AnyTraffic Labeled Routing

Transcription

1 AnyTraffic Labele Routing Dimitri Papaimitriou 1, Pero Peroso 2, Davie Careglio 2 1 Alcatel-Lucent Bell, Antwerp, Belgium imitri.papaimitriou@alcatel-lucent.com 2 Universitat Politècnica e Catalunya, Barcelona, Catalonia, Spain {pperoso,careglio}@ac.upc.eu Abstract This paper investigates routing algorithms that compute paths along which combine unicast an multicast traffic can be forware altogether, i.e., over the same path. For this purpose, the concept of AnyTraffic group is introuce that efines a set of noes capable to process both unicast an multicast traffic receive from the same (AnyTraffic) tree. The resulting scheme is referre to as AnyTraffic routing. This paper efines a heuristic algorithm to accommoate the AnyTraffic group an to fin the proper set of branch noes of the tree. The algorithm supports ynamic changes of the leaf noe set uring multicast session lifetime by aapting the corresponing tree upon eterioration threshol etection. Stuies are performe for both static an ynamic traffic scenarios to i) etermine the epenencies of the algorithm (noe egree, clustering coefficient an group size); an ii) evaluate its performance uner ynamic conitions. Initial results show that the AnyTraffic algorithm can successfully hanle ynamic requests while achieving consierable reuction of forwaring state consumption with small increase in banwith utilization compare to the Steiner Tree algorithm. W I. INTRODUCTION ITH the avent of multimeia vieo stream/content, multicast istribution from a source to a set of estination noes is (re-)gaining interest as a banwith saving technique competing or complementing cache content istribution. Nevertheless, the problems face in the 90's when multicast receive main attention from the research community are still present. Routing protocol epenent multicast routing schemes (such as Distance Vector Multicast Routing Protocol an Multicast Open Shortest Path First) have been replace by routing protocol inepenent routing schemes such as Protocol Inepenent Multicast (PIM) an Core Base Trees. However, number of entries in routing an forwaring tables (states) an their maintenance is an remains a major problem. Two forwaring approaches are commonly use in current atagram networks, namely 1) forwaring on a set of point-to-point (P2P) paths to encapsulate whether unicast or multicast traffic (i.e., multicast traffic is replicate as many times as the number of ege noes processing multicast traffic); an 2) forwaring on a set of eicate P2P paths for unicast traffic an eicate point-tomultipoint (P2MP) paths for multicast traffic. The latter can be either root-initiate as in source-specific multicast or leafinitiate as in any-source multicast. Regarless of the unerlying forwaring paraigm, a router must maintain membership state for each multicast group. Multicast membership states are store as entries in the routing table that is subsequently use to erive a forwaring table. The latter etermines the actual forwaring of an incoming packet to a router's outgoing interfaces. However, unlike unicast routing, there is no natural aggregation in multicast forwaring states thus a router may take a long time to look up the forwaring state for each arriving packet when there are a large number of multicast group [1]. This results in limite scalability of any multicast routing eployment. Several research efforts have propose methos to reuce the number of multicast forwaring state through aggregation [2] [3], tunneling [4], an no-branching state elimination [5] [6]. Even if some of these techniques might be consiere as acceptable, the propose concept is totally new an tries to improve such existing algorithms by achieving lower state consumption at low banwith consumption increment. In this paper, we investigate routing algorithms that compute paths along which both unicast an multicast traffic can be forware. Section II etails the newly introuce concept together with the joint forwaring process. The AnyTraffic heuristic algorithm is formulate in Section III for both static an ynamic routing. Performance results obtaine for both cases together with their analysis are presente in Section IV. Future work an conclusions are rawn in Section V. II. ANYTRAFFIC ROUTING CONCEPT This paper proposes a traffic routing approach, whose compute paths enable forwaring of both unicast an multicast traffic together, i.e., over the same path. For this purpose, the concept of AnyTraffic group is introuce that efines a set of noes capable to process both unicast an multicast traffic receive from the same istribution tree, the AnyTraffic tree. The resulting routing scheme is referre to as AnyTraffic routing. This paper efines a heuristic algorithm to accommoate the AnyTraffic group an to fin the proper set of branch noes of the AnyTraffic tree. It also provies for a performance evaluation of the propose scheme against two commonly use approaches. Introucing an AnyTraffic istribution tree to a group aims at reucing the total number of forwaring states by maintaining (as much as possible) a single path for both unicast an multicast traffic forwaring altogether. In other terms, a single state allows for both unicast an multicast traffic forwaring. The iea is to perform label-base forwaring (where labels encoe topological information) using a single forwaring table entry for both unicast an multicast labele traffic irecte towar the same "label". Network noes are name with estination labels that encoe topological information. These labels are use in the forwaring ecision process: each atagram carries the chosen estination in its heaer. At intermeiate noes, a iscriminator (set at network ingress noe) allows selecting either a unicast (one-to-one) or a multicast (one-to-many) forwaring entry associate to the same label entry. Differentiation between incoming unicast /10/$ IEEE

2 an multicast traffic is simply performe by means of a (single-bit) iscriminator. Thus, the propose routing scheme is applicable to any label-base forwaring technology as long as the following conitions are met: i) capability to istinguish multicast from unicast traffic by inspecting other heaer information than the estination aress (e.g. label flag to iscriminate between unicast an multicast traffic following the same path); an ii) e-multiplexing of traffic at estination noes relies on the information encoe as part of other heaer information not processe by each network noe. This scheme can be seen as a unification of the locator/ientifier split concept where the locator value space names topological en-points that are able to terminate any traffic an the ientifier value space allows istinction (at the eges) between unicast an multicast traffic. Ingress ege noes upon multicast traffic ientification tag this traffic as part of the label. Base on this inication, branch noes along the AnyTraffic tree replicate the multicast traffic onto outgoing interfaces towars ege noes registere for the corresponing multicast group(s). On the other han, the unicast traffic irecte to these ege noes is not replicate at branch noes but follows as short as possible paths. The salient feature of the propose scheme is that the multicast traffic oes not require any aitional forwaring entry on intermeiate network noe to reach the topological location where the traffic is then natively processe. The aim of the propose routing scheme is to achieve better system resource consumption (for state maintenance) while limiting the network resource consumption, i.e., mitigate the state vs. banwith resource traeoff by increasing the common path stretch. The propose approach keeps the forwaring state maintenance overhea as low as possible while avoiing banwith waste by i) avoiing replication of multicast traffic at branch noes, an ii) keeping unicast traffic forwaring over as short as possible paths. To meet this objective combine with the ecrease in hop count of P2P paths, a eficit factor an an aaptive threshol function for the selection of the branch noes are specifie to ecie where to separate the unicast from the multicast forwaring path (i.e., the placement of a branch noe). This algorithm is also esigne so as to efficiently operate in a ynamic environment where receivers are joining an releasing multicast sessions. Besie the reuction of the number of states, the AnyTraffic routing scheme can also hanle more efficiently join an leave requests. Here, as both types of requests may eteriorate the system resource performance compare to the optimal case, a reajustment mechanism is esigne so as to accommoate actual receivers ynamics by aapting the multicast tree. Finally, resulting from the type of routing information it processes, the propose routing scheme applies typically within network partitions (intra-omain). III. ANYTRAFFIC ROUTING ALGORITHM Consier a network moele by a irecte graph G = (N, L), where N represents the finite set of noes, an L represents the finite set of links. Let s, N enote a source an a estination noe, respectively. Each link l L might have an associate capacity b(l), an cost c(l). Let p i,j an p i,k,j both enote a path from noe i to noe j, where k is an intermeiate noe with i j k.let T s,m = (N T, L T ) be a connecte subgraph without cycles (i.e., a tree) of G, source-initiate at s, an with the set of estination noes M N T \ {s}, M. Hereafter, M is referre to as the AnyTraffic group, an T s,m as the AnyTraffic tree. A. Static AnyTraffic Heuristic Algorithm Let φ s,m enote a traffic request between source s an a AnyTraffic group M, where M N T \ {s}, M. If M = 1, φ s,m is a request for unicast traffic. The objective of the AnyTraffic routing algorithm is to construct a graph T s,m for a given source s an AnyTraffic group M, such that T s,m supports both unicast an multicast traffic requests. The graph T s,m is constructe by successive selection of branch noe, n* N. At a given source noe s, processing of the request φ s,m epens on its nature, i.e., it is either a unicast or multicast traffic request. We have the following alternatives: i) if a multicast traffic request φ s,m arrives an an AnyTraffic tree T s,m is available, then the request is supporte by T s,m ; otherwise, the AnyTraffic routing algorithm is execute (see Section III.A.2) to establish a new AnyTraffic tree; ii) if a unicast traffic φ s, request arrives, three situations can occur: (a) M an T s,m (with M > 1) is available an φ s,m is supporte by T s,m ; (b) M but T s,m is not yet create an thus a shortest path must be setup; or (c) M an thus a shortest path must be setup. The AnyTraffic routing algorithm comprises two phases, namely, the initialization an tree computation phase. 1) Initialization Phase Let x i,j enote the cost of the shortest path from noe i to j, i j, as compute by the Dijkstra algorithm on the (positive integer) link cost c(l), l L. The hop count is use as tiebreaker. Methos for computing the cost c(l) of each link l L can be foun in [7]. Accoringly, x s, enotes the cost of the shortest path from the source s to the estination M. Among all path costs, c max correspons to the shortest path of maximum cost. Let F(x): + + be efine as: g ( x) = + c max F ( x) x 1 e (1) This function specifies the threshol for the maximum cost of an alternative path to the path of cost x [7]. In particular, F(x s, ) limits the acceptable cost eviation of an alternative path p s,, M, from the path given by the Dijkstra algorithm. The function g(x): +, is efine as g(x) = αx - β, where parameters α, β [0,1[ efine the shape of the threshol function. High values for α an β woul make the function too restrictive, allowing only for low path stretch. On the other han, low values woul result into too high path stretch. Having efine F, we can specify the maximum eficit factor M s, for each shortest path p s,,: s, = F( xs, ) s, s, g ( x) c max Δ M x = x e (2) This factor etermines the acceptable cost increment(s) of an alternative path against the shortest path, i.e., it quantifies the tolerable cost eviation when forwaring both multicast an unicast traffic on that path without incurring too much amage

3 compare to unicast traffic forwaring along the shortest path. Being only epenent on the topology, x s,, c max, g(x s, ), an M s, can be compute uring the initialization phase for any pair (s,) N (values remain constant uring the tree computation phase). 2) Tree Computation Phase Let s efine a leaf as the tuple ω υ,λ = {υ, Λ}, where υ N is a leaf see an Λ M is a subset of the AnyTraffic group. We efine Ω as the set of leaves remaining to be processe. At the beginning, this set comprises only the initial leaf, Ω = {ω s,m }, where s is the see from where computation is initiate, which comprises all estination noes M. We also efine the initial graph T s,m = ({s}, ). The algorithm terminates when there is no leaves left in Ω an all estinations M can be reache from s in T s,m. At each iteration step, an arbitrary leaf ω υ,λ is pulle out from Ω an the algorithm searches for a branch noe n* N to be inclue in T s,m such that s is connecte through n* to a subset of noes comprise in Λ. For this leaf ω υ,λ, a set of caniate branch noes A ω is foun. The set A ω is restricte to unvisite noes in previous iterations that are ajacent to υ an have a noe egree equal or greater than three, i.e., the noes that have at least two outgoing links, apart from the outgoing link to noe υ. In case the noe egree of an ajacent noe a is two, the first noe with noe egree equal or greater than three an laying on a path going from υ through a is inclue into A ω. At each caniate branch noe n A ω being evaluate, one alternative path p v,n, per estination M, starting at υ but force to pass through n is compute. A pruning conition etermines if the set of alternative paths from υ to each L an passing through n coul be accepte. Inee, each path p v,n, may introuce higher cost (x v,n + x n, ) when compare to the cost x v, of the shortest path p v,. Therefore, a local eficit L v,n, is compute for each Λ by means of: ( ) Δ L = x + x x (3) υ, n, υ, n n, υ, For each Λ, a cumulative path eficit P s,, sums up, at noe n, the local eficits prouce by the alternative path p s, passing by alreay accepte branch noes n 0 (= s), n 1,,n u of T s,m an the caniate branch noe n u+1 (= n): u u ( ) i i+ 1 (4) i i+ 1 Δ P = Δ L = x + x x s, i= 0 n, n, i= 0 n, n n, s, Then, for each Λ, a comparison between the cumulative path eficit (Eq.4) an the maximum eficit (Eq.2) is performe. If the maximum eficit constraint P s, M s, is verifie, i.e., if the cumulative eficit of an alternative path p s, oes not excee the maximum eficit, the alternative path can be accepte. Otherwise, the algorithm removes noe from ω υ,λ an creates a new leaf. When all caniate branch noes have been evaluate, branch noe selection can be performe by running the pruning conition for each Λ. The ecision is taken by consiering the minimum total eficit among all caniate branch noes n A ω. However, to reach ecision fairness, consiering the eficit base on the cost metric only is insufficient. Hence, we further poner the eficit of each caniate branch noe n by i) summing a fraction γ of the local eficit (Eq.3) to a fraction (1 γ) of a local eficit H v,n, efine as Eq.3 but using the hop count instea of the cost metric; ii) multiplying by a factor σ the ratio r, efine as the number of alternative paths meeting the pruning conition ivie by the total number of paths that can reach all estinations, i.e., Λ, via n A ω. The parameter γ governs the selection trae-off between longer but lower cost paths among the successful alternative paths meeting the pruning conition (high γ values), an shorter paths thus, lower probability to aggregate paths (low γ values). The parameter σ is a weight factor that favors caniate branch noes with a higher number of successful alternative paths. For each caniate branch noe, a caniate eficit C n,ω is compute as: Δ Cn, ω = γ Δ Lυ, n, + ( 1 γ) ΔHυ, n, σ r (5) The caniate branch noe n with the lowest eficit is selecte as a branch noe n*. Accoringly, T s,m is upate with all links an noes that lay on the path from υ, the see of the currently processe leaf ω υ,λ, to n*. Then, two new leaves may be create, ω 1 = {n*, Λ n* } (leaf with the subset of estination noes Λ n* that accepte n* as branch noe), an ω 2 = {υ, Λ \ Λ n* } (leaf with the estination noes remove by the pruning conition). Leaves ω 1 an ω 2 are conitionally ae to the set Ω for further processing, respectively, if Λ n* > 1 an Λ \ Λ n* > 1. If either Λ n* = 1 or Λ \ Λ n* = 1, T s,m is upate with all links an noes along the shortest path, respectively, from n* to Λ n* an from υ to Λ \ Λ n*. Branch noe n* is exclue from the set of ajacencies of υ, i.e., A ω2 = A ω \ {n*}. Branch selection is repeate for each leaf left in Ω. 3) Complexity Analysis The complexity of this algorithm is O ( M A H), where M is the size of the AnyTraffic group, A is the maximum noe egree, an H is the hop istance between the source an the most istant estination noe. This boun comes from the fact that at each hop towars the estination all ajacent noes are checke as caniate branch noe for the estination noes belonging to M. In a regular connecte network (A << N ), the complexity is low an it may be further reuce by limiting the set of ajacent noes that are within a given perimeter with respect to the next noe along the shortest path to each estination noe. Results achieve by applying this metho show no performance egraation while significant reuction of running time. B. Execution Example Fig.1 shows two consecutive steps of the branch noe evaluation mechanism. We consier as initial leaf Ω s,m, where s is the noe processing the incoming requests for both unicast an multicast traffic, an the AnyTraffic group M={1,2}. Fig.1a represents the evaluation of the set A ω of ajacent branch noes for estination 1. The set A ω ={1,2,3} correspons to the ajacent noes of s with a noe egree equal or higher than three. The path through noe 1 is the shortest path an its cost x s,1 gives the value of the maximum eficit factor M s,1. For each of the remaining ajacent noes, an alternative path is compute. The alternative path through noe 2 an the one through noe 3 may introuce higher cost with respect to the shortest path; these costs efine the cumulative path eficit factor P 1 s,1 an P2 s,1 respectively. At this step, an ajacent noe is accepte as

4 caniate branch noe if the pruning conition is verifie; for example noe 2 is accepte if the cost of its alternative path P 1 is lower than M s,1 s,1. The same evaluation is then repeate for each remaining estination noe. Fig.1a also epicts evaluation for estination noe 2. Once all ajacent noes have been evaluate through the pruning conition, branch noe selection is performe. For each accepte caniate branch noe, the caniate eficit factor C n,ω is compute. The noe with the lowest value is selecte as branch noe. Assuming that the caniate branch noe 2 is selecte which correspons to this situation epicte in Fig.1b, noes s an 2 are ae to T s,m. The leaf see is now ω 2 M, the set of ajacent noes of noe 2 is A ω ={1,3,4,6}, an three alternative paths are consiere (the path through noe 4 was alreay accepte from the previous step). The same process escribe in the previous iteration is then repeate. Fig.1: Two consecutive steps of the branch noe evaluation mechanism C. Dynamic AnyTraffic Heuristic Algorithm Let φ s, an ϕ s, enote respectively, a join an a leave request between source s an estination. Graph T s,m = (N T,L T ) maintenance by the AnyTraffic algorithm uner ynamic traffic requests conitions consists in appening noe N T to the graph T s,m when a join request φ s, arrives, an releasing noe M from T s,m when a leave request ϕ s, arrives. Graph T s,m is built up by iterative selection of branch noes n N T. 1) Join request As regars join requests, the unicast traffic is forware over either i) a shortest path if the receiver is not a member of any AnyTraffic group, or ii) an existing AnyTraffic tree. As regars multicast, two other situations can occur: i) initiate a new AnyTraffic tree; or ii) join an existing AnyTraffic tree at one of its branch noe. In any case, if an existing P2P path, roote at the same source noe, is up for such receiver, it is aggregate to the establishe AnyTraffic tree. A possible approach for a receiver to join an existing tree woul be to recompute the entire tree as if a new group request woul arrive (using the static algorithm). Such computation is optimal for a given receivers group an can thus be consiere as an upper boun on the algorithm performance. The isavantage is the nee to re-establish the entire tree each time a join request is receive. To overcome this situation, we propose an extene mechanism to upate the tree without re-computing the entire tree. Using this approach, eviation from the best case (as given by the static algorithm) is controlle by the mechanism of Section III.C.3. Let s assume a new receiver noe N T attempts to join the AnyTraffic group M supporte by the tree T s,m. Upating the tree on-the-fly lies in joining the closest noe of the tree uner the maximum eficit constraint. The algorithm performs the following steps: 1) A Breath-First Search algorithm is execute to fin a set of caniate branch noes A ω N T with the shortest hop count to noe ; 2) For each noe n A ω, fin the shortest path p n, to the receiver. For each path p s,n, obtaine by splicing path p s,n, which is etermine by the tree T s,m, an p n,, calculate its eficit P s,. Then, among all these paths, select the path with the smallest eficit P s,, such that it satisfies the constraint P s, M s, ; 3) If such path p s, is not foun, step 1 is repeate by excluing the alreay processe noes from the set of caniate noes A ω ; 4) Once these steps are complete, as the receiver may still have unicast connectivity roote at the source noe of the AnyTraffic tree, the corresponing forwaring table entries are remove an traffic is forware over the tree. 2) Leave/Prune request When a multicast traffic receiver wants to leave an AnyTraffic tree, the simplest operation consists of pruning the leaves of the tree which are not use by any other remaining receivers. This leas to two cases: the leaf noe coul be either a estination noe or an intermeiate noe of the tree. Let s assume a receiver b T s,m, attempts to leave the AnyTraffic group M. The following operations must be performe: 1) if noe b is a leaf noe, then the path from branch noe n to noe b must be prune; 2) if noe b is an intermeiate noe, the entry for this noe must be remove from forwaring table. The forwaring state is not remove because some receivers are still active along the path. In both cases, a check is performe to verify if any P2P path is up for the leaving receiver. In case the receiver is a member of other AnyTraffic group an the releasing branch noe crosses one of the corresponing AnyTraffic tree, unicast traffic may be reirecte over one of the existing trees. Concerning unicast release requests, if the receiver is a member of a multicast session, then the request oes not result into any state upate if the corresponing path shares the same forwaring state with an AnyTraffic tree. 3) Deterioration Control In a ynamic environment, after a certain perio, join an leave requests eteriorate the entire AnyTraffic trees, ue to the unpreictability of events. The process of locally reaapting the tree pursues the etection of eterioration, i.e., eviation of the re-aapte tree from the best case. The eviation is compute by the formula w D s + (1-w) D b (Eq.6), where D b an D s accounts respectively for the banwith an state consumption ifferences. To penalize higher state consumption, D b an D s are weighte asymmetrically by the weight factor w. Higher w values imply re-computation when

5 excessive states are use compare to the best case; lower values mean that eviation in terms of consume banwith leas to re-computation. The pre-etermine eterioration threshol value is use to ecie to either continue with the on-the-fly aapte tree (up to a certain eviation from the best case) or instea shift to a full tree re-computation. A high threshol value means less re-computation; on the contrary, a low value means stricter control, avoiing banwith an state consumption at the expense of more computation. 4) Complexity Analysis The time complexity is O (A H' N T ), where A is the maximum noe egree, H' is the hop istance between the noe to be attache to the tree an the most istant noe of the tree, an N T is the number of noes of the tree. Inee, the number of iterations the algorithm performs epens mainly on the caniate branch noe search, implemente by the Breath-First Search algorithm. At each hop, the algorithm explores ajacent noes looking for caniate branch noes. Then, for each caniate noe, the constraint compliance proceure is applie. In the worst case, all noes have to be checke. The time complexity can be approximate by O( N T ) since any noe of the graph G is visite at most only once. IV. PERFORMANCE ANALYSIS Simulations are performe to estimate the performance of the AnyTraffic algorithm in terms of banwith an state consumption, uner the following scenarios: i) non-blocking static traffic; ii) ynamic traffic with limite capacity per link. Two reference approaches are use for comparison purpose: approach 1 (AP1) that forwars both unicast an multicast traffic along "as short as possible" paths (shortest path routing); an approach (AP2) that makes use of shortest path routing for unicast traffic an replication of multicast traffic at branch points of a tree as compute by the minimum-cost path algorithm, a Steiner Tree Heuristic (STH) [8]. For the ynamic scenario, the latter has been extene with a Greey treebase algorithm [9] to process ynamic requests. A. Experimental Setup Experiments are execute on the a-hoc simulator evelope in [7] an here extene to operate on an event-basis. In orer to etermine their topological epenencies, ifferent network topologies are consiere: 37-noes Cost266 [10]/Ran37 an 50-noes Germany50 [10]/Ran50 networks. Ran topologies are generate from a ranom sequence of noe egrees [11]. Each network noe is an ingress-egress noe generating, in a boun an iscrete process, 150 (200) traffic requests for the static (ynamic) scenario. Both unicast an multicast traffic are generate within a range of two iscrete traffic classes: class 1 of 2 Mbps, an class 2 of 8 Mbps. Different unicast an multicast traffic percentages are consiere, namely 50%- 50%, 75%-25%, an 95%-5%. For each multicast session, the size of the estination noe set M ranges between log 2 (N) an [log 2 (N)] 2, where N represents the number of noes. After performing a number of experiments, we set α=0.7 an β=0.3 in the function F(x) (Eq.1), an selecte the values γ=0.5 an σ=2 for the caniate eficit C n,ω (Eq.5). State consumption measures the number of forwaring states require to accommoate each traffic ratio. We also efine the relative gain as the percentage of performance gain in terms of either banwith or state consumption, attaine when AnyTraffic routing is compare to AP1 an AP2. A negative gain means a loss for the AnyTraffic algorithm. B. Results 1) Static Scenario The simulation steps consist in i) creating the network entities (trees) for the AnyTraffic groups, an then ii) processing the unicast requests looking for the minimum cost path among the create trees. Fig.2 shows the results obtaine for the Cost266 an Ran37 networks in terms of relative gain in state consumption with respect to the generate percentage of unicast an multicast traffic ratios. Banwith consumption figures are not shown but results analyze here below. Fig.2: State Consumption for Cost266 an Ran37 networks From Fig.2, AnyTraffic routing shows goo performance in terms of state consumption compare to both AP1 an AP2 for the range 50% to 95% of unicast traffic. As the latter increases, the gain increases (from approximately 8 to 73% in the AP2 case). However, in terms of banwith consumption, AnyTraffic routing oes not lea to the same performance gain ue to the longer paths followe by unicast traffic. For example, when compare with AP2, it consumes from 4.4% to 7.2% more banwith in the Cost266 network, an from 4.5% to 5.6% in the Ran37 network. AnyTraffic routing shows better performance compare with AP1: it consumes between 25% an 80% less banwith than AP1. The same behavior is observe for both German50 an Ran50 networks although a bit less favorable. In terms of state consumption, the gain ecreases from 32% to 6% for the range 50% to 95% of unicast traffic when compare to the Cost266 network. This observation reflects that more noes with higher noe egree influence the performance of the AnyTraffic algorithm. We also observe, for networks of ientical size but lower clustering coefficient, that the algorithm performs better because it favors path aggregation at a lower eficit P s,. The epenency of AnyTraffic routing with respect to the size of the group has also been stuie. In terms of state consumption, although the gain is always positive for the whole set of unicast-multicast traffic pairs, a ecreasing tren is observe. As the group size increases, the create AnyTraffic trees are pushe up to their limits (i.e. stretche) by becoming longer an thus requiring more states. As regars banwith consumption, the worst gain is never lower than

6 -8%. The concave shape observe for the 50%-50% an 75%- 25% traffic pairs is steeper as the percentage of unicast traffic increases (as longer tree branches increase the banwith consumption). Fig.3: 100-noe network: State an Banwith consumption gain Fig.4: Cost266 network: State consumption gain for the AnyTraffic The overall algorithm s behavior for larger topologies is close to the small topologies experimente in [7]. Fig.3 shows the performance of the AnyTraffic algorithm for a 100-noe network topology. To reuce computational time, only 25% of noes as ingress-egress noes are consiere. As regars state consumption, the algorithm emonstrates goo performance compare with AP2 in the range 50%-95% of unicast traffic. The gain curve follows an exponential growth from 4% up to 70%. In terms of banwith consumption, AnyTraffic routing shows worst performance (up to -10%) for unicast traffic ue to the longer paths followe by this traffic. Although the banwith consumption gain remains negative, it shows a positive tren from -10% to -7%. Inee, as less AnyTraffic trees are create by multicast requests, forwaring unicast traffic requires more P2P shortest paths (consuming less banwith). Therefore, the value of -10% can be consiere as an upper boun in terms of banwith consumption. 2) Dynamic Scenario Simulations consist in processing several ynamic requests in which receivers join an leave an AnyTraffic group uring its lifetime. Such scenario is moele as a sequence of join an release requests where the banwith resources are limite to a maximum link capacity set to 10Gbps. Each simulation step represents one request processing for every noe in the network. A probability that follows a non-stationary istribution is associate to each join/release request. This istribution starts with a 100%-0% join/leave probability up to a 50%-50% balance stage, after several simulation steps. Fig.4 shows the state consumption gain of the AnyTraffic algorithm when performing with control of eterioration (Section III.C.3). The eterioration threshol to ecie either to continue with on-the-fly tree setup or to perform the entire tree re-computation is set to 20%. After several simulation iterations, we set w=0.6 in Eq.6. From Fig.4, it can be observe that re-computation gain graually grows to stabilize aroun 3% for the 50%-50% traffic pair an aroun 2% for the 75%-25% pair. The ifference in the percentage of multicast requests explains this 1% gain variation. Fewer trees ecrease the number of common forwaring entries for both unicast an multicast traffic. The low gain values obtaine when recomputing the entire tree means that eviations from the optimum are not significant. Note that similar behavior is observe for the banwith consumption (not shown). In orer to avoi waste of computational resource, a perioic eviation control can be performe when computing the tree on-the-fly. V. CONCLUSION The initial results obtaine with the AnyTraffic routing algorithm, when applie to labele-base forwaring (labels encoe topological information) are promising. By stretching the shortest path for unicast traffic forwaring, common forwaring entries can be share for both unicast an multicast traffic forwaring along the AnyTraffic tree towar the labele topological locations, an thus the number of forwaring states significantly reuce. Future work inclues i) investigation of other maximum eficit function; ii) execution of the algorithm on Internet-like topologies (power law ranom graphs) with increasing number of noes up to O(10k) to further etermine the epenencies of the algorithm on the noe egree, an the clustering coefficient; an iii) elaborate on istribute processing (in particular, uner ynamic conitions). REFERENCES [1] T. Wong, R. Katz, On Analysis of Multicast Forwaring State Scalability, IEEE Int l Conf. Network Protocols (ICNP 2000), Osaka, Japan, Nov [2] D. Thaler, M. 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