40 IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 1, JANUARY 2009

p-Cycle Based Tree Protection of Optical Multicast Traffic forCombined Link and Node Failure Recovery in WDM Mesh Networks

Feng Zhang and Wen-De Zhong, Senior Member, IEEE

Abstract—The extension of the p-cycle concept to tree protec-tion enables p-cycles to protect the multicast traffic for combinedlink and node failure recovery. In this paper, we present anefficiency-score based heuristic algorithm of p-cycle based treeprotection (ESHT). Simulation results show that the capacityefficiency of ESHT is close to that of optimal path pair (OPP)algorithm, while the blocking performance of ESHT is in betweenOPP-shared disjoint paths (OPP-SDP) algorithm and OPP-shared disjoint segments (OPP-SDS) algorithm. However, p-cyclebased protection approaches offer much faster restoration speed,because p-cycles are pre-cross-connected.

Index Terms—Optical multicast, survivability, tree-protectingp-cycle.

I. INTRODUCTION

IN high-capacity WDM networks, without an efficient andfast recovery mechanism, a network failure can lead to

severe disruption to network services and catastrophic lossto end customers. Currently, most optical multicast trafficprotection algorithms focus on link failure recovery [1], [2].Although less frequent, a node failure is more severe, becausea node failure is logically equivalent to multiple link failures.Because the preconfigured protection cycle (p-cycle) methodoffers ring-like fast restoration and also mesh-like high ef-ficiency [3], we consider extending the p-cycle concept tomulticast tree protection. The advantage of tree-protecting p-cycles over link-protecting p-cycles is the ability of the nodefailure recovery. This property is shared by path-based protec-tion algorithms including failure-independent path-protecting(FIPP) p-cycles [4] and the flow p-cycles [5]. In this letter,we present an efficiency-score based heuristic algorithm ofp-cycle based multicast tree protection (ESHT). The maincontribution of this letter is the application of p-cycles forcombined link and node failure recovery for both static anddynamic multicast traffic. Simulation results show that thecapacity efficiency of ESHT is close to that of the optimalpath pair (OPP) algorithm [2], while the blocking performanceof ESHT is in between OPP-shared disjoint paths (OPP-SDP) algorithm [2] and OPP-shared disjoint segments (OPP-SDS) algorithm [2]. However, the p-cycles offer much fasterrestoration time, because p-cycles are pre-cross-connected.

II. p-CYCLE BASED TREE PROTECTION ALGORITHMS

Without loss of generality, we assume that every node is offull wavelength conversion capability and optical multicasting

Manuscript received August 29, 2008. The associate editor coordinatingthe review and approving it for publication was W. D. Grover.

The authors are with Network Technology Research Centre, School of Elec-trical and Electronic Engineering, Nanyang Technological University, Singa-pore 639798 (e-mail: zhangfeng@pmail.ntu.edu.sg, ewdzhong@ntu.edu.sg).

Digital Object Identifier 10.1109/LCOMM.2009.081376

capability. All light trees and p-cycles considered in this paperare unidirectional, i.e., they are directed. We define one unitof capacity as one wavelength on a link, and denote a unityp-cycle as a directed p-cycle with one unit of capacity onevery link. Similar to FIPP p-cycles [4] protecting light pathson an end-to-end basis, tree protecting p-cycles protect lighttrees on an end-to-end basis, instead of protecting each linkand node. For the case of link failure recovery, only mutuallylink-disjoint trees can be protected by the same copy of a p-cycle, as long as they are arc-disjoint with the cycle, and theirsource and destination nodes are all on-cycle. In the opticallayer, the node failure recovery means to restore transit flowsthat pass through the failed node. Only the intermediate nodefailures can be recovered, whereas source/destination nodefailures cannot be restored by any protection algorithm. For thecase of combined link and node failure recovery, in additionto satisfying the constraints on link failure recovery, trees thatcan share the same copy of a p-cycle should be mutually node-disjoint and they are also node-disjoint with the protection pathprovided by the cycle. Note that the node-disjoint constraintsare applied to the intermediate nodes of the trees only. If alink/node in the network fails, the neighbor nodes of the failedlink/node inform the source and the destination nodes of thetrees affected, which will handle the service recovery then. Themulticast traffic carried by the multicast trees traversing thefailed link/node can be rapidly switched to their correspondingp-cycles, because p-cycles are preconfigured.

It may be difficult to find candidate p-cycles to protect largetrees, especially in sparse networks, because of the disjointconstraints and tree’s source, destination nodes must be on-cycle [6]. To solve this problem, we here propose a treepartition algorithm (TPA). If and only if no cycle can beidentified to protect a large multicast tree, it is then partitionedinto several smaller sub-trees. In the TPA algorithm, we firstcheck the disjointedness of the tree with each candidate cycle.If they are not disjoint, we record the common intermediatenodes. After the check, for each intermediate node, we sum itsrecord. The trouble node in a tree is defined as the intermediatenode with the highest record. Next, we identify the numberof branches at the source node. Case 1: If there is more thanone branch, we first partition the tree into two sub-trees: oneis the branch with the trouble node; the other one is formedby the rest of the branches. If a sub-tree is still cannot beprotected by any one of the cycles, we further partition thissub-tree into two portions in the same way, until all sub-treescan be protected. Case 2: If there is only one outgoing link atthe source node, we first partition this tree into three sub-trees:the first one is formed by the stem from the source to its closestsplitting node, and the outgoing links from the splitting node.

1089-7798/09$25.00 c© 2009 IEEE

ZHANG and ZHONG: P-CYCLE BASED TREE PROTECTION OF OPTICAL MULTICAST TRAFFIC FOR COMBINED LINK AND NODE FAILURE RECOVERY 41

Next, we partition the tree branches which originate from thissplitting node, into two sub-trees, treating this splitting nodeas the source node and following the same way as Case 1.After tree partitioning, the splitting node will appear in all thesub-trees, and each outgoing link from the splitting node willbe present in the first sub-tree and also in one of the rest twosub-trees. This overlapping is to protect the tree against thesplitting node failure.

Now, we present an efficiency-score based heuristic al-gorithm of p-cycle based tree protection (ESHT) for staticmulticast traffic protection, which can be viewed as a multicastversion of the capacitated iterative design algorithm (CIDA)in [7] and the efficiency-ratio based unity-p-cycle heuristicdesign (ERH) in [8]. Note that the CIDA and ERH wereindependently developed for link protection under the contextof unicast traffic. We introduce an efficiency-score (ES) forcycle selection. The ES of unity p-cycle j is defined as theratio of the sum of the working units of the largest set ofunprotected mutually-disjoint trees that can be protected byunity p-cycle j to the sum of the spare units required by unityp-cycle j, which is similar to the definition of actual efficiency[7], [9] used in CIDA or efficiency ratio (ER) used in [8].Given a group of multicast trees, we identify the largest set ofmutually-disjoint trees using a fast matrix algorithm. For eachtree, we record how many other trees that are not mutuallydisjoint with it. A trouble tree is defined as the tree with thehighest record. We identify the trouble tree by obtaining thecolumn sums of the matrix and delete it from the matrix.The whole process iterates until the remaining trees are allmutually-disjoint. The set of remaining trees obtained is thenthe largest set of mutually-disjoint trees. The ES of unity p-cycle j can be calculated by (1).

ES(cj) =

⎛⎝ ∑

τ∈Tmd(cj)

Wτ

⎞⎠ /|cj| (1)

cj Cycle j in the cycle set C.|cj| Number of spans (sum of spare units) of cycle j.Tmd(cj) The largest set of unprotected mutually-disjoint trees that can

be protected by cycle j. The trees inside this set is indexedby τ .

Wτ Sum of working units of tree τ .

Given the network topology and the multicast traffic de-mand, our ESHT algorithm first identifies all the candidatep-cycles. Next, we route the multicast trees by the Steinertree (ST) heuristic algorithm [10]. If and only if no candidatecycles can protect a tree, we partition it into several sub-trees.Then, we identify the largest set of unprotected mutually-disjoint trees that can be protected by each p-cycle andcalculate its ES. We choose the cycle with the highest ESand mark the trees that can be protected by it. After that,we check if there are remaining unprotected trees. The aboveprocess is iterated until all multicast sessions are protected.Next, we apply the ESHT algorithm to dynamic multicasttraffic protection. Upon the arrival of a new multicast request,we first try to route the new multicast tree using the STheuristic algorithm [10]. If and only if no candidate cyclecan protect this tree, we partition it into several sub-trees thatcan be protected, using the TPA algorithm. Then, we assignwavelengths to the sub-trees. Case 1: if the new multicast

session is successfully set up, our model attempts to protectthe new sub-trees, by using the existing cycles. If unsuccessful,additional new cycles will be configured according to theESHT algorithm. If the routing of the new multicast tree issuccessful and all its sub-trees can be protected by the exitingcycles or by a combination of the existing cycles and newlyconfigured cycles, the request is accepted; otherwise, it isblocked. Case 2: if the new multicast tree cannot be set upwithin the remaining capacity of the network, all the existingcycles are released. Then, our model attempts to route thenew multicast tree, and reconfigure cycles according to theESHT design. If this is successful, the new multicast requestis accepted; otherwise it is blocked.

Upon successful setup of the new multicast request, thenew multicast session starts service. Note that a multicast treewill be tore down and its occupied capacity will be releasedupon the completion of the service. In the mean time, thecorresponding p-cycles are also released if they no longerprotect any multicast trees.

III. PERFORMANCE EVALUATION

We select the COST239 network and the NSFNET networkas the test networks, whose average node degrees are 4.727and 3, respectively. For every multicast session, the sourcenode is randomly selected among all the nodes, and the setof destination nodes is also randomly selected among all thenodes excluding the source node. In the following discussions,we only show the results of COST239 network due to thelength limitation. (Similar results are observed for NSFNETnetwork.) In our study of static multicast traffic protection, weassume that each link has two fibers of 64 wavelengths perfiber, transmitting in opposite directions. For comparison, weextend OPP [2] and the ILP-based algorithm of spare capacityoptimization of p-cycle based tree protection (SOPT) [6] tothe combined link and node failure recovery, because OPP isreported to be most efficient in [2], while SOPT serves as thebench mark for ESHT. SOPT first groups the trees as disjointtree sets, then selects the most efficient p-cycles to protectthose sets, such that the total spare capacity used for p-cycleconfiguration is minimum [6]. Fig. 1 shows capacity efficiencycomparison for static multicast traffic protection in COST239network. For each multicast group size, we randomly generate20 multicast sessions. For every multicast group size, weperformed 20 independent simulation experiments and ob-tained the average value. As the multicast group size increases,each multicast tree traverses more links and nodes. Resultsshow that the capacity efficiency (in terms of total capacityconsumed and spare capacity required) of the ESHT is closeto that of the SOPT.

Table 1 shows the average splitting frequency. The splittingfrequency is defined as the ratio of the number of trees beingsplit to the total number of trees. As shown in Table 1, thesplitting frequency increases with the multicast group size (k).For a multicast group size of 5, 2 percent of the trees need tobe split. Note that the ESHT is much faster than the ILP SOPTalgorithm in computational speed and hence it is more suitableto be applied to dynamic traffic protection. For dynamic traffic,we assume that each link has two fibers of 16 wavelengths perfiber, transmitting in opposite directions. We also assume that

42 IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 1, JANUARY 2009

TABLE IAVERAGE SPLITTING FREQUENCY (σ) IN THE COST239 NETWORK

k 1 2 3 4 5 6 7 8 9 10σ 0 0 0 0.5% 2% 4.5% 11% 25.5% 56.5% 1

1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

350

400

450

Multicast Group Size

Cap

acit

y

ESHT Total CapacitySOPT Total CapacityOPP Total CapacityESHT Spare CapacitySOPT Spare CapacityOPP Spare Capacity

Fig. 1. Capacity efficiency comparison in COST239 network for staticmulticast traffic protection

1 2 3 4 5 6 7 8 9 1010

−4

10−3

10−2

10−1

100

Multicast Group Size)

Blo

ckin

g P

rob

abili

ty

OPP−SDSESHTOPP−SDP

(a)

multicast session requests arrive with a Poisson distributionand their holding time is negatively exponentially distributed.The total number of randomly generated multicast requestsis 105 for each network traffic load. We select OPP-SDPalgorithm and OPP-SDS algorithm [2] for comparison. OPP-SDP was reported to be the most efficient algorithm amongall the existing schemes [2].

Simulation results in Fig. 2 show that, for blocking perfor-mance, OPP-SDP is superior to ESHT and OPP-SDS. Oneof the reasons is because the tree partitions in ESHT andsegmentations in OPP-SDS divide the working tree/paths intooverlapped working domains for node failure recovery, whichrequires extra working capacity. However, OPP-SDP and OPP-SDS require complicated signaling process to inform multiplerelevant nodes to configure the backup paths, which results inlong restoration time. In contrast, p-cycles offer much fasterrestoration speed, because p-cycles are pre-configured.

33 44 55 66 77 88 9910

−3

10−2

10−1

100

Offered Traffic Load (Erlang)

Blo

ckin

g P

rob

abili

ty

OPP−SDSESHTOPP−SDP

(b)

Fig. 2. Blocking performance comparison in COST239 network for dynamicmulticast traffic protection: (a) offered traffic is fixed at 55 Erlang, (b) themulticast group size is fixed at 5.

IV. CONCLUSION

We extended the p-cycle concept to tree protection of opticalmulticast traffic for combined link and node failure recovery.We presented an ESHT heuristic algorithm for protecting bothstatic and dynamic multicast traffic. Simulation results showthat the capacity efficiency of ESHT is close to that of OPP,while the blocking performance of ESHT is in between OPP-SDP and OPP-SDS.

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