An Algorithm for Loopless Deflection in Photonic Packet-Switched Networks

Transcription

1 An Algoritm for Loopless Deflection in Potonic Packet-Switced Networks Jason P. Jue Center for Advanced Telecommunications Systems and Services Te University of Texas at Dallas Ricardson, TX Abstract In tis paper, we present a label-based approac for implementing deflection in a potonic packet network, and we introduce an algoritm for determining deflection options in a manner wic eliminates looping. A general analytical model is developed to evaluate packet loss probabilities in networks wit deflection. Te analysis may be applied to a wide class of deflection scemes and may be applied to networks wit any arbitrary topology. Te analysis is verified troug simulation. I. INTRODUCTION As telecommunication networks gradually evolve towards data-centric arcitectures, packet-based networks will be required to provide increasingly stringent quality of service requirements in order to support a growing number of ig-speed multimedia applications. Wile electronic packet-switcing tecnology is capable of providing differentiated services based on various priority and buffering scemes, te increasing transmission rates and ig wavelengt densities over eac fiber will eventually make it proibitively expensive to process eac packet electronically at eac node. Emerging all-optical switcing tecnologies will enable packets to traverse nodes transparently witout conversion to electronics. In particular, potonic packet switces ave te potential to offer te flexibility and statistical multiplexing benefits of existing packetswitced networks, wile also eliminating te cost of electronic conversion and processing at eac node. A significant issue in potonic packet switcing is contention resolution. Contention occurs wen two or more packets contend for te same output port at te same time. Typically, contention in traditional electronic packet-switced networks is andled troug buffering; owever, in te optical domain, it is more difficult to implement buffers, since tere is no optical equivalent of random-access memory. Instead, optical buffering is acieved troug te use of fiber delay lines [1]. Note tat, in any optical buffer arcitecture, te size of te buffers is severely limited, not only by signal quality concerns, but also by pysical space limitations. To delay a single packet for 5 µs requires over a kilometer of fiber. Because of tis size limitation of optical buffers, a node may be unable to effectively andle ig load or bursty traffic conditions. Anoter approac to resolving contention is to route te contending packets to an output port oter tan te intended output port. Tis approac is referred to as deflection routing or ot-potato routing [2], [3], [4]. Wile deflection routing is generally not favored in electronic packet-switced networks due to potential looping and out-of-sequence delivery of packets, it may be necessary to implement deflection in potonic packetswitced networks, were buffer capacity is limited, in order to maintain a low level of packet losses. For deflection to be practical in potonic packet networks, metods for overcoming te limitations of deflection must be developed and investigated. Deflection as been studied in a number of previous works. In [2], ot-potato routing is compared to store-and-forward routing in a SuffleNet topology. [3] and [4] compare otpotato and deflection routing in SuffleNet and Manattan street network topologies. In [5], deflection is studied in an unslotted packet network wit a Manattan Street Network topology, and a euristic for sceduling packets to minimize contention is presented. It is sown tat te euristic improves te performance of unslotted networks almost to te level of slotted networks. Since bot te SuffleNet and Manattan Street Network are two-connected (eac node as an outgoing degree of two), te coice of te deflection output port is obvious. Wen te nodal degree is greater tan two, a metod must be developed to select te alternate outgoing link wen a deflection occurs. In [6] and [7], deflection routing is studied in irregular mes networks. Rater tan coosing te deflection output port arbitrarily, priorities are assigned to eac output port, and te ports are cosen in te prioritized order. Wen deflection is implemented, a potential problem tat may arise is te introduction of routing loops. If no action is taken to prevent loops, ten a packet may return to nodes wic it as already visited and may remain in te network for an indefinite amount of time. Te looping of packets contributes to increased delays and degraded signal quality for te looping packets, as well as increased load for te entire network. Standard approaces for eliminating looping, suc as maintaining a op counter for eac packet, can lead to increased complexity wen processing packet eaders. An alternative approac to resolving routing loops is to define te deflection alternatives at eac node in a manner wic eliminates all possibility of routing loops. In [7], deflection is studied togeter wit optical buffering in irregular mes networks wit variable-lengt packets. Te nodes at wic deflection can occur, as well as te options for te deflection port, are limited in suc a way as to prevent routing loops in te given network; owever, a general metodology for selecting deflection options to avoiding looping in any arbitrary network is not given. Wile analytical models ave been developed to evaluate deflection in regular-topology networks [2], [3], [4], no previous

2 work as been done to develop analytical models for evaluating deflection in general mes-topology networks. In tis work, we investigate approaces for implementing deflection in a manner wic eliminates looping, and we present an analytical model for evaluating deflection scemes in arbitrary mes networks. Section II describes te basic network arcitecture and te deflection algoritms. Section III presents te analytical model for evaluating packet losses. Section IV provides numerical results for specific network topologies, and Section V concludes te paper Label switced pat Deflection alternatives 8 II. DEFLECTION ROUTING ALGORITHMS In tis work, we will assume tat deflection is implemented witin a label-switced environment. Eac node maintains a label database wit a number of label entries. Eac label entry indicates, for a given input port and a given label, te corresponding output port and outgoing label. Deflection options are defined by adding additional output-port/label pairs to eac entry in te label database. Wen a packet arrives to te node, te corresponding entry in te label database is referenced, te packet s label is updated to te new outgoing label, and te packet is sent to te appropriate output port. If te primary output port is occupied, ten te packet will be deflected to te alternate output port after updating te packet s label to te alternate outgoing label. In general, labels may be defined on a per-destination basis, on a source/destination pair basis, or on a per-flow basis. For simplicity, we will assume tat labels are defined on a perdestination basis. By utilizing destination-based labeling, te number of label entries at eac node can be kept to a minimum; owever, destination-based labeling also reduces te routing flexibility and traffic engineering options in te network. Figure 1 illustrates te label-switced pats for a given destination node 8, and Fig. 2 sows te corresponding label entry at node 2. Note tat, in destination-based labeling, te label of a packet will remain te same trougout te network. Furtermore, te primary label-switced pats specified for a given destination will define a spanning tree on te network, wit te destination node at te root of te tree. By examining te spanning tree for a given destination, we note tat deflectionalternative links may be added to te tree in a manner wic avoids routing loops. Te process of defining te label entries at eac node can be divided into two sub-problems. Te first problem is to determine te primary outgoing link for eac destination at eac node. In tis paper, we assume tat te link wic is on te sortest pat to te destination is cosen as te primary outgoing link at a node for tat destination. Tese links may be found by running Dijkstra s sortest-pat algoritm for eac source-destination pair in te network, and coosing te firstop link on eac of te sortest-pat routes. Te link weigts in te sortest-pat algoritm are determined by te pysical distance of eac link. An alternative approac for determining te primary links is to coose te links in a manner wic bal- Fig. 1. Label switced pats and deflection alternatives for destination node 8. input output deflect port label port label port label any Node 2 Fig. 2. Label entry at node 2 for destination node 8. ances te load in te network. Suc approaces are beyond te scope of tis paper. Te second problem is to find te set of deflection alternatives for eac destination at eac node, given te set of primary links defined in te previous problem. Te deflection alternatives at eac node must be defined in a way wic eliminates te possibility of routing loops. Te deflection-finding problem can be formulated in grap teoretic terms. Given a grap G(V,E), and a directed spanning tree, T v, rooted at vertex v, and wit edges, E Tv, directed towards te root, te problem is to find a set of edges E Dv E suc tat te directed grap R v = (V,E Tv E Dv ) is acyclic. Te following looplessdeflection algoritm is proposed to find a feasible set of deflection edges. We define δ(v) to be te nodal degree of a vertex v, and dist(u, v) to be te op distance from node u to node v. LOOPLESS-DEFLECTION: Given : A grap G=(V,E). V spanning trees, T v =(V Tv,E Tv ), eac wit a unique root vertex, v V. Find : E Dv, te set of deflection edges. Directed routing graps, R v =(V,E Rv ), v V. Step 0 : Set V = V. Set E Dv = { o}, v V. Step 1 : Select a vertex v V. Set E = {E E Tv }. Let d v be te dept of tree T v.

3 Let S i, i {1, 2,...,d v } be te set of vertices wic are distance i from te root node v. Set k = d v. Step 2 : Select vertex u S k suc tat δ(u) =min u S k δ(u ). Step 3 : Select a directed edge, e(u, w), suc tat dist(w, v) = min w :e(u,w ) E dist(w,v), if suc an edge exists. Set E Dv = E Dv e(u, w). Step 4 : Remove all edges e(i, u), i and e(u, j), j from E. Remove node u from S k.ifs k = { o},tenk = k 1. If k 0,tengotoStep2,oterwise,gotoStep5. Step 5 : Set R v =(V,E Tv E Dv ). Remove node v from V. If V { o}, ten go to Step 1, oterwise, stop. Te loopless-deflection algoritm selects nodes one at a time, and attempts to find a deflection output port at te selected node. By selecting leaf nodes wic are furtest from te root, and by deleting te node after its deflection output port as been selected, te algoritm ensures tat no deflections are made to nodes wic are furter from te destination tan te selected node, and tat packets, upon departing from te selected node, can never return to tat node. In Step 3, te algoritm attempts to coose te deflection edge wic results in te sortest pat to te destination. Te algoritm can be furter customized in Step 3 by coosing te deflection edges based on estimated link loads, or by allowing multiple deflection options for eac destination. If multiple deflection options are allowed, te options may be prioritized based on distance or load considerations. Since te proposed algoritm does not allow loops, it is possible tat a node will not ave any deflection alternatives for a given destination. In particular, tose nodes wic are closer to te destination are less likely to ave deflection alternatives tan nodes wic are furter from te destination. By restricting deflection at tese nodes, te packet losses may increase. For comparison, we also consider a deflection-finding algoritm wic allows looping. Te algoritm starts wit te grap G(V,E) and te directed tree, T v, rooted at destination v. Eac node is selected one at a time in any order. For eac node, te algoritm selects te deflection edge wic results in te sortest pysical-distance pat to destination v. Edges in te tree T v are used for primary-pat routing, terefore tese edges are not considered wen selecting te deflection edge. Unlike te loopless-deflection algoritm, nodes and edges are not deleted once a deflection edge as been cosen; tus, routing loops are possible. We will refer to tis algoritm as te sortest-pat deflection algoritm. III. ANALYTICAL MODEL In tis section, we develop an analytical model for evaluating te packet loss probabilities of te proposed deflection sceme. Te model is general, and can be applied to any irregular mes topology. Te analysis can also be used to evaluate any deflection sceme in wic te deflection alternatives at eac node are ordered and pre-defined. Te model assumes tat te network is asyncronous, and tat packet ave a fixed lengt of L seconds. Packets arrive to te network according to a Poisson process wit rate packets per second for source-destination pair sd. Eac link in te network is modeled as an M/D/1/1 queue wit no buffers. Te arrival rate, λ ij of packets to a link l ij is determined by aggregating te packet arrivals from all sourcedestination pairs wic route packets over te link. Te arrival rates will also depend on te probability of contention, P ij,on eac link in te network, and te deflection policy. To find te contention probabilities, we examine te time between packet departure instants and calculate te fraction of time tat a link is busy. Te expected cycle time, T, between two consecutive packet departures is found by adding te expected time until te next packet arrival to te expected packet transmission time: E[T ]= 1 + L. (1) λ ij Te probability tat a packet arriving to link ij encounters contention is equal to te probability tat te link is busy: P ij = L E[T ]. (2) Based on te link blocking probabilities, we can find te offered load, λ ij, on eac link l ij.wedefiner sd as te primary route from source s to destination d witout deflection. Te load on a link is te sum of te loads contributed by eac source-destination pair wic routes packets over te link: λ ij = s,d ij, (3) were ij is te rate at wic packets sourced at s and destined for d arrive to link l ij. Te load placed on a link l ij by traffic going from source s to destination d depends on weter link l ij is on a primary pat to destination d, or weter te link is a deflection link to destination d. If link l ij is on a primary pat to d, and node i is te source node s, te load applied to link l ij by sd traffic is simply. If link l ij is on a primary pat to d, but node i is not te source node, ten te applied load will be te load offered by previous-op links, l i, wic are sending packets to d troug link l ij. Te load is reduced by te amount of contention on te links l i. If link l ij is te deflection link for a primary link l sk at te source node s, ten packets will arrive to link l ij if te packets experienced contention on link l sk ; tus, te load on l ij will be P sk. If link l ij is a deflection link at an intermediate node, and link l ik is te corresponding primary link to destination d fromnodei, ten te applied load

4 on link l ij will be te incoming load from all previous-op links wic are sending traffic to d troug i, and wic encounter contention on link l ik. Tus, we ave: ij = if l ij r id, i = s (4) = i (1 P i) if l ij r sd, i s (5) = i(1 P i ) if l ij / r sd, i = s, l ij r id (6) = P sk if l ij / r sd, i = s, l sk r id (7) = i(1 P i )P ik if l ij / r sd, i s, l ik r id. (8) Once te above equations are solved to find P ij, te packet loss probability can be found for packets traveling from source s to destination d. A packetwill be lost if, on a givenop, bot te primary and deflection links are blocked. Let node i be te primarynext-opnode, andlet j be te deflection next-op node. Te packet loss probability for packets travelling from source node s to destination node d is given by: P sd loss = P sip sj +(1 P si )P id loss + P si(1 P sj )P jd loss. (9) Te packet loss probability for te entire network is found by calculating te weigted average of te packet losses for eac source-destination pair: P loss = s,d P sd loss ( s,d λs d ). (), te analysis will stop evaluating a pat if te additional load on te next link in te pat is less tan some small value ɛ. Wen evaluating te packet loss probabilities, te analysis will stop evaluating a pat once it reaces a certain number of ops. Altoug te analysis assumes tat tere is at most one deflection alternative for eac destination at eac node, te analysis can be extended in a straigtforward manner to accommodate te case in wic tere is an arbitrary number of ordered deflection alternatives for eac destination at eac node. Te analysis may also be applied to deflection scemes in wic looping is present; owever, te analysis must be modified sligtly in order to avoid infinite pat lengts. Wen calculating P ij and ij IV. NUMERICAL RESULTS In tis section, we evaluate te deflection algoritms in te 15-node network topology illustrated in Fig. 3, and in a bidirectional Manattan street network topology in wic te nodal degree at eac node is equal to 4. Packets are fixed in lengt, consisting of,000 bits eac, and te transmission rate is assumed to be Gb/s. Packets arrive to te network according Fig node network topology. to a Poisson process, and traffic is uniformly distributed over all source-destination pairs. Figure 4 sows te packet loss probability as a function of load for te 15-node network. We observe tat te loopless deflection sceme provides a sligt improvement in performance over te case wit no deflection, wile te deflection sceme witout any looping restrictions offers significantly lower packet loss probabilities tan eiter of te oter two cases. Te restrictions placed on deflections in te loopless deflection case limit te number of nodes at wic deflections can take place. Tese limitations lead to iger packet losses compared to te sortest-pat deflection sceme. Te packet loss probability for te bidirectional Manattan street network is sown in Fig. 5. In tis network, te iger nodal degree enables a larger number of nodes to ave deflection options in te loopless deflection case. Consequently, in a network wit a iger nodal degree, te loopless deflection case will provide greater benefits over te case in wic no deflections take place. In Fig. 6, we plot te packet loss probability for iger network loads in te 15-node network. We observe tat, for ig loads, te sortest-pat deflection sceme as te igest packet loss rate, wile te sceme wit no deflection as Fig. 4. Packet loss for 15-node network topology.

5 Fig. 5. Packet loss for Manattan street network topology. Average Hop Distance Fig. 7. Average op count for 15-node network topology Fig. 6. Packet loss for 15-node network topology under ig loads. te lowest packet loss rate. Under iger loads, te number of contentions will increase, resulting in a greater number of deflections in networks. Te increased deflections will increase te effective network load and cause iger blocking probabilities. Te same general results are found for te Manattan street network, wit te cross-over points occuring at iger loads tan in te 15-node network. Results for te Manattan street network are not sown due to space constraints. Figure 7 sows te average op distance traversed by eac packet as measured by simulation in te 15-node network. For te sortest-pat deflection sceme, as te load increases, more packets are being deflected, leading to iger average op distances; owever, packets are still reacing teir destinations, indicating tat deflection is successfully resolving contention. As te load increases furter, te average op distance begins to drop. Te drop indicates tat, wile packets are still being deflected, te deflected packets are not as likely to reac teir destination. At tis point, deflection starts to become detrimental rater tan beneficial. For bot te loopless deflection sceme and te sceme wit no deflection, te average op distance decreases as load increases. Tis effect indicates tat tere is some degree of unfairness in te network, since a packet wic must travel a greater number of ops to its destination as a iger cance of being dropped. V. CONCLUSION In tis paper, we investigated te use of deflection routing to resolve contentions in a label-switced potonic packet network, and we introduced an algoritm for determining te deflection alternatives in a manner wic eliminates te possiblity of routing loops. A general analytical model, wic can be applied to a wide range of deflection scemes and on arbitrary network topologies, was developed to evaluate te loopless deflection sceme. It was sown tat, under low loads, te loopless deflection sceme provides modest gains over te sceme wit no deflection, and tat te gains increase for networks wic ave a iger average nodal degree. An unrestricted deflection sceme, in wic loops are allowed, provides significantly lower packet losses at low loads, but results in iger average packet op distances. At ig loads, te deflection scemes result in iger packet losses. Overall, te loopless deflection sceme offers a reasonable trade-off between packet losses and average op distance. REFERENCES [1] I. Clamtac, A. Fumagalli, L. G. Kazovsky, et al., CORD: Contention Resolution by Delay Lines, IEEE Journal on Selected Areas in Communications, vol. 14, no. 5, pp , June [2] A. S. Acampora and I. A. Sa, Multiop Ligtwave Networks: A Comparison of Store-and-Forward and Hot-Potato Routing, IEEE Transactions on Communications, vol. 40, no. 6, pp , June [3] F. Forgieri, A. Bononi, and P. R. Prucnal, Analysis and Comparison of Hot-Potato and Single-Buffer Deflection Routing in Very Hig Bit Rate Optical Mes Networks, IEEE Transactions on Communications, vol. 43, no. 1, pp , Jan [4] A. Bononi, G. A. Castanon, and O. K. Tonguz, Analysis of Hot-Potato Optical Networks wit Wavelengt Conversion, IEEE Journal of Ligtwave Tecnology, vol. 17, no. 4, pp , April [5] T. Cic, J. Coen, and P. Fraigniaud, Unslotted Deflection Routing: A Practical and Efficient Protocol for Multiop Optical Networks, IEEE/ACM Transactions on Networking, vol. 9, no. 1, pp , Feb [6] G. Castanon, L. Tancevski, and L. Tamil, Routing in All-Optical Packet Switced Irregular Mes Networks, Proceedings, IEEE Globecom 99, Rio de Janeiro, Brazil, pp , Dec [7] S. Yao, B. Mukerjee, S.J.B. Yoo, and S. Dixit, All-Optical Packet- Switced Networks: A Study of Contention Resolution Scemes in an Irregular Mes Network wit Variable-Sized Packets, Proceedings, SPIE OptiComm 2000, Dallas, TX, pp , Oct