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1 Les Cahers du GERAD ISSN: Desgn of QoS Aware IP Network Supportng Servces wth Average Delay Requrement S. Srvastava, A. Grard, B. Sansò G March 2006 Les textes publés dans la sére des rapports de recherche HEC n engagent que la responsablté de leurs auteurs. La publcaton de ces rapports de recherche bénéfce d une subventon du Fonds québécos de la recherche sur la nature et les technologes.

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3 Desgn of QoS Aware IP Networks Supportng Servces wth Average Delay Requrement Shekhar Srvastava GERAD HEC Montréal 3000, chemn de la Côte-Sante-Catherne Montréal (Québec) Canada, H3T 2A7 André Grard GERAD and INRS-EMT Place Bonaventure 800, rue de la Gauchetère ouest, Sute 6900 Montréal (Québec) Canada, H5A K6 Brunlde Sansò GERAD and École Polytechnque de Montréal C.P. 6079, Succ. Centre-vlle Montréal (Québec) Canada, H3C 3A7 March 2006 Les Cahers du GERAD G Copyrght c 2006 GERAD

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5 Abstract In ths paper, we study the problem of determnng the capacty requrements for applcatons that requre QoS guarantees. We consder three knds of source models; Posson based, On-Off based and leaky bucket flter based, and present explct expressons capturng the requred capacty. We compare the requred capacty for average delay for these models wth the requred capacty for absolute delay and comment on the dfferental. Further, usng smulaton results, we study the average and varance of the observed delay for voce and vdeo sources and compare the three models. We found that On-Off and leaky bucket models are very powerful and ensure that the actual delays are less than the requred delay and that the varance remans acceptable. These results seem to ndcate that t may be possble to dmenson systems based on average QoS requrements and stll get adequate performance for other requrements such as jtter. Ths would then provde us wth computatonal tools to dmenson networks effcently. Résumé Nous voulons détermner le débt nécessare pour garantr aux applcatons qu en ont beson des qualtés de servce adéquates. Nous étudons tros modèles de source: Posson, On-Off et contrôlée par un leaky bucket. Nous donnons des expressons explctes pour le débt requs. Nous comparons ensute ces débts pour un déla moyen donné à celle qu serat nécessare pour une contrante sur le déla maxmum des paquets et nous dscutons de la dfférence entre les deux. À l ade de smulatons, nous étudons la varance du déla pour des sources de trafc de vox et de vdéo en comparant les tros modèles. Nous montrons que les modèles On-Off et leaky bucket sont suffsamment robustes pour garantr que le déla et la varance demeurent en dessous des bornes supéreures admssbles. Ces résultats montrent qu on pourrat dmensonner des systèmes sur la base d un crtère de déla moyen et obtenr quand même une qualté de servce suffsante en terme des autres paramètres comme la ggue. Cec nous permettra de développer des outls de dmensonnement de réseaux effcaces. Acknowledgments: We would lke to thank C. Dovrols from Georga Tech. for provdng the smulaton code for PDD schedulng.

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7 Les Cahers du GERAD G Introducton The Internet of today has grown from an expermental academc medum to the common omnpresent platform for connectng dverse networks and computers nto a common worldwde-web. Such a deep penetraton of nternet was only possble due to the smplcty and pervasveness of the Internet Protocol (IP). IP provded best-effort performance and connectvty to users, whch was suffcent for most applcatons and users. At the same tme, other technologes such as Asynchronous Transport Mode (ATM), Frame Relay (FR), etc. were proposed for supportng qualty-of-servce (QoS) based applcatons. These networks operated n a prvate doman and ther servces had to be bought at a premum prce from Internet Servce Provders (ISP). These networks had a very controlled behavor and traffc was well montored to ensure low delays, almost no packet loss and neglgble delay varatons. Companes used these servces to support applcatons such as vrtual meetngs, nventory management/regulaton, etc. The ISPs provded source-destnaton based vrtual leased lnes (VLL) or multple locatons based vrtual prvate networks (VPN) as servces to the customers. The servce level agreements (SLA) [6] were desgned exclusvely for each customer or group of users based on ther requrements and objectves. Increased pressure for compettve prcng has led to re-consderng the separate network approach (best-effort and QoS based). ISPs have started explorng the possblty of movng all the applcatons on a common IP network wth the hope of realzng massve cost savngs. However, there are some ssues. Such QoS centrc IP networks wll have to carry servce classes wth very strngent delay requrement (say voce) along sde classes wth no delay restrcton (say emal). One way of achevng ths s to ensure that the delays of all the classes should be less than the most strngent class. Ths could potentally translate nto massve over-provsonng and would have undermned the potental of QoS based IP networks [8]. If we want to avod over-provsonng, we must be able to dmenson networks s a systematc way. Ths n turn means that we need methods to dmenson networks to ascertan QoS of varous servce classes. Unfortunately, at the present tme, there are very few such models and the ones that we have are based ether exclusvely on a maxmum delay approach or are based on smplstc average delay requrement. In practce, the users who need guaranteed average delay performance, would stll want low jtter and losses for some real-tme applcatons such as voce, vdeo, etc. In ths context, dmensonng just for average delay may not gve adequate performance as far as the other QoS measures (jtter, etc.) are concerned. Fallng back on absolute delay based models wll lead to gross over-provsonng.

8 2 G Les Cahers du GERAD We present a framework, accompaned models and performance results for provdng servces wth average delay bounds. We nvestgate the extent of over-provsonng nduced by determnstc delay bounds and also evaluate the mpact of average delay based provsonng upon other QoS measures such as jtter, etc. We explore f other QoS measures can also be taken nto account whle dmensonng based on only average delay requrement. We focus on a sngle lnk only, and consder multple lnks/network wde desgn ssues n future extensons. Internet Engneerng Task Force (IETF) has standardzed the Dfferentated Servces archtecture (DffServ) for large scale deployment of IP networks wth QoS support [3]. They have provded three types of servce to packets: expedted forwardng (EF) [], assured forwardng (AF) [0] and best-effort. The applcatons requrng absolute delay bound are mapped to EF class. For provdng the average delay bound, we use the AF class. We propose to use the proportonal delay dfferentaton (PDD) model of Dovrols et.al. [4,6] for provdng dfferent delays to the subclasses wthn the AF class. The PDD based approach s unque n ts smplcty and tractablty. Recently, many real tme applcatons have been successfully mapped to delay and loss dfferentaton parameters of the PDD subclasses [5,7,8]. In ths paper, we consder varous source models such as Posson, on-off and leaky bucket constraned to determne the amount of bandwdth requred to guarantee that all the sources acheve ther average case requrement. Usng analytcal results and smulatons, we also demonstrate that many real-tme applcatons such as voce and vdeo can be effectvely supported va servces guaranteeng average delays only. We also compare the bandwdth requrements for such an AF class vs-a-vs equvalent EF class and comment on the magntude and order of bandwdth dfferental. Such a dfference could be effectvely translated nto provdng AF servces at a much more economcal prce as compared to servces of EF class. In ths paper, we focus on delay as the man performance measure. We clam that the other mportant measure, the delay jtter, could be controlled usng playout buffers assumng that the delay encountered s small enough. For non-elastc sources such as UDPbased nteractve servces havng small delays, losses mght be totally avodable. Observe that only when the delays are hgh and queues n the routers buld up, do we have losses. Snce the sources are non-elastc, losses are not coupled wth throughput. The rest of the paper s organzed as follows. In Secton 2, we provde the framework/archtecture for provdng average and absolute delay based servces n an IP based QoS network. In Secton 3, we dscuss the models for absolute delay bounds and the requred capacty. In Secton 4, we dscuss the models for average delay bounds and the requred capacty. In Secton 5, we present numercal results derved usng the explct expressons developed n the prevous secton. Further, n Secton 6, we present smulaton

9 Les Cahers du GERAD G Subclass EF Class h EF Subclass 2 h EF 2 Subclass n h EF n Source s= Source s=2 Subclass queue AF Class Subclass δ AF h AF WFQ c Source s=k Subclass 2 Subclass m δ AF 2 δ AF m PDD Fgure 2: Mappng between sources and subclasses at node A BE Class h BE Fgure : Forwardng nterface of router A results to compare the performance of varous source models for average case dmensonng. We provde summary and dscuss future work n Secton 7. 2 Core Router Archtecture In ths secton, we dscuss the archtectural detals of a forwardng nterface of a core IP router whch provdes absolute and average case guarantees for the sources. For ths purpose and towards dscussons n later sectons, consder multple sources whch want to send ther traffc from node A to node B connected by a drect lnk l. Consder now the ngress (A) and egress (B) routers. Assume that the concerned forwardng nterface on node A to node B has been confgured for n EF subclasses and m AF subclasses. At the nterface, each source s mapped to EF or AF class based on the provsons of the customer s SLA (absolute or average delay). The mappng to subclass (such as ) wthn the class s based on the source applcaton runnng at the source (voce, vdeo, etc.). The demand par (A-B) has to support a set of sources s S. In Fgure, we present the archtecture of the forwardng nterface of IP router A, supportng DffServ. Let the capacty of the drect lnk connectng router A to B be c. We assume that the

10 4 G Les Cahers du GERAD bandwdth s dstrbuted amongst the n EF subclasses, AF class and BE class usng a weghted far queueng scheduler (WFQ) where the vector h determnes the weghts used n schedulng. Ths ensures that each EF subclass on the lnk gets no less bandwdth than c EF, where Here, c EF c EF c = h BE + h AF + n. (a) = hef s the mnmum bandwdth requred for subclass n order to provde the target h EF delay D EF the AF class whch translates nto mnmal bandwdth of to the sources belongng to the class. Smlarly, h AF captures the weght for c AF = h AF c h BE + h AF + n. (b) = hef c AF s the total bandwdth avalable to the AF class such that can be shared between the m subclasses. The bandwdth c BE avalable to the BE class can be computed as c BE = h BE c h BE + h AF + n, (c) = hef In Fgure 2, we show how sources are mapped onto each subclass (EF or AF) at the ngress edge router. Let the set of sources belongng to the th EF subclass be S EF, then every source s S EF has a absolute delay requrement D s D EF. Smlarly, for the th AF subclass, sources s S AF have an average delay requrement such that D AF D s. Source s belongng to AF or EF class has an average arrval rate of r s. When generated by an On-Off source model, t has a peak rate of R s and the on perod of average length I s. Such a source can be effectvely shaped by a leaky bucket flter of parameter (σ s, ρ s ), where ρ s s the average arrval rate and σ s s the maxmum allowed burst length of the LB flter. In order to ensure low losses, t s advsable to have ρ s >.r s and hgh value of σ s. Observe that sometmes the bandwdth allocated to the AF class needs to be shared between the m subclasses such that each subclass meets ts target delay requrement. Ths s done by usng PDD schedulng [6] between the subclasses where the value of parameter determnes the extent of dfferentaton as dscussed n Secton 4. Furthermore, each AF subclass can have an end-to-end delay requrement or for the concerned hop. Provdng hop-by-hop delay allows greater flexblty and optons of better mappng the sources to subclasses. Ths s outsde the scope of current paper and s currently under study. δ AF 3 Provdng Absolute Delay Bound In ths secton, we dscuss the amount of capacty requred to provde an absolute delay guarantee to sources belongng to the EF class. The capacty s a functon of the characterstcs of the sources and ther delay requrement. Such a problem s sometmes referred to

11 Les Cahers du GERAD G as the equvalent capacty problem (see [2], and references theren). Absolute bounds on delays can be obtaned for sources whch are shaped by a leaky bucket (LB) flter. Behavor of such shaped sources has been extensvely studed n the lterature. Cruz studed such shaped sources n solaton, when multplexed and on an end-to-end bass usng flud flow models [ 3]. As dscussed before, we consder sources whose traffc s shaped by a LB of parameter (σ s, ρ s ). The value of the maxmum delay D s that can be ncurred by any packet can be determned based on the nature of the applcaton connected to the source s. Frst we consder a subclass and we defne = ρ s, = σ s. ρ EF s S EF σ EF s S EF Then the maxmum backlogged traffc from A to B for EF subclass [4] wll be Q EF σ EF. Observe that drect addton of burst lengths could be a conservatve approach. However, t s necessary n order to guarantee determnstc delays to each ndvdual source. Furthermore, we have c EF { = max ρ EF }, σef D EF. (2) The requred mnmal capacty can be ensured to the subclass by adjustng the weghts based on the equatons (). The above presented capacty requrement s only used for comparson wth the requred capacty for AF classes whch provde average delay guarantee. 4 Provdng Average Delay Bound In ths secton, we determne the mnmal bandwdth c AF requred by the AF class n order to ensure that the average delay for each AF subclass meets or exceeds ts requred average delay D AF. Recall that AF class only provdes average delay guarantee to ts sources. Such a problem was orgnally consdered by Dovrols et. al. n [5]. They accounted for the average arrval rates of the sources but dd not account for ther burstness and used smulaton to arrve at the requred capacty. The burstness of the sources mpacted the derved capacty n an ndrect way. The approach s smple yet effectve. For each AF subclass, defne the target average delay as d AF. Then, we know that D AF d AF. (3) To ascertan ths, consder an magnary queue whch s beng fed by the sources belongng to the AF class. The packets are servced at the rate c AF on a frst-come-frst-serve (FCFS)

12 6 G Les Cahers du GERAD bass. Let q AF denote the average length of such a queue. The aggregate arrval rate wll be m r AF = r s. = s S AF Recall that r s s the average arrval rate for source s S, and here we assume that r AF < c AF. Then, the requred capacty c AF s such that the magnary queue has queue length, q AF m = s S AF r s d AF. (4) Alternately, the average watng tme for the magnary queue should be d AF m r AF = s S AF r s d AF. (5) It wll ensure that each source belongng to subclass wll have an average delay of d AF or less. The approach argues that f the number of packets n the magnary queue conforms to the condton (Eq. 4) then n the real queue, PDD scheduler can dstrbute the avalable capacty amongst the contendng AF subclasses such that each one of them conforms to the desred average delay on short as well as long tme scales. The PDD scheduler requres the parameter δ AF whch can be computed as follows [5]. Wthout loss of generalty, we assume that subclass m has the maxmum delay requrement, then δ AF = daf d AF, =,2,..,m, and δm AF =. (6) m We then have to determne the capacty c AF requred to acheve an average queue length of q AF. For a gven value of average queue length, characterstcs of sources mpact the amount of capacty requred. The capacty was determned usng smulatons n [5]. The approach provdes good estmates for requred capacty but has lmted utlty towards network dmensonng. Due to the use of smulaton, t would be hard to ncorporate n an overall network desgn problem. Ths would greatly curtal ts usefulness towards the goal of desgnng QoS-based IP networks. In ths paper, we refne on the approach and use t towards the goal of determnng the value of c AF. In some cases, we do have computatonal models for the magnary queue. We can then use them n the Dovrols framework and ths gves us a fast computatonal technque for estmatng delays. We apply ths approach to Posson, On-Off and LB controlled sources. For each of the three scenaros, we develop the expressons for average queue length and use t to compute the requred capacty.

13 Les Cahers du GERAD G Posson Sources We frst consder that each source generates packets wth an exponental nter arrval tme. Such systems are farly well studed n the lterature. We know that each source s has the average arrval rate of r s,.e., ts nter-arrval tmes are exponental wth a mean of /r s. The requred capacty s referred to as c AF P. Usng the M/M/ queue length formula, we have ( r d AF AF /c AF ) 2 P = r ( ). AF r AF /c AF P The equaton can be rearranged to get, Then the requred capacty wll be ( ) c AF 2 P r AF c AF P c AF P = raf + raf = 0. daf (r AF ) 2 4r AF /d AF 2. (7) The Posson based model was also consdered n [5] and s presented here for comparson. 4.2 On-Off Sources Next we consder sources whch have a two-state, On-Off behavor. Such models are sometmes used to characterze voce or vdeo sources. As mentoned before, each source has an average rate of r s, peak rate of R s and average on-perod of I s. We develop upon the work presented n [7]. The requred capacty, referred to as c AF OO and the average delay d AF are related by r AF d AF m = ( c AF OO raf) Upon solvng, we get c AF OO = = ( r AF ) 2 d AF + s S AF m = r AF d AF + [ (R s r s ) ( ] R s c AF OO + ) r s I s raf r s. R s s S AF m = (R s r s )(R s r + r AF ) r si s R s s S AF (R s r s ) r si s R s. (8)

14 8 G Les Cahers du GERAD 4.3 Shaped Sources Now consder the scenaro where each source s polced by a leaky bucket wth parameters ρ s and σ s. For ths we consder the results presented n [9]. They have shown the followng result. Theorem The average delay for a queue servng at rate c to multplexed stream of sources (s=,2,..,s) polced by leaky bucket (ρ s, σ s ) s d = 2c ( S σ s ρ s s= c ). (9) S ρ s For ease of presentaton, defne the average regulated arrval rate for the AF class as m ρ AF = ρ s, = s= s S AF and the regulated arrval rate weghted burstness for the AF class as m γ AF = ρ s σ s. = s S AF Then the value of capacty, referred to as c AF LB should satsfy the relaton ( ) c AF 2 LB c AF LBρ AF γaf = 0, (0) 2 daf where d AF was expressed n eq. (5). Solvng the quadratc equaton and dscardng the value whch s smaller than ρ AF, we get ( c AF LB = ) ρ AF + (ρ 2 AF ) γaf 2 d AF. () Observe that the requred capacty ncreases wth burstness weghted wth average arrval rate and decreases wth ncreasng target delay. 5 Numercal Results In ths secton, we present numercal results comparng the requred capacty for provdng average delay guarantee for Posson, On-Off and shaped sources. We also present for comparson the results for absolute delay guarantees. We consder two types of on-off sources, voce and vdeo.

15 Les Cahers du GERAD G Voce Applcaton We model a voce source as a two state on-off source where t generates packets wth a determnstc nter-arrval tme of 5 msecs n the on-state. On-perods are exponental wth rate 2.5 and off-perod are also exponental wth a rate.67. Ths leads to an average rate r = Kbps, R = 64 Kbps and I = 2.5. Each source can be polced by a leaky bucket wth parameters ρ = 28 kbts and σ = 92 kbts whch ncurs losses of less than 0.%. 5.2 Vdeo Applcaton The vdeo source s also modeled as a two state on-off source. Durng each burst, the source generates 84.4 packets per second, each packet of sze 000 bytes for an packet nter-arrval tme of 5.4 msecs durng the actve perod. The length of the actve perod s exponentally dstrbuted wth an average of 0.23 secs. Ths produces an average rate r =.08 Mbps and peak rate R =.475 Mbps. Each applcaton can be polced by a leaky bucket wth parameter ρ = 200 kbts and σ = 360 kbts whch causes farly low losses. Now, we compare the values of c for absolute delay requrement on one hand, and average delay for Posson, On-Off and leaky bucket shaped sources on the other. To normalze the voce and vdeo sources, we compute the rato of capacty to the average arrval rate (c/r), referred to as overprovsonng. The amount of overprovsonng s dependent upon the source models and the delay requrements. To ensure that the lnk s not overloaded and that the queues do not buld up excessvely, we mpose the condton that the value of capacty s always greater than.05 tme average arrval rate. Furthermore, we consder two varatons, Applcaton based Parttonng and Applcaton based Sharng. 5.3 Applcaton based Parttonng Here, we reserve separate bandwdth for each subclass. In other words, dfferent applcatons such as voce and vdeo, do not share bandwdth. However, sources belongng to each subclass share the capacty. The scenaro could be useful for servce provders who wsh to guard applcatons from each other by solaton. As an outcome, benefts of multplexng between applcatons can not be yelded. Here, c /r and c 2 /r represent the overprovsonng requred to guarantee abolute delay for voce and vdeo sources., and refer to overprovsonng requred when dmensonng for average delays usng leaky bucket based model, usng on-off based model and Posson based model, respectvely. In ths regard, we present the results for voce sources n Fgure 3 and that of vdeo sources n Fgure 4. We see that the requrement of absolute delay causes an overprovsonng as hgh as 000 for voce traffc and more than 8 for vdeo traffc. Guaranteeng average delay reduces the overprovsonng to the range 2 n voce sources and less than.2 n vdeo

16 0 G Les Cahers du GERAD Requred Overprovsonng c /r Requred Overprovsonng 0 c 2 /r Value of Delay Value of Delay Fgure 3: Requred overprovsonng for sngle Voce Source Fgure 4: Requred overprovsonng for sngle Vdeo Source Requred Overprovsonng c /r Requred Overprovsonng 0 c 2 /r Value of Delay Value of Delay Fgure 5: Requred overprovsonng for 5 Voce Sources Fgure 6: Requred overprovsonng for 5 Vdeo Sources Requred Overprovsonng c /r Requred Overprovsonng 0 c 2 /r Value of Delay Value of Delay Fgure 7: Requred overprovsonng for 0 Voce Sources Fgure 8: Requred overprovsonng for 0 Vdeo Sources sources. Partcularly, desgn wth Posson models requres less than twce the arrval rate for target delays n the range 0 00 ms. For vdeo, mnor overprovsonng s suffcent to ensure the average delay of 50 to 00 ms.

17 Les Cahers du GERAD G In Fgures 5-8, we present the requred overprovsonng for 5 and 0 voce and vdeo sources. Observe that the benefts of multplexng between the sources of the same subclass further help n decreasng the overprovsonng for the average delay scenaro. For absolute delay, the values are same. Interestngly, for 5 and 0 voce sources requrng 0 ms of average delay (Fgure 5 and Fgure 7), the on-off based model requres margnally less capacty than the Posson based model. Ths can be ascrbed to the fact that for on-off based model, the packets are generated at regular determnstc ntervals durng an actve perod and hence multplexed on-off sources can lead to a smoother traffc than Posson. 5.4 Applcaton based Sharng The prevous scenaro dd not requre schedulng between the voce and vdeo sources snce they are not sharng the capacty. Now, we consder such a sharng. For the absolute delay requrement, sharng s stll not possble although WFQ ensures that capacty unused by other classes s made avalable to actve classes, but no guarantee can be provded. Therefore, we do not present results for absolute delay requrement. When consderng average delay requrements, n the prevous sectons we have dscussed that the bandwdth could be shared between the subclasses usng the PDD schedulng based on the parameter δ AF (see eq. 6). We now consder that the voce sources are allocated to AF subclass and vdeo sources are mapped to AF subclass 2. In Fgures 9, we present the overprovsonng requred to support both the AF subclasses and 2, each havng one, fve and ten sources. Here also, and refer to overprovsonng requred when dmensonng for average delays usng leaky bucket based model, usng on-off based model and Posson based model, respectvely. Note that for sngle voce and vdeo source, desgn usng leaky bucket flter requres more capacty than the on-off source based desgn model whereas for fve and ten voce and vdeo sources, on-off based model requres more capacty. Ths can be attrbuted to the way these two models derve the beneft of multplexng. The LB based model better accounts for the multplexng gan as compared to the On-Off based model. These nteractons are subjects for further work. 6 Smulaton Results The desgn models that we have examned are all based on an average delay QoS requrement. In practce, however, average delay s not suffcent for many real-tme applcatons such as voce or vdeo where jtter must also be taken nto account. We currently don t have desgn models that can take jtter nto account so we need to evaluate whether the jtter remans acceptable n a system desgned wth an average delay method.

18 2 G Les Cahers du GERAD In ths secton, we present smulaton results n order to study the delays encountered by the ndvdual voce and vdeo sources under varous provsonng scenaros and compare them wth the requred delays for voce and vdeo, respectvely. We used ns-2 to conduct smulatons. We only smulated the AF subclasses where multple sources send packets to each class, and packets of each subclass are served n the order of ther arrval whle sharng bandwdth between the subclasses usng PDD schedulng. The parameter for the PDD schedulng are determned based on the dscussons n secton 2. The smulaton model for AF class s shown n Fgure 2. We smulate a voce source usng a two state onoff model where t generates packets wth a determnstc nter-arrval tme of 5 msecs n the on-state. On-perods are exponental wth rate 2.5 and off-perods are also exponental wth a rate.67. Each packet s of sze 20 bytes. The vdeo source s modeled usng determnstc batch arrvals wth batch nter-arrval tme of 33 msecs. The number of packets n a batch are geometrcally dstrbuted wth an average of 5 packets. In each Requred Overprovsonng Requred Overprovsonng /50 0/60 Value of Delay 20/50 20/60 0/50 0/60 Value of Delay 20/50 20/60 Fgure 9: Requred overprovsonng for sngle sources Fgure 0: Requred overprovsonng for 5 sources Voce App EF Subclass Requred Overprovsonng /50 0/60 Value of Delay 20/50 20/60 Voce App Voce App Vdeo App Vdeo App Vdeo App EF Subclass 2 δ AF δ AF 2 PDD c Fgure : Requred overprovsonng for 0 sources Fgure 2: Smulaton Model for AF class

19 Les Cahers du GERAD G burst, the last packet has sze dstrbuted as unf orm(0,000) bytes. All other packets have 000 bytes. Here also, and refer to overprovsonng requred when dmensonng for average delays usng leaky bucket based model, usng on-off based model and Posson based model, respectvely. Observe that the capacty computed usng these models along wth PDD based schedulng were presented n Fgures 9 for sngle, fve and ten voce and vdeo sources. Now we use that capacty for the smulaton and compare n Fgures 3 8 the delays for sngle, fve and ten voce and vdeo sources. We have plotted the observed mean delay and error bars correspondng to twce the sample standard devaton for voce and vdeo sources. We also present a horzontal lne showng the requred average delay for each source. Note that for the Posson-based capacty model wth sngle sources, the actual mean delay s many tmes the target delay, both for voce and vdeo. Moreover, some voce packets can have a delay as hgh as 400 ms and wll be useless at the recever. For vdeo also, packets can have delays as much as sec. Such a capacty plannng s not very useful and could lead to unsatsfed customers. When we multplex 5 or 0 voce and vdeo sources, the average delays get closer to the target delays and for 0 sources, they are even acceptable for both voce and vdeo. However, there s stll a large varance n the observed delays and voce packets could stll have as hgh as 40 ms and vdeo as hgh as 00 ms. Note that such hgh delays could be tolerable f they affect only a small number of packets. Next, we consder on-off and leaky bucket based desgn models. Observe that both the approaches provde acceptable delays, average as well as average along wth two tmes standard devaton. The values are smaller than the requred delays and hence a sgnfcant fracton of packets belongng to voce and vdeo sources wll encounter less than requred delays. These models reman consstent for sngle, fve or ten sources and provde acceptable performance to ndvdual sources. Note that the leaky bucket-based model provdes delays whch are less than the target for both voce and vdeo, although t requres lesser capacty than the on-off-based models. Observe that not only the delays are acceptable but also the varance s qute small. Based on these results, t can be argued that leaky bucket-based model could be used to determne requred capacty for a source requestng an average delay QoS. When allocatng capacty for a small number of sources, t can acheve the multplexng gan and provdes mnmal capacty to meet the requred delays. 7 Summary and Future Work In ths paper, we consder applcatons that do not requre absolute delay guarantee but for whome the average delay requrement wll be satsfactory. Ths could be due to hgh

20 4 G Les Cahers du GERAD Observed Delay for Voce Observed Delay for Vdeo /50 0/60 20/50 Target Delay for Voce/Vdeo 20/60 0 0/50 0/60 20/50 Target Delay for Voce/Vdeo 20/60 Fgure 3: Delay for sngle Voce source Fgure 4: Delay for sngle Vdeo source Observed Delay for Voce Observed Delay for Vdeo /50 0/60 20/50 Target Delay for Voce/Vdeo 20/60 0 0/50 0/60 20/50 Target Delay for Voce/Vdeo 20/60 Fgure 5: Delay for fve Voce source Fgure 6: Delay for fve Vdeo source Observed Delay for Voce Observed Delay for Vdeo /50 0/60 20/50 Target Delay for Voce/Vdeo 20/60 0 0/50 0/60 20/50 Target Delay for Voce/Vdeo 20/60 Fgure 7: Delay for ten Voce source Fgure 8: Delay for ten Vdeo source relatve cost of absolute delay guarantee. For average delay guarantee, we consder AF servce class of the dfferentated servces based archtecture for QoS aware IP networks. Three knds of models were accounted for: Posson, On-Off and leaky bucket based. We present closed form expressons to determne the capacty requred to ensure average delay to each servce class. Usng numercal results, we compare the requred capacty for the three models wth the capacty requred to guarantee absolute delays for voce and vdeo applcatons. It was observed that absolute delays requre many orders of more capacty

21 Les Cahers du GERAD G than the average delay models. We then use these capacty values to smulate a typcal lnk and present results demonstratng the delays encountered by voce and vdeo sources for these capacty models. It was also found that leaky bucket based model s sutable for classes wth few sources. However, for networks wth hgh number of ndvdual sources, Posson based models can also be used successfully. We are n the process of ncorporatng other source structures such as three state, long range dependent, etc. nto the desgn models. We are also n the process of extendng the analyss to mult lnk and/or end-to-end network based models. References [] R. L. Cruz. A calculus for network delay, Part I: Network elements n solaton. IEEE Trans. Informaton Theory, 37:4 3, 99. [2] R. L. Cruz. A calculus for network delay, Part II: Network analyss. IEEE Trans. Informaton Theory, 37:32 4, 99. [3] R. L. Cruz and H. Lu. End-to-end queueng delay n ATM networks. Journal of Hgh Speed Networks, 3(4):43 427, 994. [4] C. Dovrols and P. Ramanathan. A Case for Relatve Dfferentated Servces and the Proportonal Dfferentaton Model. IEEE Network, pages 2 0, Sept/Oct 999. [5] C. Dovrols and P. Ramanathan. Dynamc class selecton and class provsonng n proportonal dfferentated servces. Computer Communcatons, 26:204 22, [6] C. Dovrols, D. Stlads, and P. Ramanathan. Proportnal Dfferentated Servces: Delay Dfferentaton and Packet Schedulng. IEEE/ACM Transactons on Networkng, 0(), [7] H. Dupus and B. Hajek. Smple Formulas for Multplexng Delay for Independent Regeneratve Sources. In Proc. INFOCOM 93, pages 28 35, 993. [8] C. Flsfls and J. Evans. Deployng Dffserv n Backbone Networks for Tght SLA Control. IEEE Internet Computng, pages 58 65, Jan/Feb [9] F. Gullemn, N. Lkhanov, R. Mazumdar, and C. Rosenberg. Extremal traffc and bounds for the mean delay of multplexed regulated traffc streams. In Proc. Infocom 2002, June [0] J. Henanen, F. Baker, W. Wess, and J. Wroclawsk. Assured forwardng PHB group. IETF RFC 2597, June 999. [] V. Jacobson, K. Nchols, and K. Podur. An expedte forwardng PHB. IETF RFC 2598, June 999.

22 6 G Les Cahers du GERAD [2] F. Kelly. Notes on Effectve Bandwdths. In F. Kelly, S. Zachary, and I. Zedns, edtors, Stochastc Networks: Theory and Applcatons, volume 4 of Royal Statstcal Socety Lecture Notes Seres, pages Oxford Unversty Press, 996. [3] K. Nchols, S. Blake, F. Baker, and D. Black. RFC 2474: Defnton of the Dfferentated Servces Feld (DS Feld) n the IPv4 and IPv6 Headers. IETF, dec 998. [4] A. K. Parekh and R. G. Gallager. A generalzed processor sharng approach to flow control n ntegrated servce networks: the multple node case. IEEE/ACM Transactons on Networkng, 2:37 50, 994. [5] W. Tan and A. Zakhor. Packet classfcaton schemes for streamng MPEG vdeo delay and loss dfferentated networks. In Proc. Packet Vdeo Workshop 0, Aprl 200. [6] K. Whte. RFC 2758: Defntons of Managed Objects for Servce Level Agreements Performance Montorng. IETF, feb 200. [7] L. Zhao,, J. Shn, J. Km, and C.-C. J. Kuo. MPEG-4 FGS Vdeo Streamng wth Constant Qualty Rate Control and Dfferentated Forwardng. In Proc. Vdeo Communcatons and Image Processng, pages , [8] L. Zhao, J. Km, and C.-C. J. Kuo. Rate Adaptaton and error control for scalable vdeo streamng over Dffserv Networks. In Proc. Symposum on Electronc Imagng, pages 20 25, 2002.