR 0-1 PROGRAMMING 27 Linear programming techniques are very useful, because the number of problems that can be formulated as problems of linear programming is very large. Linear programming problems can be successfully solved in most cases, as there exists a fair number of efficient algorithms and software developed for this purpose. LP problems, together with least-square and convex optimization problems, form a group of optimization problems for which, in a considerable number of cases, efficient solution methods exist. The Integer Linear Programming (ILP) problem is a sub-class of LP problems. It is a linear programming problem where all the variables x 1,x 2,...,x n can have only integer values. 0-1 Integer Linear Programming (0-1 ILP) problem is a special case of ILP problems. An 0-1 ILP problem is an ILP problem where all the variables x 1,x 2,...,x n can have only binary integer values, ie. the values from the set 0,1. Finally, the Mixed Integer Linear Programming (MILP) problem is a linear programming problem where some of the variables x 1,x 2,...,x n (and not all) can take only integer values. In this work, the main part of the ring design formulations are expressed as MILP and 0-1 ILP problems. These problems are then directly solved by using some of the commercially available softwares like CPLEX, or the free software lp solve. In some cases, due to the problem complexity, problems can be resolved directly only for problems of limited size. In such cases, in order to try to obtain more interesting results, heuristics are developed. Heuristics do not provide any guarantees that they will find the optimal solution, however, they can be very useful in analysis of the large instances of the problem, as their calculating time is negligible compared to the time needed for direct solving of the problem. 1.6 Nonlinear 0-1 programming In LP programs, objective function and all constraints are linear. If some of the constraints, and/or objective function is nonlinear, then such a program is called Nonlinear Program (NLP). Nonlinear 0-1 program is an NLP where all the variables are binary. In the present section, it is shown how a nonlinear inequality, containing binary variables can be linearized. Let us observe the following nonlinear 0-1 inequality: a j ( j N i Q j x i ) b, a j > 0, j N, x i {0,1}, i Q j, j N. According to [38] and [52], this inequality can be replaced with the following set of linear inequalities: a j y j b, j N

66 28 CHAPTER 1. STATE OF THE ART y j + i Q j x i Q j 1, j N, y j x i 0, i Q j, j N, y j 0, x i {0,1} i Q j, j N. This useful approximation will be used in Chapter 4, dedicated to the problem of packet-aware design. In the next section, the problem treated in this work is formulated. 1.7 Thesis problem formulation In this work, the problems related to the development of ECOFRAME network are addressed. One of the main assumptions that is taken in the analysis, is that all the traffic in a studied network is guaranteed and that it is of the same class of service (CoS). The best-effort (BE) traffic is not treated. Also, it is supposed that the slots can be taken for transmission whenever they are free. Such use of free time slots is called opportunistic. Consequently, no slot reservation mechanisms are considered. The contribution of this thesis is organized around two main axes: the contributions concerning the design/configuration of the ECOFRAME ring, and the contributions in evaluating the ring performances and choosing the optimal scheduling policy for ECOFRAME ring. The problem of designing the network is important and cannot be separated from the study of the network QoS performances. This is why, in this thesis, these problems are studied in parallel, in order to try to understand the mutual impact that different choices in design have on the ring performances, and vice versa. In the part of this thesis concerning design of the ring, the cost of different ring elements is estimated. The receivers of different sizes are studied, and their impact on ring design is studied. Traffic splitting also has a considerable impact on the ring, which was also one of the topics. Different design configurations are studied and the most convenient are identified, based on the cost and stability criteria. The second part of the work is focused on the performance analysis of the ECOFRAME ring. The appropriate queueing models are developed for the ECOFRAME ring. Also, an event-driven simulator of the network is developed. Simulator and queueing models are then compared and validated. Different points of interests are highlighted, and among them, impact of spectral multiplexing on the ring capacity, impact of the receiver size on the ring performances, impact of peer-to-peer traffic on other traffic profiles in the ring. Finally, the appropriate scheduling algorithm for ECOFRAME ring is proposed.

67 CHAPTER2 ECOFRAME Architecture Given that this work analyzes the ECOFRAME optical ring, this Chapter details the characteristics of the ECOFRAME architecture. The details of the Medium Access Control layer of the ECOFRAME ring, are also given in this Chapter. The issues that are assessed here are the type of supported client traffic, the classes of service, the type of receivers, the insertion and extraction mechanisms, the service primitives, the encapsulation and the segmentation, the reservation mechanisms and the channels for control of information and for data, as defined and used in the ECOFRAME ring.

68 30 CHAPTER 2. ECOFRAME ARCHITECTURE 2.1 Introduction This Chapter is fully dedicated to describing the architecture of the ECOFRAME ring and all of the most important functionalities of the medium access control layer of the ECOFRAME technology. The impact of the technological assumptions on the problems discussed in the following Chapters of this work is pointed out. 2.2 ECOFRAME Optical Packet Switched Ring ECOFRAME optical packet switched ring is developed for metropolitan area networks. Metropolitan area networks are the merging point between access and backbone networks. Such a position of metropolitan area network has an impact on the traffic profile that should be managed by this part of network. Metro networks should handle more or less aggregated traffic flows coming from the access. This traffic can be very dynamic, thus, in such conditions, switching of higher granularity, like optical packet switching should be a good solution to address the capacity issues in these networks. Furthermore, given that the backbone networks evolve towards packet based Multiprotocol Label Switching (MPLS) architectures, the packet structure seems to be a natural choice for the metropolitan part of the network. The second reason for introducing the ECOFRAME packet ring concept is related to the state of the art in optical WDM networks. Reconfigurable optical add/drop multipexers (ROADMs) bring much needed flexibility to optical WDM networks and thus, further increase the bandwidth efficiency of the optical WDM networks. In addition, the cost of the networks using ROADMs is lower, as the nodes become optically transparent, and consequently smaller and cheaper. However, switching granularity of the ROADM is still at wavelength, ie. lightpath, level, so the capacity use in these networks could be significantly improved. Electronic packet switching Ethernet networks have packet switching granularity, but does not support optical bypassing of the transit traffic. This means that all traffic is electronically converted at nodes of these networks, ie. these networks perform optical-electrical-optical (OEO) conversion of all traffic. For this reason, nodes in such networks are big and expensive, which should be avoided. The idea of ECOFRAME is to combine the positive features of both transparent optical WDM networks, using ROADMs, and packet switching granularity of electronic packet switching networks (Fig. 2.1). ECOFRAME network is an optical WDM ring, where network stations are connected by optical fibers (Fig. 2.2). When deployed in metro/access networks, each link is typically a fiber supporting 40 wavelengths at 10 Gb/s and is connected to the other fibers to reach a circumference of up to 300 km. Transmissions in the WDM ring are time-slotted and synchronized on the different wavelengths. On each wavelength, each time slot can support a single fixed-size optical DATA packet. Thus, ECOFRAME is a slotted optical packet switched ring. An adaptation layer is responsible for performing adaptation (e.g., concatenation and fragmentation) of the format from upper layer packets into the fixed-size packets. ECOFRAME ring is compatible with all types of client traffic. It supports datagrams, asynchronous TDM circuits (SDH, PDH, OTN,...), all types of virtual circuits, etc. ECOFRAME network functions either in connection-oriented mode (with use of virtual circuits), either in mode without connection (datagrams are transported), either simultaneously in both modes.

69 2.2. ECOFRAME OPTICAL PACKET SWITCHED RING 31 Ethernet network ROADM network ++Packet granularity (bandwidth optimization) -- OEO conversion (negative impact on node cost) ++ Optical transparency of transit traffic (reduction of node cost) -- Lightpath granularity (negative impact on bandwidth) ECOFRAME network ++ Optical transparency of transit traffic (reduction of node cost) ++ Optical Packet Switching = Packet granularity (bandwidth optimization) Figure 2.1 Idea of ECOFRAME project Node architecture At any time, the status of a time slot on a wavelength can be either busy (i.e., supporting a packet) or free. Figure 2.2 ECOFRAME optical packet ring ECOFRAME ring can be either unidirectional or bidirectional. Each node in each direction is equipped with : one fully-tunable transmitter,

70 32 CHAPTER 2. ECOFRAME ARCHITECTURE Figure 2.3 Structure of bidirectional ECOFRAME node one or multiple receivers, and a packet optical add/drop multiplexer (POADM). Thanks to the presence of tunable transmitters, each node can transmit a packet on any ring wavelengths. However, only one packet can be sent per time slot. A station can receive packets on any of its receivers wavelengths. Also, each node may locally add/drop the optical packets. The packets destined to other nodes are optically bypassed. Transparent bypass is performed by leaving the optical packet in the same time slot and on the same wavelength, without the possibility of switching the packet on a different wavelength. These functions are realized by ECOFRAME packet optical add/drop multiplexer, which is presented in Fig At the entrance to the station, the WDM comb is demultiplexed into different wavelength signals (Fig. 2.3), and the optical packets that have reached the destination are removed from the ring. Then, each wavelength channel is delayed by a Fiber Delay Line (FDL) and amplified or blocked by the use of a Semiconductor Optical Amplifier (SOA) based optical gate. Finally, at the exit of the station, wavelength channels are multiplexed again into a WDM comb, and the new optical packets, if any, are inserted on the specific wavelengths, via an optical coupler Receiver types Two types of receivers are considered within the ECOFRAME project (see Fig. 2.4): single wavelength (non-wdm) and

71 2.2. ECOFRAME OPTICAL PACKET SWITCHED RING 33 multi-wavelength (WDM) receivers. Non-WDM receivers can receive packets on a single fixed wavelength. Contrary to this, the WDM receivers allow the reception of packets on all of the available wavelengths within the same receiver. However, the effective traffic capacity received by this receiver does not exceed the capacity of non-wdm receiver. Both non-wdm and WDM receivers can receive up to 10 Gbps. After the reception with WDM receiver, the packets are queued in the electronic buffer before being transmitted to the client. When sending a packet using the WDM receiver, a node can freely choose on which wavelength of the same receiver to transmit. This leads to the improvement of the network performance, through spectral multiplexing. Also, such structure of the WDM receiver permits the support of the intervals of highly bursty traffic. Considering the organization of the wavelengths into multi-wavelength receivers, two types of multi-wavelength ECOFRAME receivers can be defined: barette or fixed-size WDM receivers, of size S (typically, S = 2, 4, 8, 10,...). unstructured WDM receivers. The main difference between the barette and unstructured WDM receivers is in the way the wavelength channels are attributed to the receivers. If the barette receivers, of size S are used in the network, it means that all the stations use a number of receivers, all of them using exactly S wavelengths for receiving data. The barette receivers can be of different types, according to the part of the WDM fiber spectrum, of size S, that they exploit. If the unstructured receivers are used in the network, it means that each station can listen to a number of wavelengths, synchronously, but neither the size of the receiver, nor the types of their channels are a priori defined. In this work, only the barette WDM receivers have been considered, since, from the equipment manufacturer point of the view, it is more likely that the size and structure of the receivers are going to be predefined. Λ i Λ i1 Λ i2 Λ in... non-wdm Rx WDM Rx 10 Gbps (a) non-wdm receiver, receiving on a wavelength Λ i 10 Gbps (b) WDM receiver, receiving on the wavelength subset Λ i1, Λ i2,..., Λ in In both cases, receiver output rate is equal to the max. wavelength rate, e.g. 10 Gbps. Figure 2.4 A functional representation of non-wdm and WDM receivers

72 34 CHAPTER 2. ECOFRAME ARCHITECTURE Data and control channels Contentions and collision of packets are avoided by an access protocol. The access protocol is based on control and management information concerning the time slot status for each wavelength and the packets carried in each time slot for each wavelength. Control and management information are transmitted on a separate wavelength (Fig. 2.2). Based on such information, each node can identify the packet that it should receive in each time slot and drop it by freeing the time slot. The optical packets with DATA payload are transmitted using the remaining WDM channels Insertion and extraction mechanisms Each node can check the time slot status on each wavelength. If the time slot is free on at least one wavelength, the node can select a packet in the electronic buffer and the wavelength to use among those with the time slot in free status. The packet is then transmitted (i.e., added) in the time slot of the selected wavelength and the status of the time slot for such wavelength is updated to busy. Packets, that are not destined to a node, bypass the node transparently and time slot status on the corresponding wavelength is kept busy. Transit packets can be dropped only if a higher priority packet is waiting for the transmission and all the wavelength time slots are in busy status. Although the main assumptions on the ECOFRAME access protocol were defined, the design of the insertion protocol, ie. of the scheduling algorithm, was an open question and a subject of study, in this work. When arriving to the node, the DATA packets, originating from the client layers, are classified into FIFO queues per destination address or per wavelength on which they are routed. In this work, both ways of classifying the DATA packets are studied. For simplicity, in this work only unidirectional ring topology of ECOFRAME is studied. 2.3 ECOFRAME Medium Acces Control layer ECOFRAME is a technology of the second layer of the ISO/OSI reference model, ie. a technology that defines the Medium Access Control (MAC) layer. This Chapter outlines the basic functionality of the ECOFRAME network MAC layer, with a focus on transport and control plane of this layer Supported types of client traffic ECOFRAME is a multiprotocol technology, ie. a technology that allows the transport of various types of customer traffic (ATM, Ethernet, MPLS, IP, etc.). In addition, ECOFRAME allows operation in two modes: 1. connected mode, in which the virtual circuits are established for each communication.

73 2.3. ECOFRAME MEDIUM ACCES CONTROL LAYER non-connected mode (when setting up of the connection is not required). ECOFRAME technology is designed for a slotted unidirectional WDM optical ring, which has 1 control channel and about 40 data channels. It supports unicast, multicast and broadcast transfer. In this work, unicast transfer is studied Functional structure of an ECOFRAME station ECOFRAME station is composed of two main entities (sublayers): 1. Adaptation Sublayer (responsible for the exchange of service primitives with the layer of the client, for creation and treatment of the received primitives, and for the communication with ECOFRAME control plane) 2. Transport Sublayer (responsible for data exchange with the physical layer) Client Layer ECOFRAME Control Plane Client Layer Creation of data SDU Creation of data PDU Creation of control PDU Reception of data SDU Treatment of data PDU Adaptation Sublayer Emission of data PDU Emission of control PDU Reception of control PDU Reception of data PDU POADM Transoport Sublayer Figure 2.5 Functional scheme of an ECOFRAME station Functional scheme of an ECOFRAME station is shown in Fig We can see that the Adaptation Sublayer consists of the entities: Creation of data SDU, Creation of data PDU, Creation of control PDU, Treatment of data PDU and Reception of data SDU. Transport Sublayer consists of the entities: Emission of data PDU, Emission of control PDU, Reception of data PDU, Reception of control PDU and POADM. SDU and PDU are the acronyms for Service Data Unit and Protocol Data Unit, respectively. SDUs are information units that are exchanged between the layers of clients, ie. the customers of service offered by the MAC layer. These units of data are included as a payload in the PDU data units, which are characteristic to the MAC layer and are used for the communication between peer MAC layer entities. Entities Creation of data SDU and Reception of data SDU have a role in segmentation, encapsulation reassembling of client frames. Entity Creation of data PDU serves to create a data PDU, starting from the received SDU unit, while the entity Treatment of Data PDU serves to perform the checking of the errors, that received data PDU may contain, before its submission to entity Reception of data SDU.

74 36 CHAPTER 2. ECOFRAME ARCHITECTURE Entity Creation of control PDU is used to create a PDU control unit, by using the information obtained from the control plane of the ECOFRAME MAC. Transport Sublayer has entities that belong to the electronic and optical domain. The entity POADM belongs to the optical domain, while all the other entities of this sublayer belong to the electronic domain. Entities for the emission and reception of data and control PDU, aim to control the order of sending and accepting of PDU units, ie. their exchange with the physical layer. In this section there are the admission buffers, for the PDU units, before they are sent or received. During each time slot, the mentioned entities are obliged to receive, process and resubmit at least one control PDU. Optical POADM entity is used for optical insertion of PDU units in the optical medium (optical fiber) and for extracting of PDU units destined to the ECOFRAME station Structure of SDU and PDU units One SDU is formed from a single frame of the client. SDU data units have a variable size, which depends on the size of frames received from the client, and the maximum size of PDU data, while the PDU data units have a fixed size. The SDU and PDU frames are created by the Adaptation Sublayer of the ECOFRAME MAC layer. Here we give a brief overview of the basic fields that constitute the SDU and PDU units. Each SDU is composed of a header and a payload. PDU unit is composed of a header, a payload consisting of more variable length SDUs and eventually, of bits of jam, which are added to fill the frame until its full size. The main fields of SDU units are: QoS indicator indicator of the client layer length of the SDU frame indicator of the flow (to show if network operates in connected mode) identifier of the client frame payload PDU data unit comprises: the detection/error correction bits payload length indicator payload PDU control units transmit control information. As already noted, in ECOFRAME network, a special wavelength is reserved for control channel, which is used to inform stations about the content of time slots on all the wavelengths carrying data, about the destination address,

75 2.3. ECOFRAME MEDIUM ACCES CONTROL LAYER 37 the source address and the class of service of optical containers and finally, about the possible reservation of that time slot, by some of the stations in the ring. The control channel is systematically listened to by each station in the ring, and this is the only channel that is systematically translated into the electronic domain. In contrast, data channels, which transmitted the client payload information, remain in the optical domain while in transit, thus significantly simplifying the structure of the station and reducing the energy consumption. It might be necessary to segment SDUs, so that they could be transferred within the multiple data PDUs. One of the algorithms for the creation of the PDU units, in ECOFRAME network, is called the Graduated Packet Filling Optimization (GPFO) algorithm [36], and is proposed by our colleagues from TELECOM SudParis. The same research group has proposed, in [66], a dynamic mechanism for the creation of optical containers (DCUM), which takes into account different classes of service in ECOFRAME Service primitives Service primitives are an important part of the service of a MAC layer, because they serve to inform the service users (ie. the clients) about the actions that are expected from them, and about the actions taken by the MAC layer. In other words, the service primitives serve for the communication between the client layer and the MAC layer. In the ECOFRAME MAC layer, the following service primitives are defined: Data Service Primitives: 1. SDU-data-request: primitive issued by a client layer and sent to the adaptation sublayer, submitting a client frame 2. SDU-data-indication: primitive issued by the adaptation layer and sent to a client layer, transmitting a client frame 3. PDU-data-request: primitive issued by the adaptation layer and sent to the transport layer, submitting a data PDU to transmit. 4. PDU-data-indication: primitive issued by the transport layer and sent to the adaptation sublayer, transmitting a data PDU. Control Service Primitives 1. PDU-control-request: primitive issued by the control plane and sent to the transport layer, submitting a control PDU to be transmitted. 2. PDU-control-statement: primitive issued by the transport layer and sent to the control plane, transmitting a control PDU. 3. SDU-setup-request: primitive issued by the control plane and sent to the adaptation sublayer, indicating the need for establishing the new virtual circuit. 4. SDU-setup-statement: primitive issued by the transport layer and sent to the control plane, indicating the need for establishing the new virtual circuit. 5. SDU-connect-request: primitive issued by the control plane and sent to the transport layer, indicating that new virtual circuit is accepted. 6. SDU-connect-indication: primitive issued by the adaptation sublayer and sent to the control plane, indicating that new virtual circuit is accepted.

76 38 CHAPTER 2. ECOFRAME ARCHITECTURE Classes of Service and Time Slot Use Methods Concerning the number of supported classes of service (CoS), ECOFRAME network can operate in: 1. mono-class mode 2. multi-class mode. As a basis for the definition of different classes of service, in its multi-class mode, ECOFRAME adopts the Metro Ethernet Forum (MEF) [76], [1] recommendations concerning the admissible bandwidth profiles and the CoS. According to [76], there are eight classes of service, determined by CoS-ID value, as specified by IEEE protocol. The two ways of the free time slot use in ECOFRAME data channels are: 1. the opportunistic use: any free slot that passes by the station, may be used to send PDU units 2. via the reservation mechanisms: free time slots, which pass by the station, can be used only if there is a corresponding reservation for their use. All stations in an ECOFRAME ring, can use only one of two methods of free time slots use. The reservation of resources is closely related to the problem of fairness in the metropolitan rings. The goal of the design of the reservation mechanisms is to establish the fairness among the stations in the ring, or to provide the operator with the tools to favor some stations rather than others. One of the most famous, but quite complicated, distributed fairness algorithms is proposed by the Resilient Packet Ring protocol [4]. Our colleagues from the French Telecom have studied a simple distributed method of reservation of time slots called SWING [17], while the colleagues from the Université de Versailles have proposed a centralized approach of reservation of the free time slots [20]. In this work it is supposed that the ECOFRAME stations use free time slots in the opportunistic manner, and that the ring operates in the mono-class mode. In this context, the problems that are discussed are: the QoS performance of the network (studied in Chapter 5), the network design (Chapters 3, 4) and the problem of choosing the right access protocol (Chapter 5) Access protocol The access protocol, or the insertion protocol, is an important part of the ECOFRAME MAC protocol. It consists of mechanisms that take into account the priority of the packets, the bandwidth profile of traffic, the reservation mechanisms that try to resolve the fairness problems and different scheduling algorithms. RPR is an example of the technology where the access protocol is a complex structure combining all these elements (for instance, see Fig. 1.4). Thus, the question of defining the access protocol is an important task, which should be carefully carried out in order to find the optimal network configuration.

77 2.4. CONCLUSION 39 Concerning the access protocol in the ECOFRAME ring, the main assumption is that each ECOFRAME station first (at the beginning of the time slot) removes data from time slots of those wavelengths, which contain packets that have reached their destination. Then, a station uses the scheduling algorithm to select the one of the optical containers that will be next sent downstream. The packet for insertion can be selected according to different criteria, for instance, according to their CoS, waiting time, reservation status, etc. Prior to insertion to ring, the data PDU packets are queued according to their destination, class of service or wavelengths on which the flows are routed. As in the ECOFRAME ring, different destinations can receive packets on different wavelengths, the choice of criteria for classifying the packets into queues will also have an impact on the scheduling algorithm. Such and similar access protocol related problems were the object of study in this work. One of the results obtained in this thesis indicates that the problem of choice of the scheduling algorithm cannot be separated from the problem of network dimensioning, because the wrong design decisions would lead to a complicated scheduler. This is case with flow splitting, as explained in Chapter Conclusion This Chapter presented the architecture of the ECOFRAME ring and pointed to its characteristics. The equipment at the nodes imposes constraints on the number of packets that can be added or dropped in each time slot. In particular, the presence of a single fully-tunable transmitter allows to transmit up to one packet on any wavelength during a time slot. Since multiple receivers may be present at each node, all packets destined to a station can be taken from the receiving wavelengths in the same time slot. However, the overall traffic sent to a destination cannot exceed a wavelength capacity, that is the equivalent capacity that can be received by a station. Such constraints impose a limit on the maximum amount of traffic that a node can transmit or receive, i.e., traffic rate to/from a node cannot exceed the wavelength capacity. In its second part, this Chapter presents a brief overview of the basic characteristics of the Medium Access Control layer, which is the basic layer defined in the ECOFRAME technology. Here, SDU and PDU unit structure and the MAC service primitives are defined, a functional organization of the typical ECOFRAME station is shown, and some other peculiarities of the ECOFRAME MAC layer were pointed out. The presented work contributes to the definition of the basic structure of ECOFRAME MAC layer and to the concept of different entities belonging to it. Aside from explaining the different functionalities of the ECOFRAME MAC layer, this Chapter points out the starting assumptions that are taken into account in the further work, as well as topics which are dealt with by the other parties participating in the ECOFRAME project. Specifically, this work has trodden the unidirectional ECOFRAME ring in which the issues of segmentation and encapsulation, ie. the creation of PDU units has been neglected. Also, the starting assumption was that all the optical data units are of the same class of service. Finally, this study considered that it is possible to transmit the optical packets by using all of the free time slots, ie. to access the medium in an opportunistic manner.

78 40 CHAPTER 2. ECOFRAME ARCHITECTURE The initial assumptions have positioned the problem of dimensioning and the performance analysis of the ECOFRAME network in a specific context in which these problems are treated next. As we shall see below, the problems of finding a stable ECOFRAME ring design and selection of appropriate scheduling rules are complex and mutually dependent. Their solution is the main contribution of this thesis.

79 CHAPTER3 Design of TDM/WDM Optical Packet Ring The number and type of receivers at each ring node and the overall number of wavelengths needed in the ring, are the subject of optimization, when looking for the ideal design, i.e. configuration of the ECOFRAME ring. In this Chapter, the problem of finding the optimal design of ECOFRAME ring is addressed from different angles, depending on the type of receivers, type of traffic flow sharing, optimization objectives and maximum number of receivers allowed per station. The problems of insertion and extraction of optical packets are neglected in this Chapter. It is assumed that ECOFRAME ring can be designed by routing the traffic demands into the TDM/WDM circuits, which is the traditional way of designing the optical WDM networks. Such approach is suitable for measuring the trade-off in number of receivers and wavelengths that are used for design. The benefits and inconveniences of different ECOFRAME ring designs are discussed and their impact on network performance is analyzed.

80 42 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING 3.1 Introduction The aim of this Chapter is to find the optimal design, i.e. the optimal configuration of the ECOFRAME ring network. The optimal design or configuration of a network is defined by: the minimum number of wavelengths needed in the ring and the minimum number and type of transmitting and receiving equipment needed to be installed at each node of the ring so that such design, or configuration is able to support a given input traffic matrix. The optimization goal is to reduce the quantity of network elements used in the design, i.e. to reduce the cost of the network. The problems of insertion and extraction of optical packets are neglected. As already pointed out in Chapter 1, the problem of designing optical WDM metropolitan rings is well studied. Traditionally, optical WDM network design consists in routing the traffic demands into the lightpaths, i.e. the optical circuits. In this Chapter, we have adopted such a way of dimensioning to find the ideal configuration of the ECOFRAME ring, with supposition that ECOFRAME traffic demands can be approximated using a set of temporary WDM circuits. We adopted such an approach in order to try to evaluate the trade-off that exists between the number of receivers and wavelengths used in the network. This trade-off depends on the receiver-to-wavelength cost ratio. 3.2 Designing the ECOFRAME Optical Packet Ring When designing a network by using the linear programming methods, the properties of the network that need to be modelled must be precisely defined. In the present section a list of ECOFRAME network properties that are included in design is presented. The problem of designing of the ECOFRAME OPS ring is analyzed from different aspects, according to the choice on the following issues : type of flow sharing, size of receivers and number of receivers per node. These issues are discussed in detail, and then the designs of interest are identified Modelled network properties As already explained in the previous Chapter, in the ECOFRAME ring, each node is equipped with a fully-tuneable transmitter, able to dynamically change the transmission wavelength, from slot to slot. Such a transmitter allows a node to send no more than one packet per time slot. There are two types of receivers used in the network:

81 3.2. DESIGNING THE ECOFRAME OPTICAL PACKET RING 43 single-wavelength receivers : able to receive on a single, fixed wavelength. multi-wavelength receivers : able to receive on a predefined, fixed set of wavelengths. However, the effective traffic capacity received by a multi-wavelength receiver does not exceed the capacity of a single-wavelength receiver and it is equal to the capacity of the single wavelength. After the reception with multi-wavelength receiver, the packets are queued in the electronic buffer before being transmitted to the client. On the other side, when sending a packet using the multi-wavelength receiver, a node can freely choose on which wavelength of the receiver to transmit. S-receiver is a joint notation for both single and multi-wavelength receivers, where S (S 1) is the number of wavelengths per receiver. In each instance of the ring, all nodes use receivers of the same size S. The number of receivers per node is not limited and depends on the ring input traffic matrix. The following assumptions are made when designing the ECOFRAME ring: only a unidirectional ring is considered; no wavelength conversion is available, i.e., a traffic demand transmitted on a wavelength must be routed and received on the same wavelength; any traffic demand matrix can be passed as input; to account for the slotted TDMA nature of the ring, the traffic demands are expressed in terms of bit/s (in alternative, the bit rate of the traffic demands can be normalized to the wavelength capacity); cases where splitting of traffic demand (from a given source to a given destination node) on two or more different wavelengths or wavelength sets is allowed or not should be compared; different traffic demands can be aggregated on the same wavelength channel up to the available wavelength capacity; traffic demands can be added and dropped from the wavelengths, provided that (when adding) the above capacity constraint is ensured; receiver and wavelength cost are included in the objective function; the overall wavelength cost is proportional to the number of wavelength used; no transmitter nor fibre cost is accounted; receivers of different size S should be considered; if a station sends more than the capacity corresponding to the single wavelength capacity, it is considered that this station possesses more than one fully-tuneable transmitter, i.e. the number of fully-tuneable transmitters that is sufficient to satisfy such traffic demand. An example of the unidirectional ring design that accounts for the above assumptions is sketched in Fig. 3.1, when each traffic demand has a transmission rate equal to one half the wavelength capacity. The figure shows the required wavelengths and receivers at each node. The ECOFRAME ring design problem accounts for the receiver and wavelength cost. Please, notice that this problem is not equivalent to minimizing only the receiver cost or only the

82 44 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING Figure 3.1 Example of design of a four-node unidirectional ring (a) Design at minimum receiver cost (b) Design at minimum receiver cost with the minimum number of wavelengths Figure 3.2 Examples of ECOFRAME ring design wavelength cost. Indeed, a ring design with the minimum number of receivers (i.e., at minimum receiver cost) does not imply that the minimum number of wavelengths is used. An example is given in Fig. 3.2(a) that displays the design at minimum receiver cost, i.e. with two receivers, while using two wavelengths. However, it is possible to design the ring with the same minimum number of receivers, but with only one wavelength (Fig. 3.2(b)). Vice-versa, a ring design using the minimum number of wavelengths does not imply that the minimum number of receivers is used. An example is given in Fig. 3.3(a) that displays the design using the minimum number of wavelengths, i.e. two wavelengths, but requiring four receivers. The minimum number of required receivers is three, but three wavelengths would be necessary (Fig. 3.3(b)). Therefore, the optimal design at minimum receiver and wavelength cost needs to account for the ratio between receiver cost and wavelength cost. A detailed discussion about the network equipment cost is given next. Then, different designs for studied optical packet switched ring are proposed, depending on the way the traffic flows

83 3.2. DESIGNING THE ECOFRAME OPTICAL PACKET RING 45 (a) Design at minimum wavelength cost (b) Design at minimum receiver cost Figure 3.3 Examples of ECOFRAME ring design are shared, the allowed number of receivers per node and the size of receivers Discussion about the cost of network equipment The main driving costs to be included in the cost function, or objective function, of the design problem are given by the transmitters, the receivers, and the wavelengths. In order to assess the practical relevance of the design problem and cost function, the impact of the component cost on the design is addressed and a preliminary estimation of the component costs and their ratio is carried out (a detailed economical analysis of optical packet switching in WDM rings is beyond the scope of this work). The use of fast tuneable lasers at the ring nodes is a key hypothesis for transmitter technology. Under this assumption, the laser can be tuned to any of the wavelengths supported by the laser, on a packet per packet basis. Also, assume that each laser can be tuned on a wavelength range wide enough to include all the wavelengths of the ring. Under such assumptions, a single transmitter is necessary at each node. Therefore, for a given ring topology, the number of transmitters is equal to the number of nodes and cannot be further minimized nor optimized. The transmitter cost is a fixed component of the ring cost and, thus, can be removed from the cost function to be optimized. On the other side, receiver and wavelength cost are both contributing to the cost function in the design problem, as explained in the previous section. However, wavelengths and receivers are two rather different entities: while a receiver represents a part of equipment, a wavelength cannot be easily materialized. The cost of a receiver is related to the equipment architecture. As a general estimation, the cost of a non-wdm receiver can be assumed to be comparable to the cost of a transmitter in a 10 GigE port. Thus, the transmitter cost should be approximately in the range of [1,2] k$. The analysis of the wavelength cost is based on the fact that a wavelength which is used for the WDM ring cannot be used for other purposes (e.g. SDH ring, RPR). In such cases, the wavelength cost can be associated to the cost of leasing a wavelength. In [92], a leasing cost of 1.5 euro/m/year per wavelength is cited, for yearly contracts. Leased wavelength fees also include access to transponders and optical multiplexer/demultiplexer at both link extremities. Since the access to such equipment is not necessary in the WDM optical packet

84 46 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING ring, the wavelength cost should be assimilated to the renting of a dark fibre, where the operator owns its transponders and multiplexers. In [92], the leasing cost for a dark fibre is evaluated between 1.2 and 0.4 euro/m/year for medium term (5 years) and long term (15 years) contracts, respectively. Thus, the wavelength cost can be estimated as a fraction of the dark fibre cost, for instance 1/40 of the dark fibre cost when up to 40 wavelengths are supported in the ring. Due to the fast evolution of network technologies and capacity requirements, it seems preferable to consider a 5 year contract. On the other hand, 5 years is also a reasonable duration for the receiver amortization period. In summary, a rough estimate of the cost of a non-wdm receiver, C r (1), and the cost of a wavelength along the ring, C w, is C (1) r 300, C w 30 D, (3.1) where D is the ring length, in km. For a metro ring with a circumference of 50 km, the cost ratio is (C (1) r /C w ) 0.2. The same value of (C r (1) /C w ) we will use in our further analysis. The previous cost estimation was for the non-wdm receivers. Now we will try to estimate the cost of a WDM receiver. We will consider that the cost of a WDM receiver with n wavelengths non-linearly increases with n. This supposition could be justified with the fact that the expected price of a WDM receiver with n wavelengths is lower than the price of n non-wdm receivers. A WDM receiver is an integrated component and its price C r (n) must be cheaper. Therefore, we suppose: With α we note the sub-linearity factor. C (n) r = C (1) r n α. (3.2) Note that the cost of receivers for WDM SONET/SDH rings is typically doubling for 4-fold increase of the transmission rate, i.e. a formula of the same form as (3.2), for α = 0.5, holds in the case of SONET/SDH Design with single and multi-wavelength receivers The size of the S-receivers is a given parameter in the design. It means that all the nodes of a ring, use the same type of receivers, i.e. the receivers of the same size S. The interest of studying the receivers of different size is in the fact that receivers in the real system will not be able to listen on all of the wavelengths available in the ring, but rather on the subsets of S wavelengths (realistic values for S are for instance 2,4 or 10). Use of the S-receivers has a strong impact on the ring performance. The QoS performance of the ring is expected to be improved, due to the statistical multiplexing which is the consequence of the possibility to chose a wavelength for transmission among S wavelengths of the S-receivers. The impact of the S-receivers on the ring performances is studied in details in Chapter 3. In this Chapter, we discuss the impact of the size of the receiver on the ring design cost Design with splitting and without splitting Due to the possibility of the ECOFRAME fully-tuneable transmitter to change the emitting wavelength on a time slot basis, traffic demands could be split between two or more S- receivers. The splitting of traffic demands means that data packets belonging to the same

85 3.2. DESIGNING THE ECOFRAME OPTICAL PACKET RING 47 communication (between a given source and destination) can be transmitted by using more than one S-receiver of the same destination. If the splitting of traffic flows is prohibited, it means that each traffic demand should be routed, using a single S-receiver of a given destination. The decision to allow the splitting or to forbid it, has an impact on the ring design. More precisely, splitting of traffic demands could decrease the overall number of wavelengths in the ring. On the other side, splitting of traffic demands has an impact on the scheduling algorithms that are used in managing of the access when inserting new optical packets into ring. This is why it is interesting to consider both ring design with and without splitting of traffic flows and to compare their cost and the impact they have on the complexity of the scheduling mechanisms. It should be noted that if the splitting of traffic demands is forbidden in the ring design, it does not mean that the all the optical packets belonging to the same flow must be transported by using a single wavelength. If the size of the S-receiver is greater than 1, i.e. S > 1, optical packets can be sent by using any of the S wavelengths in the waveband of such receiver, even if the splitting of traffic demands is prohibited Considered ring designs As already pointed out, a ring design consists of a set of network properties defining admissible mappings. In order to take into account all the network properties of importance, the following ring designs are considered: 1. Single dedicated wavelength per destination (SDW) design. Flows with the same destination are aggregated on the same wavelength. This is the design considered by MATISSE networks [60]. In this design, the number of wavelengths used in the ring is equal to the number of nodes in the ring. SDW design is used as a benchmark, i.e. for the reference purposes. 2. Single shared receiver per destination (SSR) design. Each node receives on a single S- receiver but several nodes can receive traffic on the same wavelength. The number of receivers per node is limited to Multi shared receivers per destination without flow splitting (MR-N) design. Each flow between two nodes is mapped on a single S-receiver (i.e., no splitting), and each node receives on one or several S-receivers. The splitting is allowed only among the wavelengths belonging to the same S-receiver, of the same destination. 4. Multi shared receivers per destination with flow splitting (MR-S) design. Each packet flow may be split on several S-receivers, and each node receives on one or several S- receivers. In the following, the 0-1 ILP and MILP formulations of the presented ring designs of are given. In all the cases, the design problem is formalized as a multi-commodity flow problem. A flow is a stream of packets exchanged between a source-destination node pair. Traffic rate of the flow is the bit rate supported by the packet exchange and, as already mentioned, it can be expressed either in terms of bit/sec or normalized to the wavelength capacity. The input data of the problem are the unidirectional WDM ring topology and the set of flows with the corresponding traffic rates to be supported. The design problem aims at finding the

86 48 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING optimal number of wavelengths and receivers per node that minimizes the overall design cost. For this purpose, it is necessary to solve the wavelength assignment problem for the flows, while ensuring that the wavelength capacity is not exceeded. 3.3 The notation for linear programs In the present section, we define the main parameters, of the linear programming (LP) formulations that are given in this work. If, in a particular LP formulation a given parameter or variable, is different, in respect to the notation defined here, it will be redefined again in the corresponding section. The subscripts and superscripts that are used in the variable definitions are systematized in Tab s d i q k Table 3.1 Index Notation source node ID of a requested flow destination node ID of a requested flow generic node ID waveband ID requested flow ID The LP formulations are based on the parameters listed in Tab Note that waveband is the set of wavelengths on which a receiver is operating. The introduction of wavebands allow us to model the structured ECOFRAME receivers. For instance, if given parameter S is set to 4, it means that the result of design will give us the number of receivers of size S = 4 that to be installed at each station. The configuration will further define the type of receivers needed at each post, because receivers of the same size can have different types, according to the part of waveband spectrum they occupy. The cost of waveband C q is directly proportional to the cost of wavelength C w, i.e. C q = S C w. Let us also notice that for S = 1, the waveband reduces to the single wavelength, and the maximum number of wavebands Q becomes equal to the maximum number of wavelength channels in the WDM system. At the same time, the waveband cost C q becomes the single wavelength cost. The main variables that are used are listed in Tab Single shared receiver per destination (SSR) design This problem can be formalized in a form of 0-1 ILP problem. It is supposed that there are Q wavebands in the ring. They are numerated with index q. The station index is i. According to the adopted notation, y i is a binary variable which is equal to 1 if the waveband q is used in the ring, and 0, otherwise. Because of this, the cost of the wavelengths that are used in design, can be expressed by Q q=1 C q y q = Q q=1 (S C w) y q. The cost of the wavelengths needed in the ring is Q i V q=1 C r rq i, as ri q is a binary variable that is equal to 1 iff a station i receives on waveband q. Thus, an objective function of the

87 3.4. SSR DESIGN 49 Table 3.2 Given Parameters G r (V,E) a directed graph representing the unidirectional ring, where V is the set of nodes, E is the set of (unidirectional) links N = V number of nodes in the network Q maximum number of wavebands per fiber W maximum number of wavelengths per fiber S number of wavelengths in the waveband T traffic matrix: element, T k, is the traffic rate (in percentage of wavelength capacity) requested by the k-th flow B wavelength capacity (in bit/s) π k path of the k-th connection (i.e., set of links connecting node s to node d) C r receiver cost C w cost of a wavelength along the ring circumference C q cost of a waveband along the ring circumference p k q (pk w ) r i q (ri w ) y q (y w ) Table 3.3 Main variables a binary which indicates whether or not the k-th traffic demand is assigned to the receiver q (wavelength w) a binary which indicates whether or not node i requires a receiver q (wavelength w) a binary which indicates whether or not a waveband q (wavelength w) is used SSR design problem, that minimizes the overall cost of the receivers and wavelengths required in the network, is given by the expression: Min i V Q Q C r rq i + C q y q. (3.3) q=1 q=1 The 0-1 ILP formulation of the SSR problem, includes a number of constraints, which describe the problem features. The following constraint ensures that one (and only one) waveband is assigned to each traffic demand: Q p k q = 1 k : T k T (3.4) q=1 In other words, this constraint precludes the splitting of traffic demands. The variable p k q is defined in Tab The capacity of a waveband is S time greater than the capacity of a single wavelength. A constraint that ensures that traffic rate on receiver q does not exceed the waveband capacity, is expressed by the channel-capacity constraint: k:(i,j) π k p k q T k S q, (i,j) E. (3.5)

88 50 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING The following three constraints are also needed, in order to complete the description of the problem: p k q T k rq d d V, w (3.6) k:d=dest(t k ) rq i N y q q. (3.7) i V q r i q 1 i V. (3.8) Constraint (3.6) forces the use of a receiver q at destination d, by setting the corresponding value of variable r d q. Constraint (3.7) accounts if waveband q is used or not, by setting the value of variable y q to 1, iff at least one node listens to the waveband q. Constraint (3.8) ensures that only one receiver can be used per destination. The LP formulation of the SSR design is defined by the linear objective function (3.3), that need to be minimized, and the set of linear constraints (3.4)-(3.8). As all the variables in the formulation are integer, the obtained LP formulation belongs to the class of integer linear programming formulation. Furthermore, as all the variables are binary integers, the obtained ILP formulation is in the class of 0-1 ILP formulations. Let us notice that constraints (3.5) and (3.6) reveal the substantial difference between a design with single and multi-wavelength receivers. If S = 1, the overall traffic load that can be carried by a receiver on a link is limited to wavelength capacity. If S > 1, the overall link load per receiver is allowed up to S times more. This is defined by the constraint (3.5). However, as defined by the constraint (3.6), the amount of traffic load that can be received is in both cases limited to the single wavelength capacity. This is why, if the number of wavelengths in the ring is the same, the multi-wavelength receiver rings will be able to support more capacity than the single-wavelength receiver rings. This property is discussed in Chapter 3 in more details. 3.5 Multi shared receivers per destination without flow splitting (MR-N) design Multi shared receivers per destination without flow splitting (MR-N) design problem can be expressed in form of 0-1 ILP problem. Given parameters and variable definitions are the same like in the previous, SSR design. The 0-1 ILP formulation in this case is as follows. Objective Function Min i V Q C r rq i + q=1 Q C q y q (3.9) The objective function (3.9) minimizes the overall cost of the receivers and wavelengths required in the network. Constraints q=1 Q p k q = 1 k : T k T (3.10) q=1

89 3.6. MR-S DESIGN 51 p k q T k S q, (i,j) E (3.11) k:(i,j) π k p k q T k rq d d V, w (3.12) k:d=dest(t k ) rq i N y q q. (3.13) i V Constraint (3.10) ensures that one (and only one) waveband is assigned to each traffic demand. Constraint (3.11) ensures the traffic rate on receiver q does not exceed the waveband capacity. Constraint (3.12) forces the use of a receiver q at destination d. Constraint (3.13) accounts if waveband q is used or not. It can be noticed that the only difference between the SSR and MR-N design linear programming formulations is in the constraint (3.8). This constraint is necessary in SSR design in order to limit the number of receivers per node. This is why MR-N design will as a result find smaller (or at least equal) number of wavelengths necessary to support the same given traffic matrix, in comparing to the SSR case. 3.6 Multi shared receivers per destination with flow splitting (MR-S) design Multi shared receivers per destination with flow splitting (MR-S) design problem can be mathematically expressed with a mixed integer linear programming (MILP) formulation. After giving the MILP formulation in general case, for S 1, the bounds are derived and NP complexity of the problem is proved for case S = 1, i.e. for single-wavelength receivers. A heuristic algorithm is then proposed to solve the problem in the same case Mixed Integer Linear Programming Formulation The same variables and given parameters are used, like in the previous cases. The only difference with the parameters defined in Section 3.3, is that T k, the traffic matrix element, and p k q, the real variable, are expressed in bit/s, i.e. the variable pk q is not a binary integer anymore. Because of this, the obtained LP formulation belongs to the class of Mixed Integer Linear Programming (MILP) formulations. MILP Formulation Min i V Q Q C r rq i + C w S y q (3.14) q=1 q=1

90 52 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING Q p k q = T k k : T k T (3.15) q=1 p k q B S q, (i,j) E (3.16) k:(i,j) π k p k q B rd q d V, q (3.17) k:d=dest(t k ) rq i N y q q (3.18) i V The objective function (3.14) minimizes the overall ring cost, i.e., cost for the receivers and wavelengths required in the ring. In traffic-load constraint (3.15), the traffic flows are routed on the different receivers while ensuring that the requested traffic rate is supported. The limitation on the maximum load of a receiver on any link is guaranteed by the channelcapacity constraint (3.16). The placement of receivers and the number of wavelengths required in the ring are addressed by constraints (3.17) and (3.18), respectively. In particular, a receiver operating on receiver q is required at a node d if waveband of receiver q carries traffic destined to d. The wavelengths of waveband q are required in the ring if they carry some traffic, or, equivalently, if at least a receiver operating on q is placed in the ring. For S = 1, wavebands reduce to wavelengths, and multi-wavelength receivers reduce to single-wavelength receivers. The maximum number of wavebands per fibre Q reduce to the maximum number of wavelengths per fibre, noted with W Bounds Bounds on the number of receivers (R) and the number of wavelengths (W) required in the ring can be derived as follows. Bounds on the Number of Wavelengths The upper bound on the number of wavelengths is UB(W) = N, i.e., each node receives on a single distinct wavelength. Note that this bound is valuable only if the sum of traffic to each destination in traffic matrix T is in (0,B], which is the assumption taken here. The lower bound on W can be found by resorting to the lemma presented in [89]. Let L be the maximum load of a link, i.e., L = max (i,j) E The minimum number of wavelengths required to carry such load is k:(i,j) π k T k. (3.19) Λ = L. (3.20) B

91 3.6. MR-S DESIGN 53 Lemma: Given a set of flows T whose maximum load on a unidirectional WDM ring is L, then the ring can support the wavelength-continuous flows with Λ wavelengths, if the flows can be split on the different wavelengths. Proof: To demonstrate the lemma, start from the maximally loaded link. Consider all flows, and equally split each flow on Λ wavelengths. The traffic can be supported. Consider the adjacent link. Such a link carries a load of at most L, since the previous one was maximally loaded. Then, the amount of traffic that is received by the node is equal or more than what the node has to insert. Therefore, the capacity available on each wavelength is sufficient to insert the traffic to transmit, by equally splitting the traffic on the Λ wavelengths. Continue by considering all the other links in sequence. The reasoning is the same: the amount of traffic locally dropped at each node is at least as large as the amount of traffic that is added in the ring. Therefore, the capacity is sufficient to insert the traffic to transmit, provided that it is equally split among the wavelengths. Then, the lower bound on W is LB(W) = Λ. For the special case of uniform and complete traffic matrix, i.e., T k = a k, the load is N(N 1)a Λ =. (3.21) 2B In particular, when a = B/(N 1) (i.e., traffic rate to each node is B), then LB(W) = N 2. Bounds on the Number of Receivers The upper bound on the number of receivers required in the network is UB(R) = N LB(W) = N L, (3.22) B i.e. in the worst case each destination node is provided with a receiver for each wavelength. The lower bound on R is LB(R) = N, i.e. each node is provided with one receiver. Bounds on the Design Cost Let c be the minimum design cost. The upper bound on c can be found by resorting to a ring design in which a single wavelength is assigned to each node (as in RINGO project [22]), i.e. a WDM ring with N wavelengths and N receivers. This is a feasible solution of MILP formulation and provides a more stringent cost bound than the one found by exploiting the upper bounds on R and W. The upper bound on c is, thus, UB(c) = N C r + N C w. (3.23) The lower bound on the design cost can be found by resorting to the lower bounds on R and W, i.e., LB(c) = N C r + Λ C w. (3.24)

92 54 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING Design in an All-Wavelengths-Shared case An All-Wavelengths-Shared scenario is the situation when all the stations in the ring use the same set of wavelengths to receive their traffic, which is equivalent to supposing that each station in the ring is equipped with the same S-receiver. Let us notice that this case is a special case of MR-S design. Indeed, in such a scenario, the splitting of traffic within the same receiver is not forbidden, like in the case of MR-N and MR-S designs. Let us try to find the minimum number of wavelengths Λ, which is necessary to support a matrix of traffic T. Obviously, the value for Λ is given by the equation (3.20), and the Lemma from the section is applicable in this case, as well Problem Complexity Complexity of the optimization problem defined above can be derived as follows. Given an instance (G(V,E),T,B,C r,c w ) and an integer c, does there exist a receiver configuration respecting the constraints (3.15) to (3.18) such that the value of the objective cost function (3.14) is less or equal to c? Theorem: The considered design problem is NP-complete. Proof: First, since the cost function value can be computed polynomially for a given design, the problem is in NP. To complete the proof of the theorem, we first describe a polynomial reduction from the Problem 2-partition. Problem 2-partition Given : a (multi)set S = {n 0,...,n k 1 } of integers greater than zero such that 0 i k 1 2β. Question: Does there exist a subset S of S such that the sum of integers in S is equal to β? This problem is known to be NP-complete [40]. An instance (G(V,E),T,B,C r,c w ),c can be constructed from S as follows: the ring G(V,E) is such that N = 2k. in the matrix T, for each i, 0 i k 1, we set T[i,k + i] = n i. All other elements of T are equal to zero (thus, no receiver is required on nodes 0,...,k 1). wavelength capacity is B = β, cost of a wavelength and a receiver are normalized to C w = C r = 1 the value of c is set to c = k + 2. It is clear that the construction of this instance can be done in polynomial time considering the size of S. Consider first that the answer to Problem 2-partition is positive for S, i.e., a subset S with good property exists. Consider two wavelengths λ 1 and λ 2 on G(V,E). If n i S then T[i,i + k] is sent on λ 1 else on λ 2. Thus, only one receiver is needed on each node j, with n i =

93 3.6. MR-S DESIGN 55 k j 2k 1. It is also clear that the maximum load of each wavelength on any link is B. Thus the cost of such a ring design (i.e., receiver placement and number of wavelengths) is c. Consider now that there exists a ring design whose cost is equal to c (it can not be less than c since it needs at least two wavelengths and one receiver for each node from k to 2k 1). Since c = k + 2, exactly two wavelengths are used and thus exactly one receiver is used by each vertex from k to 2k 1. This implies a partition of {T[0,k],...,T[k 1,2k 1]} in two subsets. Since the capacity of one wavelength is β, then it implies a positive answer to Problem 2-partition for S. This demonstrates that the considered design problem is NP-complete Heuristic MRCF Since the ring design problem is NP-complete, it is tackled using a heuristic algorithm. The heuristic algorithm is based on the following principles. First, note that a design minimizing the receiver cost can be achieved by assigning the same wavelength to all the flows with the same destination, also referred to as group of flows. Second, partitioning a group of flows (or splitting a flow) on different wavelengths increases the overall cost, since one receiver is required on the destination node for each wavelength the flow (or the group of flows) is assigned to. Third, considering a design of the ring, it could be possible to trade wavelength cost for receiver cost by eliminating a wavelength and reassigning the flow supported by this cancelled wavelength on other wavelengths (provided that enough capacity is available). In the new design, the number of wavelengths is decreased by one, but the number of receivers may be increased. Based on such principles, the heuristic algorithm aims to find, first, a ring design that minimize the receiver cost for this reason, it is named Minimize the Receiver Cost First (MRCF). Then, MRCF algorithm attempts to trade wavelength cost for receiver cost by splitting flows and group of flows on different wavelengths and accepts the new solution if it is more costeffective. The pseudo-code of the algorithm is the following. MRCF Algorithm Input: G(V,E), T, C w, C r 1. Sort all the groups of flows by decreasing traffic rate order 2. For each group of flow taken in this order 2.1. First-fit wavelength assignment of the group of flows End 3. If (C r > C w ) then Stop // design cost cannot be further reduced End 4. Compute the overall design cost c 5. Sort the wavelengths by increasing max. link load order 6. For each wavelength taken in this order 6.1. Reroute the groups of flows from this wavelength to the other ones 6.2. If all the flow on this wavelength has been rerouted then

94 56 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING 6.3. Compute the overall design cost c without considering this wavelength 6.4. If (c < c) then 6.5. Accept the new design End // If End // If End In Steps 1 and 2, a design with minimal receiver cost is found, by assigning one wavelength to each group of flows. Wavelength assignment is performed by starting from the first allocated wavelength (first-fit wavelength assignment). If the already allocated wavelengths cannot support the traffic rate of the group of flows, then a new wavelength needs to be allocated. Steps 4-6 search for lower cost designs with fewer wavelengths but higher number of receivers. For this reason, such steps need not be executed when the condition in Step 3 is met. In Steps 4-6, all the allocated wavelengths are considered starting from the ones having the lowest traffic load on the most loaded link. The groups of flows supported by the considered wavelength are rerouted on the other allocated wavelengths. For each group of flows, wavelengths are sorted according to the load on the link close to the destination node of the group. Each group is then rerouted by fitting the flows on the least congested wavelengths. Splitting of flows on different wavelengths is performed if needed. If after rerouting the flows the design cost is decreased, the new solution is taken. Otherwise another wavelength is considered (Step 6), until all of them are considered for removal. The worst case complexity of the MRCF algorithm is O(K N 2 ), where K is the number of requested flows Results and conclusions about the ring design with splitting In the present section, results of the MRCF algorithm are compared with the optimal results on a six node ring. Then, MRCF algorithm is used to design metro rings with a larger size. Optimal results are found by solving the MILP formulation in Section 3.6 using a commercially available linear programming solver. Bounds are obtained as explained in Section Traffic matrix T is uniform and complete (i.e., flows are required between each node pair with same traffic rate). Thus, the maximum traffic rate of a flow is B/(N 1), due to the limitation on the amount of traffic that a node can receive. In all the figures, traffic rate is normalized to the wavelength capacity. Optimal vs. Heuristic Results MRCF results are compared against optimal results and bounds in Figs. 3.4, 3.5, and 3.6. The figures show the overall design cost versus the traffic rate, for different cost scenarios, in a six node ring. Fig. 3.4 considers a scenario in which receiver cost is dominant (C w = 0.1, C r = 1). Fig. 3.5 considers a scenario in which receiver cost and wavelength cost are comparable (C w = C r = 1). Fig. 3.6 considers a scenario in which wavelength cost is dominant (C w = 1, C r = 0.1). The curves are step functions due to the granularity of the wavelength capacity and also to the receiver number. The increase of design cost with traffic rate is higher when the wavelength cost is dominant. This means that efficient traffic grooming on the wavelengths is important

95 3.6. MR-S DESIGN Design cost UB MRCF OPT LB Traffic rate Figure 3.4 Six node ring: design cost vs. traffic rate for C w = 0.1 and C r = Design cost UB MRCF OPT LB Traffic rate Figure 3.5 Six node ring: design cost vs. traffic rate for C w = 1 and C r = 1 for a cost-effective design. The heuristic algorithm is able to achieve the optimal solutions for low traffic rates. For higher traffic rate, MRCF solution cost is within 33.3% of the optimal solution. In order to evaluate the impact of C r and C w, the receiver-to-wavelength cost ratio γ = C r C w is introduced. Fig. 3.7 shows the number of wavelengths and receivers, found by optimal solutions, heuristic solutions, and bounds, as a function of γ. When γ is small, the number of wavelengths is minimum and equal to the lower bound. This result is expected, as for small values of γ, the wavelength cost is dominant, thus the number

96 58 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING 7 6 Design cost UB MRCF OPT LB Traffic rate Figure 3.6 Six node ring: design cost vs. traffic rate for C w = 1 and C r = 0.1 Number of receivers and wavelengths γ OPT: R LB: R OPT: W LB: W MRCF: R MRCF: W Figure 3.7 Six node ring: number of receivers and wavelengths vs. cost ratio γ for traffic rate 0.18 of wavelengths in the design is minimized. On the other side, when γ is high, the number of receivers is minimum and reaches the number of wavelengths. This is the design in which each node operates on a single distinct wavelength (upper bound of the design cost). Notice that for few values of γ the number of receivers found by MRCF algorithm is below the optimal number. This is due to the fact that a higher number of wavelengths is selected, leading, however, to a design cost equal or greater than the optimal solution.

97 3.6. MR-S DESIGN 59 Ring Design Scalability and Cost Effectiveness MRCF algorithm is run on larger size rings, to evaluate the scalability of the design and the cost effectiveness against WDM optical packet ring with a single receiver and a single dedicated wavelength per each node (i.e., upper bound). Traffic rate of each flow is 0.08 of the wavelength capacity. Cost UB: design cost MRCF: design cost OPT: design cost MRCF: R cost OPT: R cost MRCF: W cost OPT: W cost Figure 3.8 Design, receiver, and wavelength cost vs. N for traffic rate of 0.08 and C r = C w = 1 Fig. 3.8 shows the design cost and its two components, i.e., receiver cost and wavelength cost, for increasing ring size (N) and for C r = C w = 1. Due to complexity of MILP formulation, optimal results are found for N 7. When N 8, wavelength cost and receiver cost match, i.e., a single dedicated wavelength per node is required. When N < 8, the proposed WDM ring is cost effective with respect to a WDM ring with single dedicated wavelength per node and a cost saving of up to 40% is achieved for small ring sizes. The cost-effectiveness is achieved by better exploiting the available bandwidth and thus achieving a reduction of the wavelength cost. Fig. 3.9 shows the design cost and its two components, i.e., receiver cost and wavelength cost, as a function of γ, in a ten node ring. Results are obtained by MRCF algorithm. The figure shows the trade-off between wavelength cost and receiver cost. For small values of γ, the wavelength cost in the design is dominant, while for high values of γ, the wavelength cost in the design is dominant. Thus, depending on the cost ratio it is possible to exploit the cheaper resource (i.e., wavelengths or receivers) to achieve a minimum cost design. The maximum benefits are achieved for low value of γ. For the realistic ratio estimated in Section 3.2.2, i.e., γ = 0.1, the cost savings are up to 60%. Obviously, this 60% cost reduction applies only for a part of the overall expenses. For instance, tuneable laser cost are the same for all designs and must be included in the overall cost. However, the cost reduction allowed by a proper design is still significant: for a ten station ring and with the hypothesis of Section 3.2.2, the saved amount is equivalent to more than 6 leased wavelengths. N

98 60 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING UB: design cost MRCF: design cost MRCF: R cost LB: design cost MRCF: W cost 10 2 Cost γ Figure 3.9 Design, receiver and wavelength cost vs. γ for traffic rate 0.08, N = 10 and C w = Cost comparison of different designs In the present section, the design costs of different ECOFRAME designs are compared. All the comparisons are performed for single-wavelength receiver rings. The compared designs are: SDW, SSR, MR-N and MR-S. Consider a ring with 5 nodes with client-server traffic [88]. One node (HUB) sends a flow of magnitude a (with wavelength capacity as unit) to all other nodes (clients) in the ring, while client nodes send a/4 units of traffic to HUB. The design cost is normalized to receiver cost. Fig compares the cost of each design option for a wavelength-to-receiver cost ratio of 5. Fig considers a 6 nodes ring with any-to-any traffic (flows of magnitude a between any 2 nodes). In both figures, the optimal optimization results are presented. As expected, in both Fig and Fig. 3.11: cost(mr-s) cost(mr-n) cost(ssr) cost(sdw). SSR is significantly cheaper than SDW and is more expensive than MR-N and MR-S in some cases. The costs for MR-S and MR-N are quite close. The cost is minimum for MR-W, as there are fewer constraints on the design. However, although the cheapest, MR-S design, that allows the splitting of traffic demands, demands a complicated scheduling algorithm. This is proved in the following section. The other important conclusion is that SSR design, which provides a design with single receiver per node, does increase a design cost, but not excessively. On the other side, the SSR architecture simplifies the design and provides to the operators the opportunity to install the ECOFRAME network by purchasing a single receiver per node. These properties make the SSR a good alternative to the MR-N design.

99 3.8. IMPACT OF SPLITTING ON SCHEDULER COMPLEXITY 61 Figure 3.10 Design Cost of Different Ring Architectures in a 5 nodes ring and for Client-Server traffic Figure 3.11 Design Cost of Different Ring Architectures in a 6 nodes ring and for Any-to-Any traffic 3.8 Impact of splitting on scheduler complexity This section compares the same ring architectures (SDW,SSR,MR-N and MR-S), in terms of scheduling. Once again, the single-wavelength receivers are used in the ring. Scheduling in each node implements the set of policies to be used in each time slot for selecting one packet among the set of queued packets, and one free wavelength (a free wavelength does not already carry a transit packet from an upstream node).

100 62 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING Scheduling issues are studied in detail in Chapter 5. Here, only the impact of different ring designs on the scheduling complexity is analyzed. For SDW and SSR, scheduling is limited to selecting the destination to serve, with FIFO buffers either per destination or per used wavelength. The configuration burden for this type of scheduler is minimal. Consider now MR-S which achieves the minimum design cost. A more complex scheduling function is required in order to avoid congestion. Indeed, consider a 6 node ring with stations labelled A-B-C-D-E-F in traffic direction, a wavelength-to-receiver cost ratio of 1, and a traffic matrix for which the optimal MR-S design is summarized in Tab. 3.4: Table 3.4 Optimal design for MR-S. 2 wavelengths are used, C and D receive on Λ 1, D and E receive on Λ 2 and the flow between F and D is split between Λ 1 and Λ 2 Wavelength A to D B to E E to C F to D Λ Λ A simulation study is used to compare a Design Oblivious (DO) scheduler that randomly selects an available slot with uniform probability, and a Design Enforcing (DE) scheduler that enforces, through a Leaky Bucket like mechanism, the proportion of slots used for each traffic flow on each wavelength. A DO scheduler thus independently selects the destination to serve and the slot to use, which is not the case for a DE scheduler. The ECOFRAME network is simulated the simulator esope (Appendix A). The DE scheduler supports the offered traffic matrix, and enforces the traffic mapping given in Tab On the other hand, the traffic mapping yielded by the DO scheduler is given in Tab. 3.5, which shows that the 0.3 flow from B to E is not supported. This means that node B is congested and thus argues in favour of implementing a DE scheduler that enforces the designed traffic mapping. However a DE scheduler has to be reconfigured every time the traffic mapping is modified, even when the numbers of used wavelengths and receivers are not modified. This is a heavy configuration burden, unrealistic for operational networks. DE schedulers also present the drawback of not being work conserving (some empty time slots may be left unused in presence of queued packets), which induces QoS degradations in terms of transfer delay. Thus, using a DE scheduler is not a preferable option, and should be avoided if possible. Table 3.5 Traffic mapping with a Design Oblivious scheduler Wavelength A to D B to E E to C F to D Λ Λ As illustrated in the above example, it is flow splitting that imposes the use of a DE scheduler. This is why forbidding flow splitting (i.e. using MR-N) is an attractive alternative. However, this does increase the cost of the design as seen in Tab. 3.6, since a third wavelength has to be used. According to the obtained results, there is a trade-off between network design cost and scheduler complexity. The main result of this section is that allowing flow splitting decreases the design cost while imposing a Design Enforcing scheduling policy which presents unrealistic configuration burden. Forbidding flow splitting avoids this burden but increases design cost.

101 3.9. CONCLUSION 63 Table 3.6 Optimal design for MR-N. 3 wavelengths are used, C and E receive on Λ 1, D receives on Λ 2 and Λ 3 Wavelength A to D B to E E to C F to D Λ Λ Λ The alternative of flow splitting in a load balancing framework [89] can be considered to increase capacity. The load balancing issue is discussed in more details in the next Chapter. 3.9 Conclusion In this Chapter, the ECOFRAME ring is designed by routing the traffic flows into TDM/WDM optical circuits, while the problems of insertion and extraction of optical packets are neglected. Special attention is paid to the network characteristics of importance, in order to obtain as the best possible matching of the optimal design results and the real network configurations, that are going to be installed. The trade-off between the number of receivers and wavelengths that are used in the design depends on their cost ratio and is quantified in this Chapter. The results of this Chapter are the basis for introducing the design with QoS and stability guarantees, for the analysis of the network performance, i.e. of its behavior in different circumstances and for the problem of designing of an appropriate scheduling algorithm. The presented results have shown that the problems of choosing the ring configuration and designing the Medium Access Control protocol mechanisms are closely related. This fact is illustrated on several examples. The dimensioning of the ECOFRAME ring is based on the use of the methods of linear programming. Linear programming is successfully employed in the study of the optical WDM networks of all topologies. The main problem in the designing problem of the ECOFRAME ring was in the proper selection of the network characteristics that should to be modelled and in their adjustment to the specificity of the methods of linear programming. One of the characteristics of the ECOFRAME network design problem is the fact that this network is in the ring form. The classical routing and wavelength assignment [RWA] problem is thus simplified and reduced to the wavelength assignment [WA] problem. However, this does not significantly affect the complexity of the considered problem. NP-completeness of some instances of the ECOFRAME ring dimensioning problem is proven in this Chapter. The second important characteristic of the ECOFRAME ring is the optical packet switching. The impact of optical packet switching on ring design is studied separately, in the following Chapter. As we are going to see, the non-deterministic nature of the packet traffic induces stability problems in the design. In our study on design, so far, we did not study the stability of the design, as we were using the traditional methods of designing the WDM optical rings. Such an approach is valid, when the input traffic matrix is dimensioned to include the expected peaks of traffic. Different design approaches studied in this Chapter were shown to be useful in determining the design decisions that have an influence on the design of node MAC functionalities.

102 64 CHAPTER 3. DESIGN OF TDM/WDM OPTICAL PACKET RING To summarize, in this Chapter, among other things, it is found that: The Integer Linear Programming (ILP) method can be successfully used for expressing the ECOFRAME ring design. It is shown that the multi-wavelength receivers, can be modelled with meta-wavelengths. The ECOFRAME ring design problem is shown to be a very complex problem. An instance of this problem is shown to be NP-complete, in Section 3.6. For a ring of large size, the calculating time of the network configuration, when using commercially available LP solvers, becomes too great. That is why, the approximative algorithms are developed for finding the design in a general case. The imposition of a single receiver at a network node does not significantly increase the network cost, but significantly simplifies the design and enables the network operators to get a fully operational system by purchasing a single receiver per station. The results on a simple ECOFRAME design, when all the stations listen to all the wavelengths, and which is interesting from the operator s point of view, are provided in Section It is determined that the splitting of traffic demands have a negative impact on the complexity of scheduling algorithms. The fact that the wavelengths can be shared between different destinations, significantly reduces the ring cost. The decrease in the design cost, due to the wavelength sharing, in comparison to the MATISSE ring, is quantified in Section 3.6. The impact of the receiver and wavelength cost on the design is quantified in Sections 3.6 and 3.7.

103 CHAPTER4 Packet-Aware Design of Optical Packet Ring In the previous Chapter, the problem of designing the ECOFRAME ring, with approximation that traffic flows can be routed like TDM/WDM optical circuits, was addressed. In this Chapter, the problems of insertion and extraction of optical packets are taken into account and the problem of the stability of the ECOFRAME ring design is assessed. This problem is identified, mathematically formalized, and resolved in a general case. In parallel, the scheduling policies of interest are introduced. Different approaches in designing a stable ECOFRAME ring are presented and their efficiency is compared.

104 66 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING 4.1 Introduction In the previous Chapter, the optical packet switched (OPS) ECOFRAME ring is designed by using the methods for designing the optical circuit switched (OCS) networks. Mechanisms of insertion and extraction of optical packets were not taken into account. Therefore, it is assumed that the matrix of traffic, when using this method of design, is slightly overdimensioned so that the stability of the system could be preserved. In this Chapter, the mechanisms of insertion and extraction of the packets are taken into account, the problem of dimensioning of the OPS ring is placed in a new context, in which the problem of stability of the system must be directly resolved by introducing the new conditions in the existing LP formulation. The problem of finding a stable ECOFRAME ring design is, in this Chapter, tackled by: 1. assuming that the insertion process on different wavelengths can be observed independently, and 2. observing the insertion process jointly for all the wavelengths. These two approaches have led to two following solutions, which are presented in the remainder of this Chapter: Packet Aware Design with Multiple packet insertion (PAD-M). It is supposed that a station can send more than one packet per time slot, which is an approximation of the ECOFRAME station. As with the MR-N design, each flow between two nodes is mapped on a single S-receiver (no splitting), and each node receives on one or several S-receivers. Splitting is allowed only among the wavelengths belonging to the same S- receiver. Unlike the MR-N design, PAD-M design imposes the constraints of ensuring a desired level of the QoS performance of the traffic transported by the ring. Packet Aware Design with Single packet insertion (PAD-S). It is supposed that a station can send exactly one packet per time slot, which describes properly the ECOFRAME station. As with the MR-N design, each flow between two nodes is mapped on a single S-receiver (no splitting), and each node receives on one or several S-receivers. Once again, splitting is allowed only among the wavelengths belonging to the same S- receiver. As with PAD-M design, PAD-S design imposes the constraints of ensuring the stability of the obtained configuration. It is shown that the first approach guarantees stability in a limited number of cases, while the second guarantees stability in a general case. 4.2 Addressing the packet queueing performance To design the ECOFRAME ring, it is necessary to find the number of wavelengths and receivers to support a given set of origin-destination packet flows. The problem consists in solving the wavelength assignment problem for the flows, while ensuring that the wavelength capacity is not exceeded. For a general traffic matrix, the complexity of this problem can be proved to be NP-hard (Section 3.5). It can be formalized as an integer linear program (ILP), whose optimal solution potentially allows 100% utilization of the wavelength capacity.

105 4.2. ADDRESSING THE PACKET QUEUEING PERFORMANCE 67 However, when designing a packet switching ring, the capacity utilization on wavelengths should not be pushed to 100%, as when dimensioning a circuit oriented network (like SONET/SDH, for instance), because it can render the system unstable. To illustrate how the QoS performance of the ring is degraded in the case when the wavelengths are fully occupied with traffic, we consider the 6-node ring from Fig We suppose that only one wavelength, for instance Λ, is operative in the ring, and that traffic flows are as in Fig The values of a and b are normalized to wavelength capacity. We observe the latency performance of packets departing from A, which are queued prior to access to the ring. The results obtained, for different values of b, are shown in Tab The queueing delay is normalized to the duration of time slot. The simulation results are given with the confidence interval of 10%, at a confidence level of 95%. The simulation is carried out in an ns-2 simulator, enhanced with a new MAC layer package [2]. More details about the simulator can be found in Appendix A. a=0.2 A Λ B b F C E D Figure 4.1 QoS degradation scenario Table 4.1 Mean Queuing Latency: Example from Fig. 4.1 b = 0.7 b = 0.79 b = 0.8 A C mean queueing delay (in time slots) From Tab. 4.1, it is easy to see that mean queuing delay drastically increases when b = 0.8. This is because, for b = 0.8, the wavelength is 100% saturated, so the queue with packets waiting to be inserted in the ring becomes unstable. Therefore, packet aware design of the ring is mandatory. In the following sections we present a 0-1 ILP formulation aiming at providing such a design Stability condition for Packet Aware Design with Multiple packet insertion (PAD-M) To account for the packet nature of the traffic, ECOFRAME nodes are modeled as queues. There are different ways of packet classification, as explained in Chapter 2. The packets can

106 68 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING be queued according to their destination, or according to the wavelength on which they are routed. The main supposition that we make is that packet queues can be observed independently, which basically means that a node can simultaneously send packets from different queues, during the same time slot. This supposition is approximate, but it allows us to address the problem in some cases of interest. The design obtained we will call a Packet Aware Design with Multi packet insertion (PAD-M). Under the assumption of Bernoulli arrivals of packets at each node, the input queue at each node can be approximated as a Geo/Geo/1 queue with packet arrival rate λ (i.e., flow rate entering at the node), packet service rate µ (i.e., µ = 1 λ t where λ t is the transit flow rate) and utilization factor ρ = λ/µ. The Bernoulli arrival assumption is made valid by the high aggregation currently observed in metro networks. It is well known that, to ensure the stability of the queue, the utilization factor should be ρ < 1, i.e., the utilization of the wavelength capacity should be clearly below 100%. Fig. 4.2 shows the queuing delay experienced by the packets in a ring node, versus λ, for different values of rate (1 µ) of the transit flow. Simulation results and analytical results based on the queuing model are both included µ=0.5, simulation µ=0.5, Geo/Geo/1 µ=0.8, simulation µ=0.8, Geo/Geo/1 Expected queueing delay [number of time slots] λ Figure 4.2 Mean queuing time experienced by packet arriving at rate λ inserted on a wavelength already occupied by a transit flow of rate (1-µ) The figure indicates the correctness of the queuing model and the impact of λ, µ, and ρ on the packet delay. To ensure that the queuing delay is not unbounded, the utilization factor can be limited to a maximum value ρ < γ, where γ < 1. The impact of γ on the queuing delay is shown in Fig. 4.3 for increasing values of µ. Low values of γ limit the utilization factor and thus the delay. Once γ is selected, the constraint, rewritten as λ γ(1 λ t ) = γ µ (4.1)

107 4.2. ADDRESSING THE PACKET QUEUEING PERFORMANCE γ=0.8 γ=0.9 γ=0.95 γ=0.99 Expected queueing delay [in number of time slots] µ Figure 4.3 Mean queuing time experienced by packets inserted on a wavelength when utilization factor is limited by different values of γ should be enforced at each node and for each wavelength. PAD-M stability condition, expressed by the inequality (4.1), is valuable for both rings with single and multi-wavelengths receivers. However, the condition (4.1) can be further simplified in the case of multi-wavelength receivers, as shown below. Let us observe a S-receiver, any wavelength of which is characterized with a parameter µ, defining a probability that, during the observed time slot, the time slot on that wavelength is free. Thus, we suppose that every wavelength has the same occupancy probability, if it belongs to the same receiver. Let µ(s) be the probability that a time slot will be free on at least one of the S wavelengths of the receiver. The condition (4.1) could be then written as: λ γ µ(s). (4.2) Let us look at Fig. 4.4, in order to find the formula expressing µ(s). In Fig. 4.4, an ECOFRAME station is illustrated. It is supposed that the station sends traffic to a single destination, and that all the packets towards this destination are queued in a FIFO queue. The destination receives packets on wavelengths Λ 1, Λ 2, Λ 3 and Λ 4. The head-of-line optical packet in the observed time slot (Fig. 4.4) can be sent by using either wavelength Λ 2 or Λ 3, because wavelengths Λ 1 and Λ 4 already contain optical packets in this time slot. In other words, the optical packet can be inserted only on the wavelengths that contain a free time slot. We take into account the fact that an ECOFRAME station can send only a single optical packet per S-receiver and per time slot, i.e. that exactly one of the wavelengths, of the same receiver, with free time slot, will be chosen for the transmission. At the same time, it is supposed that a station equally balances its traffic over all the available wavelengths. This technique is called load-balancing, and its benefits are proven in Chapter 5.

108 70 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING Λ 1 Λ 2 Λ 3 Λ 4 Λ 1,Λ 2,Λ 3,Λ 4 optical packets Figure wavelength WDM receiver This allows us to write the following formula which holds for WDM receivers of size S (S 1): µ(s) = 1 (1 µ) S. (4.3) Thus, stability condition (4.2) for multi-wavelength receivers in PAD-M design becomes: λ γ(1 (1 µ) S ). (4.4) The stability condition (4.4) can be used for design of both rings with single and multiwavelength receivers. It is possible to include this condition as a linear constraint in the ILP formulation of design. However, the PAD-M stability condition (4.4) provides stability only when a ring node sends its traffic by using no more than a single S-receiver, due to the starting assumption about the independence of the observed queues. An example of a case, in which the PAD-M gives a stable design, is, for instance, a pure concentration traffic scenario, i.e. the case when one, chosen station in the ring (called a HUB), receives traffic from all the other stations. It will be further discussed later (subsection 4.2.6) as to why the PAD-M stability condition (4.4) is not appropriate for designing the ring when stations send traffic by using more than one wavelength or waveband. In the remainder of the section, the 0-1 ILP formulations for packet-aware PAD-M design are given, when receivers are : with single wavelength and with multiple (S) wavelengths PAD-M design for single-wavelength receivers The packet-aware design with multiple packet insertion, for single-wavelength receivers, can be mathematically formalized in the form of an 0-1 integer linear programming (ILP) formulation, as follows. Note that all the variables and given parameters are as defined in Section 3.3.

109 4.2. ADDRESSING THE PACKET QUEUEING PERFORMANCE 71 Objective Function Min i V W W C r rw i + C w y w (4.5) w=1 w=1 The objective function (4.5) minimizes the overall cost of the receivers and wavelengths required in the network. Constraints k:i π k,i=source(t k ) W p k w = 1 k : T k T (4.6) w=1 k:(i,j) π k p k w T k 1 w, (i,j) E (4.7) k:d=dest(t k ) p k w T k r d w d V, w (4.8) rw i N y w w. (4.9) i V p k w T k γ(1 k:i π k,i source(t k ),i dest(t k ) p k w T k ) w, i. (4.10) Constraint (4.6) ensures that one (and only one) wavelength is assigned to each traffic demand. Constraint (4.7) ensures the traffic rate on wavelength w does not exceed the wavelength capacity. Constraint (4.8) imposes the use of a wavelength w at destination d. Constraint (4.9) decides whether wavelength w is used or not. Constraint (4.10) ensures that the portion of traffic inserted by station i on a wavelength w does not exceed γ (γ [0, 1)) of the capacity of that wavelength. This constraint implements the PAD-M condition 4.1. Indeed, on the right side of the inequality, we find the expression k:i π k,i=source(t k ) pk w T k, which is the sum of all the traffic that is inserted on some wavelength w, while the expression 1 k:i π k,i source(t k ),i dest(t k ) pk w T k, on the right side of the inequality, represents the free capacity of wavelength w ( k:i π k,i source(t k ),i dest(t k ) pk w T k is the transit traffic on wavelength w) PAD-M design for multi-wavelength receivers (S > 1) The packet-aware design with multiple packet insertion, for multi-wavelength receivers, can be mathematically formalized in the form of an 0-1 ILP formulation, as follows. However, as the stability condition (4.4) is not easily implemented, the proposed 0-1 ILP formulation is approximate. Note that all the variables and given parameters are as defined in Section 3.3, except:

110 72 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING 1. the set of given parameters β i, which are the values that limit the portion of the waveband occupied by the transit flows. β i are the real numbers from the interval [0,1]. The number of constants β i depends on the wanted depth of the approximation. An example of a set of β i is {0,0.1,0.2,...,1.0}. If the cardinal number of the set of β i is not finite, i.e. if all the points of the interval [0,1] are included in the set of β i, then the following approximative 0-1 ILP formulation becomes exact. 2. the binary variable m d q,i, which indicates whether or not the transit flow rate on waveband q at node d should be limited by β i. 0-1 ILP: Objective Function Min i V Q Q C r rq i + C w y q (4.11) q=1 q=1 The objective function (4.11) minimizes the overall cost of the receivers and wavelengths required in the network. 0-1 ILP: Constraints Q p k q = 1 k : T k T (4.12) q=1 p k q T k S q, (i,j) E (4.13) k:(i,j) π k p k q T k rq d d V, w (4.14) k:d=dest(t k ) rq i N y q q. (4.15) i V k:d π k,d=source(t k ) p k q T k γ i k:d π k,d source(t k ),d dest(t k )p k q T k S i ( 1 β S i ) m d q,i, q, d. (4.16) β i m d q,i, q, d. (4.17) m d q,i 1, q, d. (4.18) i Constraint (4.12) ensures that one (and only one) waveband is assigned to each traffic demand. Constraint (4.13) ensures the traffic rate on receiver q does not exceed the waveband capacity. Constraint (4.14) forces the use of a receiver q at destination d. Constraint (4.15) decides whether waveband q is used or not. Constraints (4.16) and (4.17) ensure that the ingress delay is bounded. Constraint (4.17) ensures that the transit rate is bounded by β i. Constraint (4.18) ensures that constraints (4.16) and (4.17) are satisfied for only one of the i values of β i.

111 4.2. ADDRESSING THE PACKET QUEUEING PERFORMANCE 73 Proof of the stability condition implementation Let us suppose that β i has been selected. Let λ be the overall traffic inserted on a receiver (waveband), µ be the probability that time slot is available for insertion on a wavelength of the receiver and µ(s) the probability that at least one wavelength of the receiver S is free for transmission. Then, from (4.16) and (4.17) we have: λ = k:d π k,d=source(t k ) p k q T k γ ( 1 βi S ) and k:d π 1 µ = k,d source(t k ),d dest(t k ) pk q T k S respectively. This is equivalent to : and λ γ ( 1 βi S ) β i, Finally, we obtain: which we wanted to prove. µ(s) = 1 (1 µ) S 1 β S i. λ µ(s) γ ( ) 1 β S i 1 βi S = γ, All-Wavelengths-Shared ring An all-wavelengths-shared ring is a ring where all the nodes can listen and transmit on the same set of wavelengths. Each station performs load balancing, i.e. it equally splits the traffic on all the wavelengths. PAD-M stability condition in this case corresponds to (4.4). For station i, the overall arriving traffic λ i should satisfy the following condition: λ i < 1 (1 µ i ) W, (4.19) where W is the number of wavelengths in ring, and µ i is the service rate per wavelength, for station i. Obviously, W arg max i log(1 λ i ) log(1 µ i ). (4.20) Let us note with W MIN1 the minimum number of wavelengths W for which the inequality (4.20) is satisfied.

112 74 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING Let L be the maximum occupancy of a link in the ring, and B be the capacity of the wavelength. The minimum number of wavelengths necessary to support this traffic (ie. needed for design) is: W MIN2 = L. (4.21) B Finally, by combining (4.20) and (4.21), we obtain the minimum number of wavelengths needed in the all-wavelengths-shared ring: W min = max(w MIN1,W MIN2 ). (4.22) Results on PAD-M design We illustrate the PAD-M by considering a concentration traffic matrix where a particular node (the hub), in a single-wavelength receiver ring, receives traffic from the other nodes. The PAD-M for ECOFRAME ring has been optimally solved by using a commercially available ILP solver. Optimal results in Figs. 4.5 and 4.6 are obtained on a 6 node ring with flows of identical rate r from each node to the hub. Fig. 4.5 shows the number of wavelengths (and thus the number of receivers at the hub node) versus the flow rate, when PAD-M and packet-unaware approach (i.e., γ = 1) are used. It shows that optimal PAD-M requires additional resources (i.e., wavelengths and receivers) only when the flow rate falls into a limited range of values. This means that PAD-M is able to guarantee the bounded delay with or without minimal additional resources. The amount of additional resources depends on the value of γ, as shown in Fig. 4.6, which is plotted for a fixed value of flow rate (r = 0.195). Low values of γ (i.e., γ < 0.88 in the figure) request the utilization of an extra wavelength to guarantee the bounded delay. On the other hand, a lower value of γ has the advantage of limiting the insertion delay (Fig. 4.3). This clearly indicates the trade-off between high dynamic performance and cost-effectiveness of the ring. The results of Fig. 4.5 show that a circuit design is always cheaper than a PAD-M, which is obvious for a given traffic matrix, as PAD-M implies one additional constraint. This disadvantage may, however, be counterbalanced when considering how the traffic matrix is obtained. Indeed, the traffic matrix for a circuit-based design has to assume that peak traffic volumes are achieved simultaneously for all source-destination flows, which is not necessarily the case in a metro packet network where different types of users may generate different busy hours (e.g. a residential area will have its busy hour in the evening whereas a commercial area will be busiest during the day). To summarize, the presented PAD-M design has the advantage of enforcing the transfer plane performance (i.e., bounded queuing delay experienced by the packets) during the ring design and, thus, avoids the need for a two-step approach iterating between design optimization and transfer plane performance evaluation Limitations of the PAD-M approach In the present section, we have tried to address the stability by limiting the insertion latency of the queued packets. The stability condition (4.4) addresses stability independently for

113 4.2. ADDRESSING THE PACKET QUEUEING PERFORMANCE Number of wavelengths PAD M, γ=0.8 PAD M, γ=0.9 packet unaware design flow rate Figure 4.5 Minimum number of wavelengths versus flow rate obtained by PAD-M and packet-unaware approach 2.5 Number of wavelengths γ Figure 4.6 Minimum number of wavelengths versus γ when applying PAD-M (flow rate = 0.195) each wavelength on which a station inserts. This is the approximation which limits the use of PAD-M design, when designing an ECOFRAME ring. In an ECOFRAME ring, it is supposed that station can send its traffic to the same destination by using different wavelengths, i.e. wavebands. In the next section it is shown that another

114 76 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING stability condition is necessary to assure the stability in general case. Here, a simple example showing why stability condition (4.4) does not guarantee stability in general case is given. Let us suppose the following scenario (Fig. 4.7): a station sends traffic on two wavelengths: Λ 1 and Λ 2, Λ 1 and Λ 2 have a free time slot with probability µ = 1 and the insertion load per wavelength queue should not be greater than γ = 0.9. λ 1 µ 1 µ 2 λ 2 Figure 4.7 Limitations of the PAD-M design: an example Let us try to calculate the admissible arrival rates λ 1 and λ 2. According to stability condition (4.1), λ 1,λ 2 γ µ = 0.9. However, as the ECOFRAME station can send no more than a single packet per time slot, the obtained bounds are not correct. Indeed, let us analyze what happens if a free wavelength is chosen with uniform probability. Then, each of the wavelengths Λ 1 and Λ 2, is available with the probability 0.5. The real stability condition is λ 1,λ 2 γ 0.5 = Thus, this simple example confirms that stability demands more strict conditions. In the next section we consider the stability of the ECOFRAME optical packet ring in a general case. 4.3 Addressing stability in general case The stability of the ECOFRAME optical packet ring with w wavelengths, in a general case, is considered. It is assumed that each station can send a single packet per slot, and that there is a single FIFO queue in front of each available wavelength. The obtained design is named Packet Aware Design with Single packet insertion (PAD-S) design. Let us observe a station that can send packets on each of w wavelengths. It is also assumed that during a time slot, at most one packet can arrive at the station, with probability λ i, toward the wavelength i. Obviously, i λ i < 1. Finally, it is also assumed that the probability that the wavelength is free in a given time slot is constant, equal to µ i, 0 µ i 1.

115 4.3. ADDRESSING STABILITY IN GENERAL CASE 77 Let us look at the stability condition of such a system. Since only one packet can be sent per slot, it is necessary to specify the scheduling policy, i.e. the method used to select a packet to transmit when several packets are queued in the station. We first introduce the scheduling policies of interest and then we show, on a simple example, how the stability of the system depends not only on obvious parameters, such as input and service rates, but also on the scheduling policy Scheduling policies When designing an optical packet ring, the stability conditions should be satisfied. However, the scheduling policy also has an impact on the stability. The ring can be properly designed, but if the scheduling policy is not appropriate, the system will become unstable after some time. In the scheduling process, a major decision to be taken is on which wavelength to transmit. As splitting of the traffic flows among receivers is forbidden (Section 3.8), each traffic flow is allocated to the set of wavelengths of exactly one receiver. That is why the wavelength for transmission will be chosen from the set of wavelengths of the receiver used by the destination for the reception of the flow. In order to make this feasible, each node must know the ring design, i.e. on which wavelengths/receivers any potential destination listens. Three criteria for choosing the wavelength are considered, calculated according to the optical packet creation time, the length of the wavelength queues, and the reserved bandwidth for a connection: 1. Oldest Packet First (OPF) policy : According to this policy, the packet that will be chosen for transmission is that which was waiting for the longest period of time at the head of a queue to some wavelength. The inconvenience of this policy is that the processing units need to know the exact date of creation of every optical packet, which is memory consuming. 2. Longest Queue First (LQF) policy : This policy always chooses the packet for transmission which is at the head position of the longest queue. This policy is easy to implement but its use may lead to the starvation of the short queues, which is a well known result. 3. Largest Virtual Waiting Time First (LVWTF) policy : A modified LQF which weights the length of the queue by a factor inversely proportional to the rate used for dimensioning the system. LVWTF policy, for each station i, considers the variables size j /a ij for eligible queues, where a ij is the flow to transport originating from station i and routed on wavelength j (normalized to the wavelength capacity) and serves the queue for which this value is maximum. 4. Random (RAND) : uniformly chooses a queue to be used among the queues containing the eligible packets; 5. Priority queueing : one or more queues are served with priority in respect to the other queues. In the following section, a simple example is presented showing that stability of the ECOFRAME ring depends not only on the input traffic matrix and the configuration, but also on the chosen scheduling policy.

116 78 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING Load of queue 2 and total load OPF, total load priority queueing, total load OPF, queue 2 load priority queueing, queue 2 load λ 1 Figure 4.8 Maximum values of λ 2 and total maximal load versus λ Impact of scheduling policy choice on stability Consider 2 wavelengths Λ 1 and Λ 2. A slot on Λ 1 (respectively Λ 2 ) is free with probability µ 1 (respectively µ 2 ); in our example, µ 1 = 1 and µ 2 varies between 0.1 and 0.9. The arrival rates are λ 1 and λ 2. The scheduling policy is as follows: as long as there are packets in the first queue, they are served. Packets from the second queue are served only if the first queue is empty. Obviously, the first queue is stable, as long as λ 1 < 1. On the other hand, the probability that a time slot can be used for serving the second queue is µ 2 (1 λ 1 ), which is significantly more severe than λ 2 < 1. Figure 4.8 presents the maximum class 2 load and total load versus class 1 load for both priority scheduling and a reference scheduling, OPF, where the oldest packet is selected for transmission. Figure 4.8 shows that the stability region for the priority queue is far smaller than the stability region of OPF. In other words, it means that the stability conditions are different for two compared scheduling policies. Another example that illustrates the same problem is as follows. A 6-node ring network with single-wavelength receivers (like that of Fig. 4.1) is designed by using the rules of MR-N design. The input traffic matrix is symmetric and uniform in this example, with traffic rate per destination-source pair of 0.16 (normalized to wavelength capacity). The scheduling policy used in this example is RAND, i.e. the packets are chosen for the transmission randomly, among the packets destined for different destinations. The mean delay of packets entering the network at node A is measured, for the same value of traffic for which the ring is designed. The obtained results are shown in Fig From Fig. 4.9 it can be seen that congestion, due to the use of RAND scheduling policy, and inappropriate ring design, generates large and non-symmetric delays.

117 4.3. ADDRESSING STABILITY IN GENERAL CASE 79 Figure 4.9 The delays induced by the congestion due to 100% load of the wavelengths State of the art on stability A more general system has already been considered in [84], its stability has been assessed and some results on this topic have already been obtained. The work started there is further generalized in [83]. Based on these two contributions, we are able to formulate a lemma defining the stability condition in our case. Before this, however, we give a short overview of the previous work on stability, in the domain of stochastic network optimization. Stability conditions according to Tassiulas & Ephremides Proposition 1. Consider w wavelengths {Λ i,i = 1,..,w}. There is a FIFO queue in front of each wavelength. Assume that n queues are served by a single server that can send at most a single packet per time slot. Let µ i be the probability that wavelength Λ i is available for transmission in a given slot, and let λ i be the arrival rate for queue i. The existence of a scheduling policy for which all queues are stable implies the following set of conditions: (1 µ i ) for all Q {1,2,..,w} (4.23) i Q λ i < 1 i Q Proof. Actually, this is a direct application of the principal result in [84]. An intuitive argument can also be considered: for each subset Q, the left hand term in the inequality is the traffic that has to be carried on Q, and the right hand term is the probability that at least one wavelength in Q is free for transmission in a given slot. If all queues in Q are stable, the probability that a slot can be used for transmission of a packet from these queues is larger than the left hand side of the inequality (the classical λ < µ condition for a single server queue). Furthermore, the probability that a slot can be used for transmission of a packet from these queues is smaller than or equal to the right hand side of the inequality which completes the proof. Next, with a simple example, we will show that the stability condition from [84] is not too strict. For instance, if the number of queues is 3, the stability condition says that the following

118 80 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING inequalities must be satisfied: λ 1 < µ 1,λ 2 < µ 2,λ 3 < µ 3, (4.24) λ 1 +λ 2 < 1 (1 µ 1 )(1 µ 2 ),λ 1 +λ 3 < 1 (1 µ 1 )(1 µ 3 ),λ 3 +λ 2 < 1 (1 µ 3 )(1 µ 2 ), (4.25) λ 1 + λ 2 + λ 3 < 1 (1 µ 1 )(1 µ 2 )(1 µ 3 ). (4.26) We prove that (4.25) is not redundant in this set, i.e. that the conditions (4.24) and (4.26) are not sufficient for stability. Proof. Let us suppose that (4.24) and (4.26) are sufficient for the stability of the system, i.e. that the system remains stable for every vector (λ 1,λ 2,λ 3,µ 1,µ 2,µ 3 ) that satisfies conditions (4.24) and (4.26). Let us take λ 3 = 0 and µ 3 = 1. In this case, the stability condition (4.24)-(4.26) is equivalent to: λ 1 < µ 1,λ 2 < µ 2, (4.27) λ 1 + λ 2 < 1. (4.28) On the other hand, we know that a system composed of 2 queues is stable iff: λ 1 < µ 1,λ 2 < µ 2, (4.29) λ 1 + λ 2 < 1 (1 µ 1 )(1 µ 2 ). (4.30) Obviously, for vector (λ 1,λ 2,λ 3,µ 1,µ 2,µ 3 ) = (0.4,0.4,0,0.5,0.5, 1), the condition (4.27)- (4.28) is satisfied, while the condition (4.29)-(4.30) is not satisfied. This lead us to contradiction, which ends the proof. Proposition 2. If Longest Queue First (LQF) or Largest Virtual Waiting Time First (LVWTF) is the scheduling policy, the set of conditions (4.23) implies the stability of the model. Proof. For LQF, the proposition is proven in [84]. Here we use the same approach to prove the proposition for LVWTF. In LVWTF, the selection of the queue is based on the value obtained by multiplication of the queue length with a constant (1/λ i ). In the proof from [84], the queue lengths X i (t) are sorted according to their value, by using a permutation of the queue indexes: i {0,1,...,N} e i {0,1,2,...,N}, such that X ei X ei 1. Thanks to this type of labeling, queue e i will be empty, only if all the queues e j, such that i j are empty as well. This property of LQF is used in obtaining the equation (3.13a) from [84] (page 470).

119 4.3. ADDRESSING STABILITY IN GENERAL CASE By proposing the permutation of the queue lengths X i (t) such that X ei X ei 1, λ ei λ ei 1 the labeling of queues has the same property as in the case of LQF policy, so the same proof from [84] can be used in proving that condition (4.23) is the sufficient stability condition for LVWTF. Thus, (4.23) is a necessary stability condition. For LQF and LVWTF, (4.23) is also a sufficient stability condition, but it is less obvious to show that (4.23) is a sufficient stability condition for all scheduling policies of interest (including Oldest Packet First, OPF).We wish to use the seminal paper by Stolyar regarding MaxWeight scheduling [83]. However, the stability conditions in [83] are not similar to (4.23). After briefly discussing the Stolyar stability conditions, we formulate a theorem which connects the stability conditions in [84] and [83]. Stability conditions according to Stolyar In his work [83], Stolyar defines the necessary and sufficient conditions for the stability of a generalized switch. It is easy to notice that ECOFRAME station inserting packets on the ring can be considered as an instance of a generalized switch. The notion of a Static Service Split (SSS) scheduler is introduced in [83]. In ECOFRAME, a scheduler selects the queue to be served in each time slot. A SSS selects the queue depending only on the availability of wavelengths in the slot, and independently of the state of the set of queues. Let {e 1,..,e m } be a partition of the states of the time slot, in terms of available wavelengths; actually, if the system presents n wavelengths, m = 2 n, and each state corresponds to a given subset of wavelengths that are available, while the other wavelengths are not available. Let π k be the probability of e k. A SSS rule is defined by a set φ m,k,0 φ m,k 1, k φ m,k 1 where φ m,k is the probability that the server attempts to serve file k when the time slot is in state m, and does not offer any service with probability (1 k φ m,k). The total service rate offered by the SSS to queue k is m φ m,kπ m. Proposition 1 in [83] states the following: Proposition 3. if there exists a SSS such that the system is stable, then for each k, λ k m φ m,k π m. (4.31) if there is a SSS such that for each k, λ k < m φ m,k π m, (4.32) then the system is stable for this SSS. As pointed out in [83], these conditions are intuitive, especially for ECOFRAME. Indeed, if we consider each queue k as a single server queue in isolation, λ k is its arrival rate and m φ m,kπ m its service rate. The above proposal is similar to the traditional λ < µ stability condition.

120 82 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING Another important contribution of Stolyar, concerns the throughput-optimality of the MaxWeight scheduling policy. Before formulating the Stolyar result, let us introduce the following notation: let Q i (t) be the size of the ith queue and W i (t) the delay of the first packet of the ith queue at time slot t let V i (t) = c Q i Q i(t)+c W i W i (t), where c Q i,cw i are fixed constants such that c Q i 0,c W i 0 and c Q i + c W i > 0 let MaxWeight be the scheduling discipline which always chooses a decision k maximizing γ k V k (t) β (β > 0, γ i > 0, i), that is Here, γ i and β are the fixed positive constants. k arg max i γ i V i (t) β. (4.33) The following proposition is one of the results from [83]. Proposition 4. Let an arbitrary set of positive constants β and γ i, i, be fixed. Then MaxWeight scheduling rule has the maximum stability region; namely, it makes the system stable as long as necessary and the sufficient stability condition (4.32) holds. Other related work Except in [84] and in [83], the problem of stability of queueing systems with interdependent scheduling has been studied in a number of papers. First results on MaxWeight scheduling appeared in [85], where Tassiulas & Ephremides presented a throughput optimal scheduling for multi-hop packet radio networks. In their subsequent paper [84], the same authors considered the stabilizing scheduling policy for wireless network with time-varying connectivity. Stolyar studied MaxWeight scheduling under heavy-traffic regime conditions in [83]. The same author, with his research group, analyzed the use of different variants of MaxWeight scheduling algorithms in different radio systems, in papers [78], [77] and [10], where these algorithms are shown to be the throughput optimal. MaxWeight scheduling was considered in a context of cross-layer control and resource allocation in wireless networks, in a paper by Georgidias, Neely and Tassiulas [41]. Furthermore, the MaxWeight policies were considered in [61], for the throughput optimal scheduling of input queued switches. It was shown that Longest QueueFirst (LQF) scheduling policy may lead to the starvation of the short queues. Necessary stability conditions were also considered in [75]. These stability conditions are sufficient for a special class of scheduling rules, named Projective Cone Scheduling (PCS) rules. However, MaxWeight scheduling remains more interesting for this study, as it encompasses a wider class of scheduling algorithms than PCS scheduling. In [70], the authors studied the limitations of MaxWeight scheduling policies, in conditions where the collection of active queues dynamically varies, with some sessions ending and some starting. However, such suppositions are outside the scope of the considered problem.

121 4.3. ADDRESSING STABILITY IN GENERAL CASE MaxWeight Scheduling in ECOFRAME The results on MaxWeight scheduling, found so far, have shown that MaxWeight scheduling is a wide family of algorithms, applicable in numerous scenarios. Some of them include different radio systems, input-queued cross-bar switches, and the discrete time version of a parallel server system. ECOFRAME is also a system for which the results obtained for MaxWeight scheduling can be applied. In the present section, we show that the scheduling policies that we would like to study (introduced in Section 4.3.1), belong to the MaxWeight class. Oldest Packet First Oldest Packet First (OPF) is obviously a MaxWeight scheduling discipline. Indeed, for β = 1, γ i = 1 and c Q i = 0 ( i), discipline (4.33) reduces to OPF: k arg max W i (t). (4.34) i Longest Queue First Longest Queue First (LQF) is also a MaxWeight scheduling discipline. Indeed, for β = 1, γ i = 1 and c W i = 0 ( i), discipline (4.33) reduces to LQF: k arg max i Q i (t). (4.35) Largest Virtual Waiting Time First Largest Virtual Waiting Time First (LVWTF) is a MaxWeight scheduling discipline. Indeed, for β = 1, γ i = 1/λ i and c W i = 0 ( i), discipline (4.33) reduces to LVWTF: k arg max i Please note that λ i are constants, i.e. these parameters are fixed. Q i (t) λ i. (4.36) As OPF, LQF and LVWTF are the MaxWeight policies,it means that they, like all other MaxWeight policies, stabilize the system, when it is in its stability region, as defined by the condition (4.32). Random queueing A random selection (RAND) scheduling discipline, which chooses a wavelength for transmission randomly, with uniform probability, among those eligible, is obviously not a MaxWeight rule. As c Q i + c W i > 0 and β > 0, packet selection depends on the size and/or age of packets in the queue. Thus it cannot be reduced to RAND rule. Let us observe a system with two queues/wavelengths, characterized with λ 1, λ 2, µ 1 and µ 2. We will show that RAND scheduling policy does not provide stability even if condition (4.23) is satisfied.

122 84 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING Condition (4.32) states: λ 1 < µ 1,λ 2 < µ 2, λ 1 + λ 2 < µ 1 + µ 2. (4.37) Let us note with P 1 the probability that the first queue will be served. Then, P 1 = µ 1 (1 µ 2 ) + µ 1 µ (4.38) Consequently, in stationary regime, for the stability of the first queue the relation: must be satisfied. λ 1 < P 1, It is easy to show that for µ 2 = 1 and µ 1 2 < λ 1 < µ 1, the condition (4.37) is satisfied, while previous condition is not satisfied, thus the system is unstable under RAND, even when the necessary stability condition holds. Priority queueing Priority queueing, i.e. a scheduling discipline in which one queue (wavelength) systematically has the priority, does not provide stability even if condition (4.23) is satisfied. It is shown in [84]. On the other hand, priority queueing is obviously not a MaxWeight scheduling policy (according to definition (4.33)), because there exists no combination of parameters that can be substituted in (4.33), which will reduce the general expression for MaxWeight scheduling to the priority scheduling rule Stability theorem We are looking for the design of the ECOFRAME ring that will be stable in the sense defined by the above propositions. As already mentioned, such a design shall be called the Packet Aware Design with Single packet insertion (PAD-S). Theorem. The necessary and sufficient condition for the stability of the queueing model in PAD-S design problem is: i Q λ i < 1 i Q (1 µ i ), Q {1,2,...,w}. (4.39) In other words, the above theorem states that the Tassiulas & Ephremides (4.39) and Stolyar (4.32) stability conditions are equivalent. The interest of having such a theorem is in the fact that the condition (4.39) gives a direct relation between λ i and µ i, and can be used, after the linearization, in the ILP formulation for the ECOFRAME ring design. Proof of the necessity of the stability condition (4.39) is a direct consequence of Proposition 1. Proof of the sufficiency of the condition (4.39) is more difficult to show. Basically it is sufficient to show that:

123 4.3. ADDRESSING STABILITY IN GENERAL CASE 85 λ i < 1 µ i ), Q {1,2,...,w} i Q i Q(1 ( (( ( i)( m)( φ mi [0,1]) (i {1,2,...,w}) (λ i < m π m φ mi ) ) )) w π m φ mi = 1. i=0 m (4.40) We have proven the last implication in cases of w = 2 and w = 3. The proof seems to be very cumbersome for greater system size. Proof in the case of w = 2 In this section, it is assumed that 4.23 is true, for w = 2, and an SSS is identified in that case such that for k {1,2}, λ k < m φ m,kπ m. According to the above Proposition 2, this proves that the system is stable under the selected SSS. It is convenient to partition the states according to the set of available bandwidths. This is shown in Figure Let π 0 denote the probability that none of the wavelengths are available in a given time slot, π i,i = 1,2 denote the probability that only wavelength Λ i is available, and π 12 denote the probability that both wavelengths are available. π 1 π 12 π 2 π 0 Figure 4.10 State Partitioning in the case n = 2 Clearly π 0 = (1 µ 1 )(1 µ 2 ) (4.41) π 1 = µ 1 (1 µ 2 ) (4.42) π 2 = µ 2 (1 µ 1 ) (4.43) π 12 = µ 1 µ 2 (4.44)

124 86 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING For w = 2, the set of conditions 4.23 reads as follows: λ 1 < µ 1 (4.45) λ 2 < µ 2 (4.46) λ 1 + λ 2 < µ 1 + µ 2 µ 1 µ 2 (4.47) It should be proved that, as long as the above conditions are true, the coefficients φ i,0 φ i,φ 1 + φ 2 1 such that can be found. λ 1 < π 1 + φ 1 π 12 (4.48) λ 2 < π 2 + φ 2 π 12 (4.49) Now, if φ i,0 φ i,φ 1 + φ 2 1 are identified, consider the SSS scheduling rule which behaves as follows: when only Λ i is available, the server selects queue i; when both wavelengths are available, the server tries to serve queue i with probability φ i, decides not to serve any file with probability 1 φ 1 φ 2 ; when no wavelength is available, no packet is served. Note that if the queue being selected by the SSS is empty, no packet is transmitted. Now we shall prove that conditions (4.45)-(4.47) imply (4.48) and (4.49). If (4.45)-(4.47) are satisfied for vector (λ 1,λ 2 ), then there exists a strictly positive ε (ε > 0), such that the inequalities (4.45)-(4.47) are satisfied for (λ 1,λ 2 ) = (λ 1 + ε,λ 2 + ε), as well. Note, that in the following we will prove that λ 1 and λ 2 can be represented in the form of λ 1 = π 1 + φ 1 π 12 and λ 2 = π 2 + φ 2 π 12, which will straightforwardly mean that conditions (4.48) and (4.49) are satisfied, i.e. that the theorem holds for w = 2. There are two cases of interest: 1. If λ 1 < π 1, then α > 0 exists, such that λ 1 = α π 1. Then there exist β and γ, (1 β,γ 0) such that λ 2 = βπ 2 + γπ 12. By taking φ 1 = 0 and φ 2 = γ, the theorem is obviously satisfied. A similar proof holds if λ 2 < π The remaining case is when λ 1 > π 1 and λ 2 > π 2. Then, there exist α and β, (1 > α,β 0,1 > α + β > 0), such that λ 1 = π 1 + απ 12 and λ 2 = π 2 + βπ 12. For φ 1 = α and φ 2 = β, the theorem obviously holds. The proof in case w = 3 can be found in Appendix B. In the following, we give an 0-1 ILP formulation which exploits the stability theorem.

125 4.4. PAD-S DESIGN FOR RINGS WITH S-RECEIVERS PAD-S design for rings with S-receivers The 0-1 ILP formulation is given for the general case of S-receivers. As always, S represents the number of wavelengths per receiver, and the given parameters and variables for the 0-1 ILP formulation, are as defined in Section 3.3. However, some new variables, which are specific to PAD-S design, are introduced. New Variables binary z j helps to linearize the problem. Objective Function Min i V Q Q C r rq i + C w y q (4.50) q=1 q=1 The objective function (4.50) minimizes the overall cost of the receivers and wavelengths required in the network. Constraints Q p k q = 1 k : T k T (4.51) q=1 p k q T k < S q, (i,j) E (4.52) k:(i,j) π k p k q T k rq d d V, q (4.53) k:d=dest(t k ) rq i N y q q (4.54) i V Constraint (4.51) ensures that one (and only one) waveband is assigned to each traffic demand. Constraint (4.52) ensures that the traffic rate on receiver q does not exceed the waveband capacity. Constraint (4.53) imposes the use of a receiver q at destination d. Constraint (4.54) decides whether waveband q is used or not. In order to complete the formulation, the following constraint should be included: q Q M,k:d=source(T k ) i.e. p k q T k < 1 q Q M k:d=transit(t k ) p k q T k, d,( Q M )(Q M Q Q M 2), p k q T k + p k q T k < 1, d,( Q M )(Q M Q Q M 2). q Q M,k:d=source(T k ) q Q M k:d=transit(t k ) (4.55)

126 88 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING The inequality (4.55) is the implementation of the condition (4.39) in the design. Note that it does not contain case Q M = 0 (empty set) nor case Q M = 1, as it is already included in (4.52). It guarantees the stability of the system. Unfortunately, this inequality is nonlinear. The inequality (4.55) can be rewritten as: j k:(q,k) Q j T k where sets Q j are defined with Q j Q M T and j k:(q,k) Q j T k (q,k) Q j p k q = (q,k) Q j p k q < 1, d,( Q M )(Q M Q Q M 2), (4.56) q Q M,k:d=source(T k ) p k q T k + q Q M k:d=transit(t k ) p k q T k, d and ( Q M )(Q M Q Q M 2). This is illustrated below, by a simple example. A well known way to linearize the inequality (4.56) [52], presented in Section 1.6, is to express it with the following set of constraints: ( j z j + k:(q,k) Q j T k ) z j < 1, d,( Q M )(Q M Q Q M 2), (4.57) (q,k) Q j p k q Q j 1, d, j,( Q M )(Q M Q Q M 2), (4.58) z j p k q 0, j, (q,k) Q j, d,( Q M )(Q M Q Q M 2). (4.59) Thus, the 0-1 ILP formulation for the case of ring design with single-wavelength receivers, including the PAD-S stability condition, is given by the expressions: (4.50)-(4.54) and (4.57)- (4.59) Proof of validity of constraints used Here we prove the validity of the constraints (4.57)-(4.59). When comparing (4.56) and (4.57)-(4.59), we can see that z j = (q,k) Q j p k q, j, d,( Q M)(Q M Q Q M 2). It means that constraints (4.56) and (4.57) are equivalent iff z j and (q,k) Q j p k q have the same values for j, d,( Q M )(Q M Q Q M 2). This is ensured by (4.58) and (4.59). It also means that binary z j should be zero if at least one of the variables p k q is equal to zero. This is achieved with the constraint (4.59). If all the variables p k q are different from zero, constraint (4.59) says that z j {0,1}, i.e. this constraint has no impact on the value of binary z j. Let us suppose that all the variables p k q are equal to 1. From (4.59) we have z j {0,1}, while constraint (4.58) reduces to:

127 4.4. PAD-S DESIGN FOR RINGS WITH S-RECEIVERS 89 z j ( Q j (q,k) Q j p k q ) 1. Q j is equal to the number of variables p k q. As all the variables p k q are equal to 1, it means that Q j = (q,k) Q j p k q, i.e. (4.58) further simplifies to: z j 1. The last inequality is satisfied iff z j = 1. Finally, let us suppose that one or more variables p k q z j = 0, while constraint (4.58) reduces to: have value 0. From (4.59) we have 0 + p k q Q j 1, (q,k) Q j which is obviously satisfied, as Q j > (q,k) Q j p k q when at least one variable p k q is set to 0. The previous analysis is exhaustive, thus it proves the validity of constraints (4.57)-(4.59). A simple illustration example In order to show that inequalities (4.55) and (4.56) are equivalent, in this example, we calculate the subsets Q j for case of a ring with 4 nodes (labeled with indexes l {1,2,3,4}) and 2 available wavebands {q 1,q 2 } and a traffic vector T ki where all the connections are different from zero and index i is calculated as i = (l source 1) 4 + l dest. In this situation, the inequality (4.55), for node 1, and set Q M = {q 1,q 2 }, is equivalent to: p k 2 q 1 T k2 + p k 3 q 1 T k3 + p k 4 q 1 T k4 + p k 2 q 2 T k2 + p k 3 q 2 T k3 + p k 4 q 2 T k4 + (p k 10 q 1 T k10 + p k 14 q 1 T k14 + p k 15 q 1 T k15 )(p k 10 q 2 T k10 + p k 14 q 2 T k14 + p k 15 q 2 T k15 ) < 1, p k 2 q 1 T k2 + p k 3 q 1 T k3 + p k 4 q 1 T k4 + p k 2 q 2 T k2 + p k 3 q 2 T k3 + p k 4 q 2 T k4 + p k 10 q 1 T k10 p k 10 q 2 T k10 + p k 10 q 1 T k10 p k 14 q 2 T k14 + p k 10 q 1 T k10 p k 15 q 2 T k15 + p k 14 q 1 T k14 p k 10 q 2 T k10 + p k 14 q 1 T k14 p k 14 q 2 T k14 + p k 14 q 1 T k14 p k 15 q 2 T k15 + p k 15 q 1 T k15 p k 10 q 2 T k10 + p k 15 q 1 T k15 p k 14 q 2 T k14 + p k 15 q 1 T k15 p k 15 q 2 T k15 < 1. (4.60) Let us note that this is equivalent to: where 15 T ki j=1 k i :(q i,k i ) Q j p ki q i < 1, (4.61) (q i,k i ) Q j Q 1 = {(q 1,k 2 )},Q 2 = {(q 1,k 3 )},Q 3 = {(q 1,k 4 )},Q 4 = {(q 2,k 2 )},

128 90 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING Q 5 = {(q 2,k 3 )},Q 6 = {(q 2,k 4 )},Q 7 = {(q 1,k 10 ),(q 2,k 10 )}, Q 8 = {(q 1,k 10 ),(q 2,k 14 )},Q 9 = {(q 1,k 10 ),(q 2,k 15 )}, Q 10 = {(q 1,k 14 ),(q 2,k 10 )},Q 11 = {(q 1,k 14 ),(q 2,k 14 )}, Q 12 = {(q 1,k 14 ),(q 2,k 15 )},Q 13 = {(q 1,k 15 ),(q 2,k 10 )}, Q 14 = {(q 1,k 15 ),(q 2,k 14 )},Q 15 = {(q 1,k 15 ),(q 2,k 15 )}. As the inequality (4.61) is equivalent to (4.56), the inequalities (4.55) and (4.56) are equivalent, which we wanted to show Comparison of PAD-M and PAD-S designs We have implemented the previous 0-1 ILP formulation (for PAD-S design) in lp solve. The obtained ILP formulation is valuable for all input traffic matrices, and wavelength-to-receiver cost ratios. Here, for the illustration, we present the optimal results of the PAD-S design of an ECOFRAME ring, versus the offered load per source-destination pair, for a symmetric and uniform input traffic (any-to-any traffic matrix), in two cases: 1. case N = 5 (5-station ring) and S = 1 is presented in Fig. 4.11; 2. case N = 6 and S = 1 is presented in Fig Design Cost PAD S, design cost PAD S, number of receivers PAD S, number of wavelengths PAD M, design cost PAD M, number of receivers PAD M, number of wavelengths Offered Load Figure 4.11 Five node ring: design cost vs. traffic rate for C w = 1 and C r = 1, PAD-M (γ = 0.9) vs PAD-S comparison In Figs and 4.12, the results of design PAD-S are compared with the results of design obtained when using the PAD-M design method for γ = 0.9. The offered load (amplitude of any-to-any traffic) is normalized to the single wavelength capacity. As expected, in Figs and 4.12, we can see that the overall cost of the ring increases with the amount of traffic that needs to be carried.

129 4.5. CONCLUSION Design Cost PAD S, design cost PAD S, number of receivers PAD S, number of wavelengths PAD M, design cost PAD M, number of receivers PAD M, number of wavelengths Offered Load Figure 4.12 Six node ring: design cost vs. traffic rate for C w = 1 and C r = 1, PAD-M (γ = 0.9) vs PAD-S comparison From Figs and 4.12, we can also notice that PAD-M design is slightly more expensive than PAD-S design, for γ = 0.9. This is expected, because the maximum amount of traffic that can be inserted on a wavelength is limited by γ, in case of PAD-M design. Theoretically, for γ 1, the maximum amount of traffic that can be supported by a single wavelength is the same in PAD-M and PAD-S designs. Note that PAD-S design guarantees the stability for uniform and symmetric traffic of any amplitude, while the PAD-M design does not necessarily provide stability for all values of offered load. PAD-M design offers stability to stations which send their traffic by using no more than a single receiver (in this case, wavelength). Thus, in the case analyzed in Figs and 4.12, the PAD-M offers a stable design for the small values of offered load. 4.5 Conclusion The granularity of packet switching places the optical WDM ring design problem in a new context, which is identified in this work. Namely, it was found that the problem of dimensioning of the optical packet switched ring cannot be identified with the problem of finding the optimal configuration of an optical circuit switched network. When dimensioning an OCS network, the absolute occupancy of all the wavelengths is possible. On the contrary, this is not possible when designing a network in which traffic has a packet, i.e. a nondeterministic nature. An absolute occupancy of the links in this case would have resulted in instability of the system, i.e. of the queues containing the optical packets waiting to access the network. Therefore, it is necessary to introduce an additional constraint, which will take into account the problem mentioned. In this Chapter the necessary condition is formulated and its validity is proven mathematically.

130 92 CHAPTER 4. PACKET-AWARE DESIGN OF OPTICAL PACKET RING When addressing this problem, the process of insertion and extraction of optical packets has been taken into account. In this Chapter, the problem of stability of the design is tackled by taking two different approaches. In the first case, namely, in the case of packet aware design with multiple packet insertion (PAD-M), the station queues are observed independently, i.e. it is supposed that a station can send more than a single packet per time slot. In this case, the stability constraint actually provide the guarantees of the QoS performance of the traffic that is transported in the network. In the second case (packet aware design with single packet insertion, PAD-S design), the queues are observed jointly, and the stability condition is identified starting from the station configuration and the parameters describing the arrivals of the packets and service rates at the different wavelengths/wavebands. The introduction of the new constraint in the ILP formulation results in a more expensive design. However, one should not forget the fact that a traffic matrix is calculated differently when designing an optical packet switched network and an optical circuit switched network. In the second case, the network is dimensioned for a traffic matrix which assumes that the peaks of traffic are reached simultaneously across the entire network, which is not necessarily the case in a metro network (for example, business customers and home users could have peaks of traffic at different times). In other words, increased granularity of switching, which is a feature of an ECOFRAME OPS ring, allows more precise definition of the traffic demand matrix and thus saves the network resources. The PAD-M design is limited to the cases where a station does not send on more than 1 wavelength/waveband. The PAD-S design is applicable in all cases of interest. To summarize, the main results obtained in this Chapter are: The necessary and sufficient conditions for the stability of the ECOFRAME ring are identified and formulated. It is shown that absolute priority is not a MaxWeight scheduling policy. When trying to express the stable ECOFRAME ring design in the form of a LP formulation, the problem of taking into account the non-linear constraints appears. This problem is resolved, and the resulting LP design formulations are given in Sections and 4.4. The LP formulation for a stable, All-Wavelengths-Shared design is found (Section 4.2.4). In the following Chapter, it is supposed that the problem of ECOFRAME ring design is already resolved, and with such an assumption, the performances of the ring are studied and a scheduling policy comparison is performed.

131 CHAPTER5 Performance analysis In this Chapter the ECOFRAME ring was studied by means of queueing theory models and by computer simulation. Quality of service (QoS) performances of the ECOFRAME network are analyzed as the single-wavelength ring and the multi-wavelength ring. Special attention has been paid to understanding the impact of peer-to-peer service architecture on the other service architectures in the ring and to the choice of the efficient, low-complexity scheduling algorithm for ECOFRAME rings.

132 94 CHAPTER 5. PERFORMANCE ANALYSIS 5.1 Introduction The main goals of the ECOFRAME ring analysis, that is conducted in this work, is to find: 1. a stable configuration of the network 2. an appropriate scheduling algorithm, to control the process of insertion of the packets into the optical medium. The first objective is assessed in Chapters 3 and 4. In Chapter 4, the conditions that lead to the stable design (configuration) of the ring, are identified. In the current Chapter, it is supposed that the problem of finding a stable ECOFRAME ring configuration has been solved. In Chapter 3, it is shown that the splitting of traffic flows, among different receivers, leads to a complex scheduling. To avoid this, in the current Chapter, it is supposed that the splitting of traffic flows among different receivers of the same destination is forbidden. The second objective is studied in the present Chapter, while taking into account the above and some other assumptions. The complete list of the assumptions taken in the present Chapter is the following: the ring has a stable design, all the traffic entering into the ring is compatible with the ring configuration, different classes of service (CoS) of optical packets (PDU units) are not considered, best-effort traffic (BE) is not considered, splitting of traffic among different receivers is forbidden (result of Chapter 3), there is no packet loss in our study (because ECOFRAME is a transport network, and it is configured for the guaranteed traffic only), client traffic segmentation process and PDU unit creation process is not considered (this problem is studied by Eido, Nguyen and Atmaca in [36] and [66]), the time slot use is opportunistic, ie. every time slot that is free, can be used for the transmission. The reservation mechanisms are not considered in this work (the slot reservation problem is studied in [17] and [20]). In order to facilitate the analysis, two cases are studied separately: single-wavelength ring and multi-wavelength (WDM) ring. In both cases, first the queueing and simulation models are developed, and their results are compared. QoS indicators that are usually used are packet delay and jitter. In the context of the single-wavelength ring, the problems of impact of different routing strategies on the ring capacity are assessed. In multi-wavelength rings, two main issues are addressed:

133 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING the positive impact of the WDM receivers on the QoS of PDU units, 2. the problem of scheduling in the ECOFRAME ring, in the ring design context (for instance, splitting or no-splitting of traffic flows is a design decision with a significant impact on the scheduling rule complexity). Some of the results from this Chapter were published in [90], [89] and [26]. 5.2 Performance Analysis of the Single-Wavelength Ring In the present section we concentrated on the analysis of performance of ECOFRAME ring with one wavelength. The main problem that we discussed is how different traffic profiles, which exist in the metro ring, with reference to the position of the router in the ring, determine, ie. impact the overall traffic capacity that can be transmitted in the ring. Traditionally, the traffic profile in the metropolitan ring network is of aggregation+distribution type, that is client-server type. This means that all traffic passes through a single station, called HUB, which serves to connect the network to other metro networks and backbone network. In contrast to this profile traffic, in ECOFRAME network it is possible to route the traffic at all network stations, ie. the so-called peer-to-peer (P2P) traffic profile might exist. This is made possible by the existence of the addressing, at the level of ECOFRAME Protocol. In the present section, we have compared the traditional versus P2P traffic profiles in metropolitan ring network. P2P traffic profile allows the spatial reuse phenomenon, thus it can be expected expect that the overall capacity of P2P networks, will be improved, in comparison to the client-server architecture. This improvement is quantified below Modeling of the system by using Queuing theory When modeling the described optical packet ring network, with an access to the medium occurring at discrete time instants, the discrete nature of the system must be taken into account. The Bernoulli process is often used for modeling the arrival process ([34], [47]), or for modeling the behavior of the medium (channel traffic, [24]) in discrete time systems. Some optical systems and components analyzed by this simple stochastic process are multi-channel optical slotted rings [24] and synchronous optical packet switches [86]. We thus approximate the arrival process of packets in each station by a Bernoulli process, assuming that during each time slot, 1 packet at most arrives to be transmitted on the ring by the station with probability λ, independently of what happens in the other time slots. It may be argued that this approximation is unrealistic. However, the ECOFRAME network is a MAN, which means that each station multiplexes a large number of independent flows. Under this assumption, it has been shown that the traffic tends to behave as a memoryless process [21] which justifies our hypothesis. The number of time slots I elapsing between two consequent arrivals of the packets in the queue is geometrically distributed on the set of positive integers [45], i.e.

134 96 CHAPTER 5. PERFORMANCE ANALYSIS λ Geo/Geo/1 Queueing System µ Time Slots Figure 5.1 Queueing Process Modeling P(I = k) = λ(1 λ) k 1, for k 1. (5.1) As already mentioned, a packet can be sent by a station only if the time slot is not already occupied by a packet. In order to derive a queueing model of the system, we model time slot occupancy by another Bernoulli process, i.e. the queuing process at a given station (Fig. 5.1) is modeled by a Geo/Geo/1 model. We assume an AF (Arrival First) policy. This is the major approximation of our model: indeed, even if all input traffics are Bernoulli, the resulting occupancy on the ring is not necessarily Bernoulli. We assess the validity of this approximation in later sections. In Fig. 5.1, λ is the probability of an arrival in the queue, during a time slot, while µ is the probability that the next slot is empty. In the following, we explain how λ and µ can be related to the different traffic profiles generated by P2P or CS applications. In the remainder of this section we shall assess the performance of the system by analyzing the waiting time in each station. The Geo/Geo/1 queue is a well known model [50]. We report here the main results that are used in the paper. The mean waiting time for a Geo/Geo/1 queue is given by: where α = λ(1 µ) µ(1 λ) and θ is the slot duration. The waiting time distribution tail is given by: E[W] = θ α λ (1 α), (5.2) P(W Kθ) = 1 γ K. (5.3)

135 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING 97 where γ = 1 µ. Here, Kθ is a threshold, where K is a number of slots. 1 λ Furthermore, the maximum arrival probability for which the probability of the waiting time being greater than a given threshold Kθ is smaller than a given ε is obtained by solving the following inequality: P(W > Kθ) < ε, i.e. λ < 1 1 µ K ε. (5.4) Simulation model of ECOFRAME single wavelength ring We simulate a single data channel optical packet ring by developing a new MAC for ns-2. The ring topology, the slotted medium and the synchronous access to the medium are simulated. We simulate the slotted medium, the synchronous access to the medium and the other functionalities of the system s second layer, by developing a new MAC layer and adding it to the existing ns-2 functions (detailed explanation of the simulator is given in the Appendix A of this document). The new MAC layer is written in C++ and is added to the current ns-2 package, ns-2.31 (Fig. 5.2). Node entry Agent uptarget_ Link Layer arptable_ ARP mac_ downtarget_ MAC uptarget_ uptarget_ New MAC layer added to ns-2.31 PHY downtarget_ Channel uptarget_ Figure 5.2 The new MAC layer added to NS The new MAC layer is actually a C++ class derived from Mac base class in ns-2. Each instance of the new MAC layer, belonging to some station in the network, is an object of this new C++ class. The work of the stations in the network is synchronized, as the access to the medium is on a periodical basis. The main attribute of the class is a static array keeping track of the slots currently used in the network. This attribute provides the synchronous behavior of the stations in the ring.

136 98 CHAPTER 5. PERFORMANCE ANALYSIS Flow 3, VBR Flow 2, VBR Flow 1, CBR Figure 5.3 A simulation scenario comparing single class with multiclass transport The main method of the class is a timer procedure, defining the actions performed by a station, on a regular basis. This procedure also contains the scheduling algorithm, providing different treatment of packets of different priority classes. Lastly, a ring architecture should be implemented. ns-2 is suitable for simulating local area networks (LAN) with an appropriate MAC layer, but the LAN technology offered is usually a bus (for the simulation of wired networks). We need the stations to be connected within a unidirectional ring, and to use the new MAC layer. An excellent example of how a ring architecture can be implemented in ns-2 is given in [3]. Our ring architecture is created in a similar manner. The new classes and procedures enabling ring architecture are written in OTcl language. Thus, our major contribution in enhancing the current version of ns-2 is the creation of a new MAC layer supporting the use of the medium on a discrete time basis, while adapting a previously developed ring architecture. A simple example is now given to illustrate the behavior of the MAC when two classes of traffic are supported by the ECOFRAME MAC. A simulation example We simulate a network composed of six stations, shown in Fig The ring is supposed to be composed of unidirectional links, with node numbers increasing in the transmission direction. The traffic flows used in the simulation scenario are presented in Fig. 5.3 as Flow 1, Flow 2 and Flow 3. Flows 2 and 3 are Variable Bit Rate (VBR), while Flow 1 is Constant Bit Rate (CBR). In the simulation, the VBR traffic is generated according to an Exponential On/Off distribution. The CBR traffic is generated according to a deterministic rate, with constant size packets. In both cases, the transport protocol is UDP.

137 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING x Flow 1 jitter [µs] Flow 3 traffic load [%] Figure 5.4 Jitter values for Flow 1 versus Flow 3 traffic load (single traffic class) Flow 1 and Flow 2 both have a mean rate equal to 25% of the link capacity. Station 2 has to insert Flow 1 on the link between stations 2 and 3 which already carries Flows 2 and 3. We perform 2 sets of simulations. In the first scenario, all flows have the same priority; in the second scenario, Flow 3 has a lower priority level than Flows 1 and 2. We measure the jitter experienced by Flow 1 in the first scenario (Fig. 5.4) and the loss experienced by Flow 3 in the second scenario (Fig. 5.5), versus the amount of Flow 3 load. In our experiment, jitter is defined as the difference between a lower (0.01) quantile and an upper (0.99) quantile of the delay distribution. Buffer size in each station is sufficient so that the only losses are due to the preemption of best-effort traffic by high priority traffic. The results in Figs. 5.4 and 5.5 are given without the confidence intervals, which explains the mild irregularities of the curves. Fig. 5.4 shows that in the first scenario, the jitter performance for Flow 1 is degraded since slots occupied by Flow 3 packets can not be preempted. We do not show the jitter for the second scenario since it is negligible. Figure 5.5 shows that the loss performance for Flow 3 is quite high. Indeed this loss performance seems to be almost independent of the load offered by Flow 3. This is because the preemption level relates to the load offered by Flow 1 (a priority flow) and not to the load offered by Flow 3 (a best-effort flow) ECOFRAME Routing Service Architectures We assume here that the ECOFRAME network is used as Metro-Access (Metro-Edge) network; in other words, Access Nodes are accessing the Metro network through stations on the ECOFRAME network, which is then linked either directly to the backbone network, or more probably to a Metro-Core network which aggregates several Metro-Access networks. The ECOFRAME optical ring is shown in shown in Fig Station S is the single station connecting (ultimately) the ring with a backbone and the other (S 1) stations are used by access nodes. Although our model can deal with heterogeneous access nodes, we assume

138 100 CHAPTER 5. PERFORMANCE ANALYSIS Flow 3 traffic loss at station 2 [%] Flow 3 traffic load [%] Figure 5.5 Flow 3 traffic loss at station 2 (two traffic classes) Neighboring Network A D a d a d 1 S S-1 a d... Traffic Direction... a d i d a Figure 5.6 ECOFRAME optical ring here, for the sake of simplicity, that all access nodes have identical traffic profile, i.e. send and receive the same amounts of traffic. In Fig. 5.6, a and A are respectively the probabilities of a packet arrival in the queue at an access node i (i < S) and at node S. Similarly, d and D are respectively the probabilities that a packet will exit the network at stations i (i < S) and S. In the present section we consider different service architectures, that is, traffic profiles, in connection with a possible position of the routers in the ECOFRAME ring. Basically, two

139 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING 101 different traffic types can appear in a MAN: 1. Client-Server (CS), which supposes the existence of a single router in the ring and 2. peer-to-peer (P2P) traffic, which supposes that routers can exist at each ring node. When applications use the traditional CS scheme, each user requests the downloading of (large) files from a distant server. This corresponds to the server generating more downstream traffic than the client generating upstream traffic, and translates as a < d in Fig Globally, it also corresponds to A > D since A is the sum of all downstream traffic sent to all access nodes and D is the sum of all upstream traffic generated by the access nodes on the ring. On the other hand, P2P applications usually try to reach a good equilibrium between upstream and downstream traffics, as this fairly shares the burden of running the application between community members. Consequently, we model the traffic profiles in the P2P case, as a = d and consequently, A = D. Clearly, λ is obtained as a or A depending on the station. On the other hand, µ is less easily derived. In the following section, we derive µ for each station (access/gateway to backbone) from the traffic parameters a, d, A, D under various assumptions. Actually, we compute p = 1 µ, which is the probability that a given slot cannot be used for transmission by a station. Computing the Slot Occupancy Probability For the sake of simplicity, we discuss separately client and server case of the CS traffic type. Let p i denote the probability that a time slot cannot be used by node i (i.e. it carries a packet that is not received by i). Server traffic Server traffic is observed when one of the stations in the network acts as a server sending traffic to all the other stations on the ring. This corresponds e.g. to a server located in station S, or to station S linking the ring to the backbone, with all downstream traffic for the access nodes transiting by S. Here, a = D = 0 since there is no upstream traffic. Under the assumption that all access stations receive the same amount of downstream traffic, A = (S 1)d is the amount of downstream traffic entering the ring at station S. Parameter p i in the Server traffic case is given by: p i = S 1 i (S 1)d = (S 1 i)d. (5.5) S 1 The maximum value for p i, called p max i is achieved for the station with index i = 1: p max i = p 1 = (S 2)d. (5.6)

140 102 CHAPTER 5. PERFORMANCE ANALYSIS Table 5.1 The probability p i for the SERVER, CLIENT and PEER-TO-PEER traffic type Fig. 5.6 parameters: (a,d,a,d) p i (i = 1,2,...,S 1) Server (0,d,(S 1)d,0) (S 1 i)d Client (a,0,0,(s 1)a) (i 1)a P2P (a,a,(s 1)xa,(S 1)xa) (S 3)(1 x) (S 2)xa + a 2 Client traffic Client traffic corresponds to the network playing the role of an aggregation network that transmits all upstream traffic towards the backbone. Obviously d = A = 0 and D = (S 1)a in Fig Parameter p i in the Client traffic case is given by: The maximum for p i is achieved for station (S 1): p i = (i 1)a. (5.7) p max i = p S 1 = (S 2)a. (5.8) Peer-to-peer traffic In the peer-to-peer traffic case, we assume that a = d and is constant for each access station. P2P applications are run by user communities whose members are not necessarily geographically close. We shall model this distance by a new parameter x : for each station i (i S), xa denotes the packet arrival probability for the access station s traffic which leaves the network at station S, i.e. x (such that 0 x 1) is the proportion of the P2P traffic that is exchanged with remote stations that are not attached to this particular ring. On the other hand, (1 x)a denotes the packet arrival probability for the access station s traffic which leaves the network at station j, j i (1 i,j S 1). We assume that the destination 1 station j is selected with the same probability for every j. S 2 The overall traffic leaving the network at station S is thus (S 1)xa. The overall traffic entering in the network at station S, has the same volume (S 1)xa, as each community member sends as much traffic as it receives. Thus, the peer-to-peer traffic model is presented in Fig. 5.6 for a 0, d = a, A = (S 1)xa and D = (S 1)xa. Parameter p i in the P2P traffic case is obtained as : p i = p local + p dist, (5.9) where p local corresponds to the part of the P2P traffic exchanged between the access stations on the ring and p dist corresponds to the part of the P2P traffic exchanged with the remote stations.

141 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING 103 p local is obviously independent of i and is given by: [ S 3 p local = (1 x)a S 2 + S 4 S ], (5.10) S 2 i.e. p local = (1 x)a(s 3). (5.11) 2 p dist is the sum of the probability that traffic generated by a remote node occupies the slot ((S 1 i)xa) and of the probability that traffic generated by a local node for a remote node transits through station i ((i 1)xa). Both terms depend explicitly on i, but their sum does not : p dist = (S 1 i)xa + (i 1)xa = (S 2)xa. (5.12) Finally, p i is given by: p i = (S 2)xa + (1 x)a(s 3). (5.13) 2 We shall explicitly investigate two P2P traffic scenarios: the P2P local scenario (x close to 0) and the P2P distant scenario (x close to 1). In the first case, the main part of the P2P traffic is exchanged between the stations of the local network. In the second case, the main part of the P2P traffic is exchanged with remote stations. The analysis assumptions and results for the server, client and peer-to-peer traffic types are shown in Tab CS traffic The client-server traffic models the traffic generated by CS applications. It is the combination of the client and server cases. In Fig. 5.6, this case is presented for a 0, d 0, A = (S 1)d and D = (S 1)a. In order to assess different situations, we introduce a new variable y linking a to d : d = ay, where y 1, which means that each station receives y times more traffic than it sends to the server. In other words, y measures the relative volume of server traffic versus client traffic. In the CS case, p i is given by : p i = (S 1 i)ay + (i 1)a. (5.14) Since downstream traffic is larger than upstream traffic, the maximum value for p i is achieved for the station with index i = 1: p max i = p 1 = (S 2)ay. (5.15)

142 104 CHAPTER 5. PERFORMANCE ANALYSIS General case The general case, under the assumption of identical loads in each access station, is a combination of the above client-server and peer-to-peer traffic profiles. In order to assess the impact of the mix of these 2 traffics, we introduce a last variable z (0 z 1), which is the proportion of P2P traffic to be transmitted by each access station ; the amount of P2P traffic transmitted by each access station is a P2P = az. Then, (1 x)a P2P and xa P2P (0 x 1) are respectively the P2P local and the P2P distant traffics to be transmitted by each access station. The client traffic transmitted by access station i is a a P2P, and the server traffic received by access station i is d a P2P = y(a a P2P ). We obtain A = (S 1)y(a a P2P ) + (S 1)xa P2P, (5.16) D = (S 1)(a a P2P ) + (S 1)xa P2P. (5.17) p i is composed of two parts corresponding respectively to client-server and peer-to-peer traffic: p i = p CS + p P2P. (5.18) where p CS = (S 1 i)y(1 z)a + (i 1)(1 z)a, (5.19) p P2P = (S 2)xza + (1 x)(s 3) za. (5.20) 2 The maximum value for p i is achieved for the station with index i = 1: p max i = p 1 = (S 2)y(1 z) + (S 2)xz + (1 x)(s 3) z. (5.21) Validation of the analytical and simulation models We now compare results obtained with the Geo/Geo/1 model to the performance indicators obtained using the simulation platform described previously. Let us consider a six nodes network. The buffer size in each station is set to 2000 packets (40Mbits). We assume that the time slot duration is 2µsec. We shall assess the accuracy of the model in the two cases, P2P and CS traffics.

143 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING 105 CS traffic with Bernoulli arrivals We simulate Bernoulli arrival processes, both at the access stations and at station S = 6. The mean queueing time for the packets at station i, E i [W], can be obtained from eq. 5.2, by substituting λ and µ with a and 1 p i, respectively, and by subsequent multiplication of the obtained expression with the time slot duration θ. In the CS traffic case, p i depends on a as defined by the eq. 5.14, so E i [W] can be expressed as a function of a. Figure 5.7 (a) shows E[W] versus a for station 2, computed either by simulation or using the analytical model. We do not show the results for station 1 since the analytical model exactly represents the system at this station, which is not true for station 2. We now define W max as the quantile such that P(W > W max ) < ε. (5.22) In the Geo/Geo/1 queue, using the eq. 5.4, we see that W max is given by W max i log ε = θ p i. (5.23) log 1 a W max obtained by simulation and by the Geo/Geo/1 model are compared in Fig. 5.7 (b) for ε = Figure 5.7 show that the Geo/Geo/1 queue provides a good approximation of the system behavior under CS traffic. Actually, the case under study (y = 2) is pessimistic since it allows a large amount of client traffic whereas a more realistic case (y = 20, not shown here due to lack of space) presents an even better approximation. P2P traffic with Bernoulli arrivals We now address the P2P case in Fig. 5.8, comparing E[W] and W max obtained by simulation and using the Geo/Geo/1 model. The results are given for stations 1 and 5. Note that in P2P case for the Geo/Geo/1 model, E[W], as well as W max are identical for all network stations, as p i in 5.23 does not depend on i (p i is defined by the eq. 5.13). We can see in Fig. 5.8 that the Geo/Geo/1 model is still quite valid, but is more accurate for station 5 than for station Impact of P2P traffic on single-wavelength ring performance In all the following examples we consider the network shown in Fig. 5.6, where station S is the gateway to the backbone network. The link capacity in the network is supposed to be 10Gbit/s.

144 106 CHAPTER 5. PERFORMANCE ANALYSIS 8 7 Geo/Geo/1 simulation 6 E 2 [W] [µs] a (a) E[W] versus offered load Geo/Geo/1 simulation 30 W 2 max [µs] a (b) W max versus offered load Figure 5.7 CS model and simulation results for station 2 (N = 6, y = 2, ε = 0.01) Limiting conditions for a In this subsection, we use the Geo/Geo/1 model and compute limiting conditions for a in the client-server, peer-to-peer and general case, where p depends on network traffic profile. A first upper bound for a derives from the fact that slot occupancy probability on each link is always limited by 1. Another limit, derived using the Geo/Geo/1 model, is obtained from eq. 5.4, for λ = a and

145 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING all stations, Geo/Geo/1 station 5, simulation station 1, simulation 80 E[W] [µs] a (a) E[W] versus offered load all stations, Geo/Geo/1 station 5, simulation station 1, simulation 350 W max [µs] a (b) W max versus offered load Figure 5.8 P2P model and simulation results for stations 1 and 5 (N = 6, x = 0.1, ε = 0.01) µ = 1 p, where a and p are linked as shown in Section V: a < 1 p K ε. (5.24)

146 108 CHAPTER 5. PERFORMANCE ANALYSIS Maximum throughput for CS traffic By using the expressions 5.24 and 5.15, we obtain a limiting condition for a: a < ( 1 + ) (S 2)y 1. (5.25) K ε In order to avoid the congestion of the link between the station S and the station 1, the value for a should also be such that: a < Finally, the limiting condition for a in the CS case is obtained as : where F 1 = (S 2)y, while F 2 = (S 1)y. 1 (S 1)y. (5.26) ( ( a < min 1 + F ) ) 1 1,F 1 K 2. (5.27) ε Maximum throughput for P2P traffic By using the equations 5.24 and 5.13, we find the limiting condition for a in this case: a < [ ( 1 + (S 2)x + ) ] (S 3)(1 x) 1 ( K ε) 1. (5.28) 2 It can be proved that this result includes the limit for a due to finite link capacity constraints. Maximum throughput in the general case It can be shown that the limiting condition for a is given by the expression: ( ( a < min 1 + F ) ) 1 3,F 1 K 4, (5.29) ε where F 3 = (S 2)zx+z(1 x)(s 3)/2+(S 2)y(1 z), F 4 = (S 1)y(1 z)+z(s 1)(1+x)/2 and z = a P2P /a. Note that the condition a < F 1 4 corresponds to the finite link capacities. Impact of P2P traffic on CS traffic Figure 5.9 shows the maximum amount of server traffic (d a P2P ) max and the maximum amount of traffic d max received by an access node versus z, proportion of P2P traffic generated by this access node. The two curves correspond to the cases: P2P local and P2P distant. The value for (d a P2P ) max is obtained as d a P2P where a takes the maximum value allowed by condition Similarly, d max is obtained as the value for d taken when a takes the maximum value allowed by condition 5.29.

147 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING peer to peer local, x=0.1 peer to peer distant, x= (d a P2P ) max [Gbit/s] z (a) (d a P2P) max vs. z peer to peer local, x=0.1 peer to peer distant, x= d max [Gbit/s] z (b) d max vs. z Figure 5.9 Maximum allowed value for d a P2P and d in general case versus z = a P2P/a (S = 7, y = 5, K = 1000, ε = 10 6 ) Clearly, a network dimensioned for pure CS traffic will behave differently when P2P traffic is sent by the users. First, as seen in Fig. 5.9 (a), the amount of server traffic that can be received significantly decreases when P2P traffic increases, and even more in the case of distant P2P traffic. Considering now Fig. 5.9 (b), we see that when P2P traffic increases, the global amount of received traffic (and accordingly the global amount of downstream traffic for the access network) also increases. However, this increase is significant when most of the traffic is local P2P.

148 110 CHAPTER 5. PERFORMANCE ANALYSIS (S 1)d [Gbit/sec] peer to peer local, x=0.1 peer to peer distant, x=0.9 client server S Figure 5.10 Traffic received by the stations (S 1)d versus S in P2P and CS cases, for maximum value of a (K = 1000, ε = 10 6 ) P2P vs CS service architectures In the present section we assess the impact of the service architecture on the throughput of the Metro Network. As pointed out previously, CS architectures assume that powerful servers deliver high volumes of data to users who generate small amounts of traffic; on the other hand, P2P architectures assume that information is collectively stored into users machines, which leads to symmetrical upstream and downstream traffic volumes. Fig compares the maximum amount of traffic that can be received by the access nodes in the network, (S 1)d, versus the number of nodes in the network, for P2P and CS traffic. The value of a is the maximum value derived in the previous section. Note that value of variable y characterizing CS traffic is not pointed out in Fig. 5.10, as the maximum amount of received traffic does not depend on y. A first remark to make regarding Fig is that the maximum amount of traffic received by the set of access stations on the ring is almost independent from the number of stations on the ring. This result is obvious in the case of CS traffic since in that case, the first link is the bottleneck. It is less obvious for P2P traffic, but can be explained by the fact that we assume balanced traffic matrices. A more surprising fact observed in Fig. 5.10, is that the maximum of the overall received traffic is almost twice as large as in the case of P2P local compared to the CS traffic model. However, the gain is much smaller in the case of P2P distant. This is due to the well known Spatial Reuse policy that is made possible by the fact that the access node that receives a packet frees the time slot, which can then be reused. As an illustration of the previous remark, consider a VoD service ; the three possible methods of locating the video servers in a metro ring are illustrated in Fig Fig shows that locating the video servers in all access networks allows to use the MAN capacity far more efficiently than in the case where servers are located on the ring or on the backbone.

149 5.2. PERFORMANCE ANALYSIS OF THE SINGLE-WAVELENGTH RING Backbone Access 3. Access 3. MAN Access Possible positions of the video servers: 1. between backbone and MAN network 2. on the metro ring 3. in the access Figure 5.11 Three possible ways of video traffic distribution in a metro ring P2P storage is one method for locating the video files on all the access nodes ; in this case, video files are stored locally in all user machines. A VoD service using P2P storage will be more efficient than a VoD service relying on classical CS architecture, as long as the users are led to retrieve files from other users on the same network (as seen from the P2P local curve) and not from remote users (as seen from the P2P distant curve). Another point to address to take advantage of P2P traffic is the location of the first node that accesses the IP layer. Traditionally, the metro network operates at layer 2, and the first IP node is located at backbone boundary. If this network architecture is used in future metro networks, then, whatever the service architecture is (P2P or CS) all traffic is collected in the MAN to be sent to the first IP node. In other words, the P2P scenarios analyzed previously are not realized. This argues in favor of accessing the IP layer at all access nodes in the metro network in order to avoid the mandatory traffic concentration towards a distant first IP node Conclusions on Single-Wavelength Ring Performance The present section introduces a simple discrete queuing model of the ECOFRAME ring with one wavelength. The model is based on the assumption that the packet arrival process can be approximated with the Bernoulli process. The model has been successfully validated by using simulation and then it has been used to verify the impact of different routing service architectures on the ring capacity. The impact of peer-to-peer (P2P) service architecture on the performance of singlewavelength ring is discussed. It is shown that P2P traffic profile has a bad influence on the performance of client-server (CS) traffic and that the overall capacity of the ring is larger if routing is not centralized, as in the traditional concentration+distribution networks, but is accessible at all nodes of the ring.

150 112 CHAPTER 5. PERFORMANCE ANALYSIS 5.3 Performance Analysis of WDM ECOFRAME ring: Impact of WDM receivers on ring capacity We now address the multi-wavelength WDM ECOFRAME ring. We consider receivers of different types, which are defined in Chapter 2. As already noted in the introduction to the present Chapter, when analyzing the performance of the ECOFRAME ring, we always suppose that the problem of designing the ring has been successfully resolved. Also, we take the simple hypothesis of the absence of the classes of traffic, the prohibition of traffic splitting, the absence of packet losses, the opportunistic use of time slots and the neglecting of the process of client packet segmentation. Two main issues that we discuss are: 1. the impact of WDM receivers of QoS performance of the ring and 2. the problem of scheduling in a ring (in relation to the rules for sizing the ring, which we studied in Chapters 3 and 4). In the present section we analyze the impact of use of WDM receivers on ECOFRAME ring performances and present simple queueing models describing insertion and extraction queueing processes. Next section (5.4) is dedicated to the problem of scheduling in ECOFRAME ring First motivation example Let us first present a simple example where the potential gains of using packet switching in optical WDM rings are identified. This example should help us to understand the potential benefits of optical packet switching in ECOFRAME. S1 Λ 1 Λ 3 S2 S4 S3 Λ 2 Figure 5.12 Supporting a given traffic matrix with optical circuits: a simple example Consider the WDM ring in Fig There are only 3 traffic flows that are routed in the counter-clockwise direction of the ring:

151 5.3. IMPACT OF WDM RECEIVERS ON RING CAPACITY one demand from S 1 to S 4, 2. one demand from S 3 to S 1, 3. one demand from S 4 to S 2. Assume that the rate of each flow corresponds to the rate of a single wavelength and that the network initially has non-wdm receivers. Without wavelength converters, 3 wavelengths are required to support the traffic flows. Indeed, assume that Λ 1 carries the flow from S 1 to S 4 and Λ 2 carries the flow from S 3 to S 1 ; Λ 1 is unavailable between S 1 and S 2, while Λ 2 is unavailable between S 4 and S 1. It is, therefore, necessary to activate another wavelength Λ 3 to support the third traffic demand. On the other hand, if there is a wavelength converter in S 4, 2 wavelengths are sufficient to accommodate the traffic demands. However, optical wavelength conversion technologies are not mature enough for practical deployment, i.e. wavelength conversion implies the use of Optical-Electrical-Optical (OEO) conversion on each packet. Another solution to reduce the number of wavelengths from 3 to 2 is to consider packet switching. This benefit is well-known in WDM rings with OEO conversion in all or in some selected nodes. OEO conversion allows to perform wavelength conversion, as well as to electronically aggregate, or groom, the traffic. A well known example of this architecture is the Resilient Packet Ring network (RPR) [55]. In RPR, if traffic flows are split into packets, 2 wavelengths are sufficient to accommodate the 3 flows 1. However, packet switching as understood in ECOFRAME also allows the same gain, while avoiding OEO at transit nodes. Indeed, in an ECOFRAME network, where each station has WDM receivers, only 2 wavelengths are required if each source station splits its flow equally on Λ 1 and Λ 2 and if we suppose that each WDM receiver provides the station with the ability to listen to both wavelengths. In other words, by exploiting WDM and packet switching, optical traffic grooming can achieve the same benefits as electronic traffic grooming. Actually, the so-called optical traffic grooming is just the design of the packet insertion process on the WDM optical packet ring. The traffic is groomed because different flows can share wavelengths although they may have different sources and different destinations on the ring. This is highly desirable, since avoiding electronic traffic grooming and replacing it by optical traffic grooming allows to design a network that is less energy consuming [87]. However, the gain to be expected in using optical traffic grooming (i.e. packet switching, coupled with optical transparency in transit nodes) does not come for free. To achieve the above mentioned benefits, an optimal ring design is required. The optimal design of the ECOFRAME ring has been studied in Chapters 3 and 4 of this work. As we have been able to see, the cost of WDM receivers is higher in comparison to the cost of single-wavelength receivers. Thus, the overall design cost of the ring with WDM receivers is likely to be more expensive than the overall design cost of the ring with non-wdm receivers. Also, the impact of the number of wavelengths per receiver on the network capacity should be studied. In the present section we show that the capacity of rings using WDM receivers is greater in comparison to rings using non-wdm receivers, at equal number of wavelengths in the ring. Before presenting this result, we mathematically demonstrate the impact of loadbalancing on the ring capacity and introduce queueing theory models to quantify the gain in performances when transmitting on more than one wavelength. 1 The statistical nature of packet multiplexing is neglected.

152 114 CHAPTER 5. PERFORMANCE ANALYSIS The positive impact of load balancing on ring capacity Let us observe a ring network with K stations and n wavelengths, where each source station S s is able to transmit on any wavelength (which is an assumption that is made in the ECOFRAME framework) and where each destination station S d has a WDM receiver, ie. it can listen to the complete set of wavelengths used in the ring. Consider the set of n-tuples (a 1,...,a n ), where for all i, 0 a i 1, and a a n = A. It is obvious that the minimum of max{a 1,a 2,...a n } is obtained for a i = A/n for each i. This result directly applies to the considered ring network. Any given traffic matrix mapped on a set of n wavelengths induces different loads on the different links between stations. On a given link, let a i denote the amount of traffic carried by wavelength Λ i (expressed as a proportion of the optical channel capacity). A robust dimensioning is obtained when the remaining bandwidth on the most heavily loaded wavelength is maximized. Obviously, this is obtained if the total load to carry on the link is equally balanced over the set of n wavelengths. A perfect load balancing on each link is easily obtained if each source station S s balances the traffic for any destination station S d over the n available wavelengths. In the remainder of this work, perfect load balancing is called, simply, load balancing. Thus, the load balancing technique maximizes the overall traffic that can be carried over the ring. However, this policy supposes that each station can listen to all the wavelengths, ie. that the ring stations possess WDM receivers. Clearly, if stations have non-wdm receivers it is not possible to benefit from load balancing. The configuration in which each station can listen to all the wavelengths is called All- Wavelengths-Shared case, and some design related issues concerning this configuration have already been studied in Sections and Here, we have shown that All-Wavelengths- Shared design, in combination with load-balancing, can support the maximum traffic load, in comparison to all the other ECOFRAME ring configurations, with the same number of wavelengths. However, it is reasonable to expect that the industry provides receivers for sets of size k (e.g. k = 4 or k = 10 seem likely choices). Let m denote the number of wavelengths yielded by a dimensioning process assuming that each receiver can listen to all active wavelengths on the network. If m > k, providing a single receiver per station is not sufficient, and a more complex dimensioning process should be conducted, and the dimensioning methods presented in Chapters 3 and 4 should be used. Because of its positive impact, load balancing is a technique that is taken into account in the network planning, in this work. Note that the splitting of traffic among the wavelengths belonging to the same receiver is allowed in all of the design techniques, that are studied in Chapters 3 and 4, ie. the supposition that every station can perform load-balancing on all the wavelengths belonging to some destination is not in contradiction with our designing methods Modeling of the system by using Queuing theory This section assesses the gain of use of WDM receivers on the insertion time of the packets. This gain is expected because of the statistical multiplexing which arises when a station has the opportunity to choose between several wavelengths for sending its packets. We also show that due to statistical multiplexing, the extraction time slightly increases with the increase of

153 r 5.3. IMPACT OF WDM RECEIVERS ON RING CAPACITY 115 number of wavelengths on which a destination receives. However, this increase is negligible in comparison to the insertion time decrease. The following assumptions are taken. The packet arrival process at each station follows a Bernoulli process with parameter λ. The probability that a time slot on a given wavelength is idle (i.e., available) is assumed to follow a Bernoulli process with parameter µ. The occupancy on the different wavelengths is assumed to be independent. Let us then assume that each station can receive packets on any of n wavelengths. Since each station can insert a packet in a time slot on any idle wavelength, the above independence assumption yields that packet insertion in a slot is possible with probability µ(n) = 1 (1 µ) n The insertion time can thus be modeled by a Geo/Geo/1 queue, with Arrival First policy [44]. The mean number of customers in the queue is thus λ(1 λ)/(µ(n) λ). Due to the Arrival First hypothesis, this is also the mean number of customers seen in the system by an arriving customer. Little s formula then yields the mean insertion time in the ring expressed in slot times: E(I n ) = 1 λ µ(n) λ = 1 λ 1 (1 µ) n λ. (5.30) Note that E(I n ) is always larger than 1 (since it takes at least one time slot to insert a packet), and that it decreases quickly to 1 when n increases. E(I n ) is presented in function of ρ and µ in Figs and 5.14 for n = 1 and n = 4. Different colors correspond to different numbers of time slots. In Figs and 5.14, color-scale is limited to 10 time slots. Expected insertion time [ number of time slots] greater or 10 equal to 10 ρ µ Figure 5.13 Expected insertion time for n = 1

154 r 116 CHAPTER 5. PERFORMANCE ANALYSIS Expected insertion time [ number of time slots] greater or 10 equal to 10 ρ µ Figure 5.14 Expected insertion time for n = 4 Fig shows that for low values of µ, which corresponds to states of high wavelength occupancies, E(I n ) has larger values. From Fig we can see that already for n = 4 expected insertion time is very small except for µ < 0.1, which is not a very realistic value for µ anyway. In order to more precisely evaluate the expected gain in the sojourn time in the ring, Fig identifies working condition where the mean insertion time is larger than 2 time slots for increasing values of n. For a given value of n, the area on the right hand side of the curve corresponds to systems (characterized by µ and ρ = λ/µ) where the mean insertion time is smaller than 2 time slots. This curve shows that if µ is at least 0.5, the mean insertion time is always smaller than 2 as long as n 2. Also, if µ is at least 0.2 (that is if each wavelength is occupied 80% of the time), the mean insertion time is less than 2 if n 5. However, with WDM receivers, there is a demultiplexing stage at the egress station since several packets can arrive at destination in a single time slot. Once again, we can model the arrival of a packet for the station on any wavelength by a Bernoulli process with parameter λ/n (since each source performs load balancing on all available wavelengths). A model for the extraction time is then a ngeo/d/1 queue, where the duration of a service time is 1 (slot time). The mean extraction time from the ring is thus: E(E n ) = /n 2(1 λ). (5.31) The limit for the mean extraction time is the mean sojourn time in an M/D/1 queue with parameter λ/n. It is limited to a few slot times, unless λ is very large (which is very unlikely in an operational MAN environment). These conclusions are illustrated with Figs and The above results show that WDM receivers drastically improve the delivery performance even for a small value of n: the increase in extraction time is negligible compared to the