protecting light forest in survivable wdm mesh networks with sparse light splitting

Int. J. Electron. Commun. (AEÜ) 63 (2009) 1043–1053

www.elsevier.de/aeue

Protecting light forest in survivable WDM mesh networks with sparselight splitting

Xiong Wang∗, Sheng Wang, Lemin Li

Key Lab of Broadband Optical Fiber Transmission and Communication Networks, University of Electronic Science and Technology ofChina, Chengdu 610054, China

Received 10 September 2007; accepted 2 September 2008

Abstract

As multicast applications become popular, provisioning survivable multicast connections in wavelength-division-multiplexing (WDM) networks is an important issue. To reduce the network construction cost, the nodes capable of lightsplitting are always sparsely placed in a WDM network. In this paper, we study the problem of multicast protection in sparsesplitting WDM networks, and propose an efficient protection algorithm called sparse splitting constrained multicast protection(SSMP) algorithm. Differing from previous works, the backup paths derived by SSMP can share wavelength channels withprimary tree in sparse splitting WDM networks. To achieve wavelength sharing between primary tree and backup paths, alayered graph model is developed. Simulation results show that SSMP can achieve better performance in terms of averagenetwork cost and blocking probability than existing algorithms.� 2008 Elsevier GmbH. All rights reserved.

Keywords: Wavelength-division-multiplexing; Light tree; Light forest; Sparse splitting; Multicast protection

1. Introduction

With the development of internet, there is a growing de-mand for bandwidth-intensive multicast applications suchas high-definition television (HDTV), video-conferencing,video-on-demand (VoD), interactive distance learning,live auctions, distributed games, etc. This is encouragedby the promise of terabit fiber bandwidth that the nextgeneration optical backbone network with wavelength-division-multiplexing (WDM) technology would support.Nevertheless, how to efficiently support multicast in opticalnetwork, i.e. optical multicast, remains a current researchproblem. Research interest on optical multicast has grownin recent years [1,2].In all-optical WDM networks, multicast communications

can be supported by establishing a light path from the source

∗Corresponding author. Tel./fax: +862883201113.E-mail address: [email protected] (X. Wang).

1434-8411/$ - see front matter � 2008 Elsevier GmbH. All rights reserved.doi:10.1016/j.aeue.2008.09.001

node to each of the destination nodes. However, two or morelight paths of the same multicast connection may go throughthe same link resulting in a waste of bandwidth. In order toconserve bandwidth, it is desirable to establish a tree-shapedpath that shares the wavelength on all links on the tree-shaped path from the source node to all destination nodes.A tree-shaped path is called a light tree [3].

In order to realize a light tree in an all-optical WDM net-work, the node(s) at the branching point(s) of the light treemust be capable of splitting an input light signal into two ormore output signals. A node with such capability is calleda multicast capable (MC) node or a splitter [4,5]. While anode with the capability to drop a small amount of opticalpower from the wavelength channel passing through it iscalled as a multicast incapable (MI) node or a drop and con-tinue (DaC) node [6]. When a signal goes through a splitter,the power of the output signals is degraded by a factor ofthe number of output signals. To maintain the power levelof the signal, a costly active amplification device is required

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1044 X. Wang et al. / Int. J. Electron. Commun. (AEÜ) 63 (2009) 1043–1053

to be installed in the splitter. Therefore, a MC node is muchmore expensive than a MI node. An all-optical WDM net-work in which all nodes are MC is quite expensive. Thus theconcept of sparse splitting was first introduced in [7]. Withsparse splitting, only a small percentage of nodes in thenetwork are MC and the rest are MI. Due to the immaturityof all-optical wavelength conversion technology, the WDMnetworks considered in this paper have no wavelengthconverters. Without wavelength converters, a light tree mustsatisfy wavelength continuity constraint. With the sparsesplitting and wavelength continuity constraints, multiplelight trees, which are collectively called a light forest [7],may be needed to multicast data to all the destinations in amulticast session. Each of the light trees in the light forestis assigned a different wavelength.In WDM optical networks, a fiber offers huge bandwidth

by allowing simultaneous transmission of traffic on multiplewavelengths, and each wavelength channel has the trans-mission rate of over a gigabit per second. A single fiberlink failure will disrupt a lot of connection streams and leadto large data loss. Therefore, survivability has emerged asan important issue in the design of WDM optical networks[8]. Previous studies have proposed protection schemes forunicast traffic against single link failure, and those schemesinclude link protection, path protection and sub-path pro-tection (segment protection). Link failures may bring muchmore serious breakages to a multicast connection than aunicast connection. For example, when a single fiber cut oc-curs on a link near the root of a light tree, a large number ofdestination nodes would be disrupted from receiving infor-mation from the source. So provisioning survivable multicastconnection in MC WDM networks is an important issue.

1.1. Related works

Provisioning survivable multicast sessions against singlelink failure in WDM mesh network has been considered inrecent works [9–15] and several schemes for multicast pro-tection have been proposed. The works in [9–11] proposeto protect a multicast tree by deriving a link-disjoint backupmulticast tree. Two trees are said to be link-disjoint if theydo not share any link along their edges. Such link-disjointtrees can be used to provide 1+1 or 1:1 dedicated protectionwhere both the primary tree and the backup tree carry identi-cal bit streams to the destination nodes. When a link fails, theaffected destination nodes reconfigure their switches to re-ceive bit stream from backup tree. The pitfalls of this schemeinclude excessive use of resource and inability to discoverlink-disjoint trees in mesh WDM networks, which may leadto the blocking of a large number of multicast sessions whiletrying to establish them. To improve the usage of networkresources, the study in [10] proposes to protect a primarymulticast tree using the arc-disjoint multicast tree scheme,which is similar to the link-disjoint protection scheme ex-cept that, in arc-disjoint protection scheme, two trees can

share a link in opposite direction. Although arc-disjoint pro-tection scheme can reduce the usage of network resources,it may not always be possible to find an arc-disjoint backuptree once a primary tree has been discovered. The studiesin [12,13] proposes to protect multicast sessions using linkprotection, just similar to that of the unicast protection. Inlink protection, upon the working multicast tree has beendiscovered, a backup route for each link in the multicast treeis derived between the two ends of the link. In [10,14], thesegment protection schemes are proposed to protect a mul-ticast tree. In segment protection schemes, a primary treeis divided into several segments, and then a backup path isfound for each segment. The authors in [10] propose a pathbased protection scheme. In this scheme, an optimal link-disjoint path pair between source and each destination nodeis computed. One drawback of this scheme is that only thesepaths that originated at the source node and ended at eachdestination node are considered and thus cannot derive themost efficient backup paths. The authors in [15] proposed amore efficient path based multicast protection scheme calledmulticast protect through spanning paths (MPSP). Here, aspanning path is a path from a leaf node (or source node) toany other leaf node of a multicast tree. In MPSP, a backuppath for each spanning path is derived and then appropri-ately select part of these paths to protect the multicast treesuch that the total bandwidth allocated to the backup pathsis minimized. Furthermore, the multicast session protectionproblems with reliability requirement and dual-link failureare discussed in [16] and [17], respectively. Generally, pathbased protection performs better resource utilization thanlink based protection and segment based protection, whilelink based protection and segment based protection havefaster protection recovery times than path based protection.In this paper, we consider a path based protection schemethat is easier to implement in the current phase than linkbased protection and segment based protection schemes.

1.2. Motivations

In a WDM network with full splitting capability, thebackup paths can share wavelength channels with primarytree. Fig. 1a shows a full splitting WDM network and alight tree which is denoted by bold lines. The backup pathto the destination node d2 is s → u → d2. The backup link(s, u) is sharing wavelength channel with the primary tree.This is possible because, in a multicast session, all primaryand backup paths carry replicas of the same information tothe destination nodes. As shown in Fig. 1(a), if link (s, d1)or link (d1, d2) fails, the MC node u can replicate the sig-nal for d2 through light splitting in optical layer. However,with sparse splitting constraint, the backup paths derived byexisting algorithms cannot share wavelength channels withthe working tree in same cases. For example, in Fig. 1b, thebackup path s → u → d2 to the destination node d2 cannotshare wavelength with primary tree on link (s, u), because

X. Wang et al. / Int. J. Electron. Commun. (AEÜ) 63 (2009) 1043–1053 1045

d2

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Fig. 1. (a) A full splitting WDM network and a light tree. (b) Asparse splitting WDM network and a light tree.

node u is a MI node and cannot split a signal to destinationd2 when link (s, d1) or link (d1, d2) fails. Furthermore, with-out wavelength converters, some of the current algorithmseven cannot find a link-disjoint backup path for a primarypath or segment. Without loss of generality, we take segmentprotection for instance. In Fig. 1a, we assume that the pri-mary tree is divided into three segments (s → d1, d1 → d2and s → u → v → d3). The segment protection cannot finda backup path for segment s → d1 if there is no wavelengthconverter in the network. Because to avoid wavelength col-lision, the links used by the primary tree must be removedwhen compute backup paths. But actually, we can choosepath s → u → v → d1 as the backup path for segments → d1, and the backup path can share wavelength channelswith the primary tree on links (s, u) and (u, v).In this paper, we investigate the problem of protecting

multicast sessions in WDM networks with sparse splittingcapability. The objective of this paper is trying to set up amulticast session with protection against any link failure insparse splitting WDM networks such that the wavelengthresource utilized by the multicast session is minimized. Webelieve that the problem is NP-complete because the under-lying problem of setting up a minimum cost light tree orlight forest is NP-complete problem [7]. The integer linearprogramming (ILP) formulation can be used to find opti-mal solution of the problem [9], but the computation timeis not acceptable for dynamic traffic. However, the heuristicalgorithms can provide suboptimal solutions to the problem

within an acceptable computation time. In this paper, weproposed a heuristic multicast protection algorithm, calledsparse splitting constrained multicast protection (SSMP) al-gorithm, to enhance the wavelength sharing between primarytree and backup paths in sparse splitting networks. Our sim-ulation results show that SSMP achieves better performancethan existing algorithms in sparse splitting WDM networks.The rest of this paper is organized as follows. In Section

2, we briefly present some background related to the studyin this paper. Section 3 describes the multicast protectionproblem in sparse splitting WDM networks. The heuristicalgorithm (SSMP) is presented in Section 4. In Section 5,we report our simulation results. The paper concludes withSection 6.

2. Background

In a full splitting network, where all nodes are equippedwith MC cross-connects, a multicast session is routed on alight tree [3]. A light tree is a directed Steiner tree that orig-inates from the source node and spans all destination nodes.However, due to sparse splitting, a single light tree may notbe sufficient for multicast data to all the destinations in amulticast session. An example is shown in Fig. 2, where ina random WDM network with 9-nodes, node 5 is the sourceof a multicast session, and nodes 3, 7–9 are the destinations.It is assumed that the MC nodes are indicated by hexagons,and the MI nodes are indicated by circles. When using theshortest path heuristic, for example, to construct a light tree,it is possible that nodes 6 and 8 are used to forward data tonodes 3 and 7, respectively. As a result, node 9 cannot beincluded in the light tree (represented in bold lines). In thiscase, a second light tree (dashed lines) which overlaps onlink (5, 6) with the first one has to be constructed, resultingin a light forest [7]. Source node 5 needs to send out two“copies” on link (5, 6), two wavelengths are needed on link(5, 6) in a wavelength routed WDM network, and sourcenode 5 requires two transmitters for the multicast session.The problem of constructing optimal light forest for a multi-cast session is NP-complete [7]. In [7], four heuristics were

3

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Fig. 2. An example of multicast forest in a 9-node network withsparse splitting.


proposed. Among them, member-only (MO) heuristic gen-erates the least number of trees in a light-forest and requiresthe least number of wavelengths among them. The workin [18] presented algorithm using virtual source rooted ap-proach that is guaranteed to build a single light tree for givena multicast session. But the virtual source rooted approachis not suitable for a WDM network without wavelengthconverters.

3. Problem description

We consider protection of multicast sessions in WDMoptical mesh networks with sparse splitting capability. Weassume that every MI node is DaC capable. The number andlocation of the MC nodes are pre-determined. We assumethat all of the network nodes have no wavelength convertersand all of the fiber links are bidirectional. Based on theabove assumptions, we are given the following inputs to theproblem.(1) There is a topology G = (V = VI ∪ VM, E) consist-

ing of a weighted undirected graph, where VI is the set ofvertices corresponding to MI nodes, VM is the set of ver-tices corresponding to MC nodes, and E is the set of edgesrepresenting the bidirectional links. Each link is assigned aweight to represent the cost of moving unit of traffic fromone node to the other, and each link is capable of carryinga set of wavelengths.(2) A multicast connection request r (s, D, w) has to be

established while protecting it from any single link fail-ure, where s is the source node of the multicast request, Dis the set of destinations, and w is the bandwidth require-ment. The connection is unidirectional from source to eachdestination. The group size of the session is denoted by k,which indicates the number of destination nodes. If a rout-ing algorithm discovers sufficient resources, the multicastsession is established; otherwise, the multicast session isblocked.

4. The SSMP algorithm

Because the sparse splitting constrained multicast routingproblem is a NP-complete problem, we assume that existingheuristics [7] are used to compute the light forest. The SSMPalgorithm is used to find the backup paths for each lightforest. In this section, we will present the SSMP algorithmin detail.

4.1. Overview of the SSMP algorithm

The basic idea of SSMP is to find a backup path for eachpath from source to a leaf node on the primary tree. Thereby,the links on the primary path from source to a certain leafnode can be protected by the circle formed by the primaryand backup paths to the leaf node. For example, in Fig. 1b,

s u

B

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Fig. 3. The two cases that a backup path can share wavelengthchannels with primary tree.

the backup path to leaf node d2 is s → u → v → d2, andthe links (s, d1) and (d1, d2) on the primary path from s tod2 can be protected by circle s → u → v → d2 → d1 →s. In order to sharing wavelength with primary tree, SSMPchooses path s → u → v → d2 (or path s → u → v →d3 → d2) instead of the shortest path s → u → d2 as thebackup path for leaf node d2. This is because the backuppath s → u → d2 cannot share the primary wavelength onlink (s, u), while the backup path s → u → v → d2 canshare the primary wavelength channels on links (s, u) and(u, v). When link (s, d1) (or link (d1, d2)) fails, node v cansplit a signal to destination d2. The backup path to a leafnode can share wavelength channels with primary tree intwo cases, which are shown in Fig. 3. In Fig. 3a, the backuppath to leaf node v shares wavelength channels with primarytree on the link from A to B. In this case, node B must bea MC node or a leaf node and node A can be either a MCnode or a MI node, because when link (s, u) or link (u, v)fails, node B must split a signal to node v. In Fig. 3b, thebackup path to leaf node v shares wavelength channels withprimary tree on the link from B to A. In this case, node Aand B must be MC node. This is because when link (s, A)fails, node B must be capable of splitting a signal to leafnodes u and v, respectively, and if link (A, v) fails, node Amust be capable of splitting a signal to leaf nodes v.To achieve wavelength sharing, the SSMP first constructs

an auxiliary graph AG for each light tree T in F, and thenfind the backup path on the auxiliary graph for each leafnode on T.

4.2. Construction of the auxiliary graph

From the physical network G(V, E) and a light tree T, wewill generate a directed auxiliary graph AG(Va, Ea), which


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Fig. 4. An illustrative example for implementing the SSMP algorithm. (a) The auxiliary graph for the light tree shown in Fig. 1. (b) Acandidate backup path for d2. (c) A candidate backup path for d3, and at last, this path is selected as the backup path for d3 because ithas smaller protection gain than the candidate backup path for d2. (d)The backup computed for d2.

has two layers: a physical layer and a sharing layer. Thephysical layer is used to map the network state and topol-ogy. And the sharing layer is used to represent the primarywavelength channels that can be shared by backup paths.Each layer has |V | nodes, which are corresponding to thephysical nodes in network G(V, E). For each physical nodem, the corresponding node in the physical layer and sharinglayer is expressed as mp and ms, respectively.To facilitate description, we define three types of edges

in the auxiliary graph as follows:Physical edges: Each undirected link (m, n) in the physical

network G corresponds to physical edges (mp, np) and (np,mp) in the physical layer of AG.

Sharing edges: It can be further divided into forward shar-ing (FS) edges and reversed sharing (RS) edges. For eachedge (m, n) in light tree T, there is a FS edge from ms to nsin the sharing layer of AG. For each MC node (or leaf node)u on light tree T, there is an RS edge from node us to nodevs, where vs is the parent MC node of node u on light treeT. The parent MC node of node u is defined as the nearestupstream MC node to u on a light tree T. For example, inFig. 1b, the parent MC node of d3 is node v.Adding and dropping edges: The adding and dropping

edges are used to connect the physical layer and the sharing

layer in auxiliary graph AG. For each node m in the physicalnetwork G, there is an adding edge from node mp to ms inauxiliary graph AG. And for each MC node (or leaf node) uon light tree T, there is a dropping edge from node us to upin auxiliary graph AG.

Given a physical network G and a light tree T, the auxiliarygraph AG is generated as follows:Step 1. Generate the physical layer. First, for each node

m in the physical network G, add a node mp to the physicallayer. Then, add the physical edges defined above to thelayer. If physical link (m, n) is used by the light tree T, set thecost of the physical edges (mp, np) and (np, mp) to infinite.And set the cost of other physical edges in the physical layerto the cost of the corresponding link in G.

Step 2. Generate the sharing layer. First, for each nodem in the physical network G, add a node ms to the sharinglayer. Then, add the sharing edges defined above to the layer.At last, set the cost of the sharing edges added to the layerto zero.Step 3. Connect the physical layer and the sharing layer

through adding and dropping edges defined above, and setthe cost of the adding and dropping edges to zero.An auxiliary graph for the light tree and physical network

in Fig. 1b is shown in Fig. 4a. In Fig. 4a, the edges (d3s,


Fig. 5. Network topologies used for simulations. (a) Pan-Europeantest network COST239. (b) USNET.

vs), (vs, ss), (d2s, d1s) and (d1s, ss) are RS edges. It isnotable that the RS edges in the auxiliary graph is usedto enable the wavelength sharing on the links, which is inopposite direction of the links used by primary tree (shown inFig. 3b). This kind of wavelength sharing is feasible becausethe network model considered in this paper is bidirectionalWDM mesh networks.

4.3. Procedure of the SSMP algorithm

As stated above, SSMP algorithm can be divided into twophases. In the first phase, an auxiliary graph AG is generated.In the second phase, the backup paths to leave are derived inAG. To find the most efficient backup paths for leaf nodes,SSMP first finds the backup path for the leaf node withminimum protection gain (PG). The PG for a leaf node l isdefined as follows:

PG(l) = C(BP)

C(PP)=

∑e∈BP c(e)∑e∈PP c(e)

(1)

where C(PP) and C(BP) are the cost of the primary andbackup path to a leaf node, respectively, c(e) is the cost oflink e. In SSMP, once a backup path is found, the cost of thephysical edges along it is updated to zero in AG to increase

sharing of new backup path with the already-found backuppaths.The detail of the SSMP algorithm is described as follows:

Input: a network G(V, E), a primary light forest F, anda multicast request r (s, D, w).Output: obtain backup topology BT used to protect the

primary light forest F.Phase 1: Construct the auxiliary graph AG.Step 1: Get a light tree T from F. Let LD be the set of

leaf nodes on tree T.Step 2: Construct an auxiliary graph AG for light tree T

as stated in previous subsection.Phase 2: Find backup path for each leaf node in AG.Step 3: Get a leaf node l from set LD, and let PP(s, l)

denotes the primary path from s to l in T. For each link (m,n) ∈ PP(s, l), set the cost of corresponding FS edge (mp,np) and RS edge starting at np in the sharing layer-of AG toinfinite.Step 4: Use Dijkstra’s shortest path algorithm to derive a

shortest path from source node sp to leaf node lp in auxiliarygraph AG. If a shortest path BP(sp, lp) does not exist, returnFAIL and the connection request is rejected. And otherwise,compute the PG for leaf node l.Step 5: For each link (m, n)∈ PP(s, l), set the cost of

corresponding FS edge (ms, ns) and RS edge starting at npin the sharing layer of AG to zero.Step 6: For ∀l ∈ LD, repeat Steps 3–5.Step 7: Choose the leaf node u with the minimum PG(u)

in set LD.Step 8: For each physical edge (mp, np) ∈ BP(sp, up),

set the cost of physical edges (mp, np) and (np, mp) in thephysical layer of AG to zero, and add the correspondingphysical link (m, n) in G to BL. Remove u from LD.Step 9: If LD = �, go to Step 10; else go to Step 3.Step 10: Remove T from F. If F = �, return BL, else go

to Step 1.

Fig. 4 illustrates the SSMP algorithm. The light tree Tis shown in Fig. 1b. The SSMP algorithm first constructsan auxiliary graph AG for light tree T, as shown in Fig. 4a.With this auxiliary graph, the SSMP algorithm derives apath link-disjoint with primary path to each leaf node on theprimary light tree. The computed link-disjoint paths to leafnodes d2 and d3 are shown in Fig. 4b and c with red dottedlines, respectively. And the PG for d2 and d3 is 1

2 and 13 , re-

spectively. So SSMP chooses path s → d1 → d2 → d3 asthe backup path for leaf node d3, and set the cost of phys-ical edges (d2p, d3p) and (d3p, d2p) to zero in AG. Finally,a backup path for leaf node d2 is computed in Fig. 4d.

Theorem. The time complexity of the SSMP algorithm isO(2(|D| + |D|2) · |V |2).

Proof. The time complexity of SSMP mostly dependson the running times of Dijkstra’s algorithm, whose time


Fig. 6. Average network cost of SSMP and MPSP in: (a) COST239and (b) USNET.

complexity is O(|N |2) [19], where |N | is the number ofnetwork nodes. We assume that there are k light trees in alight forest F, and a light tree ti (1� i�k) has ni leaf nodes.For a light tree ti , SSMP will run ni (ni + 1)/2 times ofDijkstra’s algorithm to compute the backup path for eachleaf node on light tree ti . Therefore, to find backup paths forall light trees in F, SSMP will run (n1 + n2 + · · · + nk)/2+(n21 + n22 + · · · + n2k)/2 times of Dijkstra’s algorithm. Here(n1+n2+· · ·+nk)� |D|, and (n21+n22+· · ·+n2k)� |D|2. Thenumber of nodes in AG is 2|V |. Thus the overall complexityof the algorithm is O(2(|D| + |D|2) · |V |2). �

5. Simulations and numerical results

In this section, we conduct a series of simulations to studythe performance of the SSMP algorithm. We compare SSMPwith the path protection based algorithm MPSP, which hasbeen reported as the most efficient protection algorithm infull splitting WDM networks.

Fig. 7. The blocking probability that the two algorithms cannotfind backup paths in COST239 and USNET.

5.1. Simulation setup

The network simulator is written in C + + and run on aPC with Intel Core E6300 processor. The simulator is basedon discrete-event system simulation framework [20]. Wesimulated the performance of SSMP and MPSP on the 11-node COST239 and the 24-node USNET, which are shownin Fig. 5. The cost of each link in the sample networks isset to 1, and each link in the sample networks carries 64wavelengths. The source node and destination nodes of amulticast connection are uniformly distributed across thenetwork. The MC nodes are placed on the sample networksby using the LDSC placement algorithm proposed in [21],and the number of MC nodes in COST239 and USNET isset to 4 and 10 (about 40% of the networks are MC), re-spectively. The MO algorithm [7] is used for deriving theinitial light forest. We study both static and dynamic per-formance of our proposed SSMP algorithm and the MPSPalgorithm. For static performance simulations, we gener-ate random multicast connections of size k and comparethe average network cost and blocking probability of the


Fig. 8. Comparison of SSMP and MPSP for dynamic provisioningof survivable multicast sessions when session size varies: (a) COST239, traffic load =150 (Erlang); (b) USNET, traffic load =80(Erlang).

two algorithms. Here, the average network cost is definedas the average sum of wavelength link cost used by multi-cast sessions. If an algorithm can find link-disjoint backuppath for each leaf node, the connection is established andis blocked otherwise. So the blocking probability is definedas the number of blocked connection requests divided bythe total number of arrived multicast request. In each sim-ulation, we repeat the experiment for 5000 different con-nections of the same group size. In dynamic performancesimulations, we dynamically inject 105 randomly gener-ated requests into the sample networks and compare theblocking probability of the two algorithms. In this part, weassume that multicast connections arrive with Poisson distri-bution, and their holding time is negative exponentially dis-tributed. The total traffic load offered to the sample networksis �=�/�, where � and � are the arrival and departure rates,respectively.

Fig. 9. Comparison of SSMP and MPSP for dynamic provisioningof survivable multicast sessions when traffic load varies: (a) COST239, session size =4; (b) USNET, Session size =10.

5.2. Numerical results

5.2.1. Static case performanceFig. 6 shows the average network cost with increasing ses-

sion size for the MPSP algorithm and our proposed SSMPalgorithm in COST 239 and USFNET. It is easy to un-derstand that with the increase of session size, the averagenetwork cost used by the two algorithms increases. As ex-pected, SSMP consistently has lower average network costthan MPSP for all group size. There are two reasons: first, asdiscussed in Section 4, the backup paths derived by SSMPcan share wavelengths with primary tree while MPSP can-not achieve wavelength sharing between primary tree andbackup paths in sparse splitting networks; and secondly, dif-ferent from MPSP, SSMP set the cost of the links in alreadyfound backup paths to zero, and hence, allows higher wave-length sharing of backup path with the already-found backuppaths.Fig. 7 shows the relationship between blocking prob-

ability and session size. In the experiment, a multicast


Fig. 10. Comparison of SSMP andMPSP for dynamic provisioningof survivable multicast sessions when the number of MC nodesvaries: (a) COST 239, session size =4, traffic load =150; (b)USNET, session size =8, traffic =80.

connection request is blocked if it cannot find a link-disjointbackup path for a leaf node. In the COST239 network, theblocking probabilities of SSMP are zero for all session size.It means that SSMP can always find a backup path to a leafnode in COST239 network. As we can see from Fig. 7, theblocking probabilities for MPSP are higher than those ofSSMP in all cases. This is because, due to the wavelengthcontinuity constraint and inability to share wavelengthswith primary tree, the backup paths derived by MPSP mustbe link-disjoint with the primary tree. While SSMP onlyrequire that a backup path is link-disjoint with its primarypath. Thus, it is easy to understand that MPSP has higherblocking probability of finding backup paths. We can seethat the blocking probability for MPSP increasing quicklywith increasing session size. This is because a light treemay include more links when session size becomes large,and it is harder to find link-disjoint path in MPSP. Wecan also observe that the blocking probability of MPSP in

Fig. 11. Computation time comparision of the SSMP algorithmand the MPSP algorithm in the two sample networks: (a) COST239, traffic load =1; (b) USNET, traffic load =1.

COST239 is much lower than that of MPSP in USNET.This is because COST239 topology is denser than USNETtopology.

5.2.2. Dynamic case performanceFig. 8 plots the blocking probability with increasing ses-

sion size for MPSP and SSMP when the traffic load is fixed.Evidently, the blocking probability of the SSMP algorithmis smaller than that of the MPSP algorithm. There are tworeasons. One reason is that as we observed in Fig. 6, the av-erage network cost for the SSMP algorithm to set up a con-nection is smaller than that for the MPSP algorithm. Andanother reason is that as we can observe in Fig. 7, SSMPhas lower blocking probability of finding backup paths thanMPSP.Fig. 9 further compares the blocking performance of the

two algorithms by varying the traffic load when the desti-nation size is fixed. As expected, SSMP outperforms MPSP


for all traffic loads. This can also be explained as that SSMPconsumes smaller average network cost than MPSP.Fig. 10 illustrates relationship between blocking proba-

bility and the number of MC nodes. We can observe fromFig. 10 that our proposed SSMP algorithm, in general, per-forms better than the MPSP algorithm. In Fig. 10, we cansee that with the number of MC nodes increasing, the block-ing probability improves for both SSMP and MPSP. And wealso observe that the blocking probability performance forboth SSMP and MPSP improves very little when the num-ber of MC nodes beyond 4 in COST239 and 10 in USNET.In the worst case, the computation complexity of SSMP

and MPSP is O(2(|D| + |D|2) · |V |2) and O(|D|2|V |2), re-spectively. The two algorithms have the same computationcomplexity in theory. To exactly evaluate the computationtime of the two algorithms, we conduct a series of simula-tions. Fig. 11 compared the computation time of the two al-gorithms. From Fig. 11 we can see that the SSMP algorithmhas a longer computation time than the MPSP algorithm.This is because that the SSMP algorithm runs Dijkstra’s al-gorithm on an auxiliary graph, whose nodes number is twicelarger than that of the original network.

6. Conclusions

To reduce the network construction cost, the nodes capa-ble of light splitting are always sparsely placed in a WDMnetwork. In this paper, we studied the problem of protect-ing multicast sessions in sparse splitting WDM networksand a heuristic algorithm called SSMP was proposed. Withsparse splitting constraint, the backup paths derived by ex-isting algorithms cannot share wavelength channels with pri-mary tree. SSMP developed a layered auxiliary graph modelto implement wavelength sharing between primary tree andbackup paths. Compared with existing algorithms, SSMPhas much better performance in terms of average networkcost and blocking probability.

Acknowledgments

The authors would like to thank the reviewers for theirvaluable comments. This work is supported by NationalKey Basic Research Program of China (973 Program2007CB307104 of 2007CB307100), National NaturalScience Foundation of China (NSFC) under Grant no.90604002 and 60472008, the Program for New CenturyExcellent Talents in University (NCET) under Grant no.NCET-05-0807, and State 883 Project under Grant no.2007AA01Z242.

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Xiong Wang was born in Sichuan,China, in 1980. He received a B.S.degree in Communication and Infor-mation Engineering from ChongqingUniversity of Posts and Telecommuni-cations, China, in 2003, and a Ph.D.degree in communication system fromUniversity of Electronic Science andTechnology of China, China, in 2008.He is currently a Research Member inthe Key Lab of Broadband Optical Fiber

Transmission and Communication Networks, School of Commu-nication and Information Engineering, University of ElectronicScience and Technology of China. His research interests includerouting, traffic grooming, and multicast schemes and algorithmsin WDM networks.

Sheng Wang was born in Sichuan,China, in 1971. He received his B.S.,M.S., and Ph.D. degrees in Electri-cal Engineering from University ofElectronic Science and Technology ofChina, Chengdu, China, in 1992, 1995,and 1999, respectively. He is currentlyan Professor in the Key Lab of Broad-band Optical Fiber Transmission andCommunication Networks, School ofCommunication and Information Engi

neering, University of Electronic Science and Technology ofChina. His research interests include WDM network routing, QoS,protection, restoration, and traffic grooming and engineering.

Lemin Li was born in Zhejiang, Chian,in 1932. He graduated from ShanghaiJiaotong University, Shanghai, China, in1952, majoring in Electronic Engineer-ing. From 1952 to 1956, he was withthe Department of Electrical Commu-nications at Shanghai Jiaotong Univer-sity. Since 1956, he has been with theChengdu Institute of Radio Engineering(now the University of Electronic Sci-ence and Technology of China), where

he is currently a Professor of the Key Lab of Broadband OpticalFiber Transmission and Communication Networks. From 1980 to1982, he was a Visiting Scholar at the Department of ElectricalEngineering and Computer Science, University of California at SanDiego. He is currently a Professor in the Key Lab of BroadbandOptical Fiber Transmission and Communication Networks, Schoolof Communication and Information Engineering, University ofElectronic Science and Technology of China. His research work isin the area of digital information transmission and communicationnetworks. Professor Li is a member of CAE (Chinese Academyof Engineering).

protecting light forest in survivable wdm mesh networks with sparse light splitting

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