Cross-sharing vs. self-sharing trees for protecting multicast sessions in mesh networks q

Transcription

1 Computer Networks 0 (2006) Cross-sharing vs. self-sharing trees for protecting multicast sessions in mesh networks q Narendra K. Singhal a, *, Canhui Ou b, Biswanath Mukherjee a a Department of Computer Science, University of California, Davis, CA, USA b SBC, 2600 Camino Ramon, San Ramon, CA, USA Available online 1 July 200 Abstract In this study, we investigate a cost-effective approach for protecting several multicast sessions from any link failure in an optical network. The approach, referred to as cross-sharing, provides an optimal sharing of backup resources among several multicast sessions. Our cross-sharing approach employs the link-vector model, modified for multicast sessions, and provides significant cost savings (48% for a small six-node network and 39% for a large nationwide network) of backup resources relative to arc-disjoint and self-sharing approaches, especially for a large number of sessions. Ó 200 Elsevier B.V. All rights reserved. Keywords: Arc-disjoint; Cross-sharing; Idle-backup; Light-tree; Link-vector model; Multicasting; Protection; Wavelength-division multiplexing (WDM) 1. Introduction Recent advances in networking particularly high-capacity optical networking employing wavelength-division multiplexing (WDM) technology q A short, summarized version of this paper will be presented at the Optical Fiber Communications (OFC-0) conference in March 200 [1]. This research has been supported in part by the National Science Foundation (NSF) under Grant No. ANI * Corresponding author. Tel.: ; fax: address: singhaln@cs.ucdavis.edu (N.K. Singhal). have made bandwidth-intensive multicast applications such as HDTV, interactive distance learning, live auctions, distributed games, movie broadcasts from studios, etc. widely popular [2 9]. However, link failures in a communication network occur often enough to cause service disruption, and lead to significant information loss in the absence of adequate backup mechanisms. Hence, researchers have investigated efficient approaches such as arc-disjoint [10] and self-sharing [11] for protecting multicast trees, called light-trees [3] in the literature. Because single fiber failures are the predominant form of failures in communication networks, we focus on protecting multicast sessions from any /$ - see front matter Ó 200 Elsevier B.V. All rights reserved. doi: /j.coet

2 N.K. Singhal et al. / Computer Networks 0 (2006) single link failure in the network. We introduce a new idea of cross-sharing which allows sharing of backup resources among several light-trees and provides significant cost savings. We explain cross-sharing through the following illustration. Consider a small example network shown in Fig. 1 and two multicast sessions, S 1 ={A, B, D} ands 2 ={B, C, D}, requiring protection. In general, a multicast session S i is denoted as a set fs i ; d i1 ; d i2 ;...; d ik g where s i is the source node and d ik are the destination nodes Arc-disjoint trees The approach of arc-disjoint trees (proposed in [12,10]) constructs a backup tree which is arc-disjoint to the primary tree. Arcs are unidirectional edges and links are bidirectional with an edge in each direction. A cut on a link disrupts the traffic flow in both directions. In Fig. 1(a), the primary edges of session S 1 namely, A! B and A! D are shown in solid lines, and they form a primary tree. Similarly, the backup edges of session S 1 namely, A! C, C! B and C! D are shown in dashed lines, and they form a backup tree. The primary and backup trees of session S 1 are arc-disjoint, and they can protect the session from a single fiber cut [10]. The cost of protecting the primary tree for S 1, measured as the sum of the weights on the edges of the backup tree, is 24 units Self-sharing trees In this approach, paths to each destination node (on the primary tree) are protected by discovering a backup path which is link-disjoint to the corresponding primary path. A backup path can share not only with other backup paths but also with other edges on the primary tree. This selfsharing approach is shown to be more efficient than arc-disjoint trees in [11]. Fig. 1(b) shows session S 2 for which the primary paths (shown in solid lines) to the destination nodes, viz. B! C to destination node C and B! A! D to destination node D, form a primary tree. The backup path to the destination C is B! A! C and the backup path to destination D is B! C! D. Two backup edges (shown in dotted lines) B! A and B! C are sharing wavelength channels with the primary of the same session. This is possible because, in a multicast session, all primary and backup paths carry replicas of the same information to the destination nodes. Backup edges which share a channel with the primary of the same tree are called self-sharing edges. (Corresponding primary and backup trees are called self-sharing trees.) The remaining backup edges, which do not carry traffic, but are reserved to be used when failure occurs, are idle-backup edges, e.g., A! C and C! D shown in dashed lines in Fig. 1(b). Observe that the backup paths are link-disjoint to their corresponding primary paths and, hence, they can protect a multicast session from a fiber cut. The cost of additional backup resources for protecting is S 2 1 units Cross-sharing trees Cross-sharing adds another dimension to backup-light-tree sharing by allowing sharing of idlebackup edges from several multicast sessions. Thus, portions of backup tree of each session not only self-shares with its primary tree but also A B A B A B D C D C D C (a) S 1 = {A, B, C} (b) S 2 = {B, C, D} (c) S 1 and S2 Primary edges Self-sharing edges Non-sharing backup edges Cross-sharing edges Fig. 1. Approaches for protecting multicast trees: (a) arc-disjoint; (b) self-sharing; and (c) cross-sharing.

3 202 N.K. Singhal et al. / Computer Networks 0 (2006) cross-shares with the portions of backup tree of other sessions. Two idle-backup edges cross-share only if the primary paths protected by them do not traverse a risk group (i.e., a common link). Alternatively, cross-sharing is performed intelligently so that any link failure in a network leaves sufficient backup resources in the network to carry the rerouted traffic. An extended link-vector model is proposed and studied below for maximal crosssharing of backup resources. The idea of link-vector has found wide application in various studies (e.g., the conflict vector in [13]) to identify sharing potential among backup paths, especially in a wavelength-convertible network. We propose a modified link-vector model for determining the number of backups to be provisioned on an edge while sharing idle-backup edges of several trees. A link-vector v e for edge e can be represented as an integer set, fv e ej8e 2 E; 0 6 v e e 6 kðeþg, where ve e is the number of backup channels needed on edge e when link e fails and k(e) is the number of wavelengths on edge e. Table 1 shows the link-vector for idle-backup edges of the two primary trees S 1 and S 2. Only those links which carry primary traffic make idlebackup edges active, e.g., links A M B and D M A for session S 1. Link vectors are computed for only the idle-backup edges. When a link fails, the idle-backup edges which feed the affected destination nodes become active. Observe that only one idle-backup edge needs to be reserved on A! C, thus cross-sharing this edge between sessions S 1 and S 2. The total cost of backup edges for protecting both sessions S 1 and S 2 is computed by summing the cost of backup edges in 1(c). The backup cost is 31 units. When no cross-sharing is allowed, the cost of the backup edges for S 1 and S 2 are 24 units and 1 units respectively. Thus, cross-sharing saves eight units of resources which is worth exploiting. Note that the cross-sharing Table 1 Link-vector model for the two trees S 1 and S 2 A M B BM C CM D DM A AM C v max e A! C 1 (0) 0 (1) 0 (0) 1 (0) 0 (0) 1 C! B 1 (0) 0 (0) 0 (0) 0 (0) 0 (0) 1 C! D 0 (1) 0 (0) 0 (0) 1 (1) 0 (0) 2 also includes self-sharing of backups for multicast sessions. This paper studies the cross-sharing trees in the context of WDMnetworks. However, cross-sharing approach is easily applicable to share channels in other networks such as SONET or Gigabit channels carrying multicast traffic. The rest of the paper is organized as follows. Section 2 presents the multicast protection problem and discusses cross-sharing algorithm and mathematical formulation. Section 3 presents illustrative results obtained for small and nation-wide networks. Section 4 finally concludes the paper. 2. Problem description Given: 1. A topology G =(V,E) consisting of a weighted directed graph, where V is a set of N network nodes, and E is the set of links inter-connecting the nodes. A node in a WDMnetwork is an entity representing, for example, IP router(s) connected to a cross-connect and the links correspond to the fibers between nodes. Each link is assigned a weight (c between nodes m and n) to represent the cost of moving traffic from one node to the other. 2. Nodes are equipped with multicast-capable opaque cross-connects which convert the signal from optical to electrical to optical (OEO) domain, and hence allow full wavelength conversion. 3. A batch of b multicast sessions. Determine: Optimal cost of backup resources used to protect the b multicast sessions from any link failure Cross-sharing algorithm 1. For each multicast session i 2 b, compute a minimum-cost primary tree using an Integer Linear Program (ILP). The formulations for computing minimum-cost trees, also called as minimum-cost Steiner trees [14], have been presented in detail in [10]. For a network with

4 N.K. Singhal et al. / Computer Networks 0 (2006) a few tens of nodes, these ILPs take a few minutes for solution on 12 MB, 2.8 GHz, Pentium IV machines. P i ¼ 1ifedgem! n (m and n are indices for nodes) is on primary tree; otherwise, P i ¼ 0. P id i ¼ 1 if edge m! n carries traffic to destination d i ; otherwise, P idi ¼ For each destination d i, determine a backup path B idi idi, which is link-disjoint to P. 3. For each cut on link m $ n (m and n are node indices between which a failure occurs), determine the unreachable destination nodes d i, and assign K i ¼ 1ifanidle-backup edge of tree i on m! n becomes active for any destination node d i. K i is the link-vector of tree i for edge m! n (see Table 1). 4. For every edge m! n, determine the maximum number of idle-backup edges (v ) required for a failure on any link m! n in the network.. Optimize P the cost of idle-backup edges c v using a mathematical formulation as shown below and solve the ILP using an appropriate solver, e.g., CPLEX Integer linear program Minimize : X c v Constraints : 8i; d i ; m ¼ s i : X n 8i; d i ; m ¼ d i : X n 8i; d i ; m ¼ d i : X n B id i ¼ 1; B idi ¼ 1; fb idi Bidi nm g¼0; ð1þ ð2þ ð3þ 8i; d i ; m; n : B idi þ P idi 6 1; ð4þ 8i; m; n; m; n : X fp idi ðbid i P i Þg d i 6 N K i ; 8m; n; m; n : X i ðþ fp i Ki g 6 v. ð6þ Explanation of equations: Eqs. (1) (3) are flow equations to construct a backup path from root (the source of a multicast session or of a light-tree) to each destination node. Eq. (4) ensures that this backup path is link-disjoint to its primary counterpart. Eq. () assigns K i to 1 whenever a cut on link m $ n activates a backup edge on m! n for session i. Eq. (6) computes the number of backup edges, v, to be reserved for any link failure m $ n in the network. 3. Illustrative numerical results We study cross-sharing, first, for a small network for illustration purposes and then for a large nationwide network A small example A batch of b = multicast connections, S 1 ={(A, B, C, D, E)}, S 2 ={(F, A, B, C, D)}, S 3 ={D, A, B, F}, S 4 ={C, E}, and S ={B, D}, are established on an example network shown in Fig. 2. Each fiber link can carry W = 4 wavelength channels. The result of optimally routing the five multicast connections (obtained from ILP solver, CPLEX) using cross-sharing trees is shown in Table 2. For the optimal routing shown in Table 2, we observe the following: Idle-backup edges on D! C are shared by connections S 1 and S 3. Note that the backup D! C of S 2 could not be shared with the same backup of either S 1 or S 3. For session S 1, D! C would begin carrying bitstreams when either A M B or B M C fails. For session S 2, D! C would begin carrying bitstreams when either F M B or A M B or F A E 8 Fig. 2. An example small network. B 4 C D 2 9

5 204 N.K. Singhal et al. / Computer Networks 0 (2006) Table 2 Result from ILP showing routing of multicast connections using cross-sharing trees Multicast connections Primary edges Idle-backup edges S 1 ={A, B, C, D, E} A! B, B! C, C! D, D! E A! F, F! E, E! D, D! C, C! B S 2 ={F, A, B, C, D} F! A, A! B, B! C, C! D F! E, E! D, D! C, C! B, B! A S 3 ={D, A, B, F} D! E, E! F, F! A, F! B D! C, C! B, B! A, A! F S 4 ={C, E} C! E C! B, B! A, A! F, F! E S ={B, D} B! C, C! D B! A, A! F, F! E, E! D B M C fails. For session S 3, D! C would begin carrying bitstreams when either D M E or E M F or F M B or B M A fails. While the set of primary links protected by D M C for sessions S 1 and S 3 are disjoint, the set of primary links protected by D M C for session S 2 have common elements with the set of S 1 (A M B and B M C) and with the set of S 3 (F M A), preventing sharing of D M C of S 2 with S 1 or S 3. Idle-backup edges on A! F are shared by connections S 3, S 4, and S. Idle-backup edges on B! A are shared by connections S 2, S 4, and S. Idle-backup edges on C! B are shared by connections S 2, S 3, and S 4. Table 3 Cost-savings comparison of protection methods Protection method Optimal cost (in units) Arc-disjoint trees [10] 134 Self-sharing [11] Cross-sharing (this study) % savings w.r.t. arc-disjoint trees Table 3 compares the three methods for protecting the group of multicast connections. First, the minimum-cost primary trees for the five multicast sessions were discovered using ILP formulation [1]. Next, the backup resources for these trees were computed from solving ILP formulations for the three methods arc-disjoint trees [10], self-sharing trees [11], and cross-sharing trees. The first method, arc-disjoint primary and backup trees, is used as a baseline for cost-comparison. The table shows that the method employing selfsharing trees to provision each connection has 3% cost-savings but the method employing crosssharing trees has cost-savings of 48%, a significant gain due to sharing of backup resources among several multicast connections , ,400 1,100 1, , , ,600 1, ,300 1, , , Fig. 3. A nationwide network used in the study.

6 N.K. Singhal et al. / Computer Networks 0 (2006) Cost of Backup Resource Batch Size (b) 3.2. A large nationwide network A batch of b = 2 multicast sessions, each with destination-set size 1, is randomly generated on a nationwide network shown in Fig. 3. The weights on the links of the network represent the length of the fiber in kilometers and are used as cost metric. Thus, the cost of the resources computed in this network is in lambda kilometers. ILP formulations for the three approaches (arc-disjoint, selfsharing, and cross-sharing) are solved to reserve backup resources for the batch of sessions. Fig. 4 compares the three approaches as the size of the batch (number of session requests) increases from 1 to 2. For batch size of one, both self-sharing and cross-sharing trees require equal backup resources. However, as the batch size increases, so does the sharing potential of the backup among the sessions. As a result, cross-sharing performs significantly better than self-sharing for a large number of sessions in the network which is also captured in the lowermost savings curve shown in Fig. 4. The cost savings of cross-sharing over self-sharing, shown in Fig. 4, for a batch size of 2 sessions is 39%. 4. Conclusion Arc-Disjoint Self-Sharing Cross-Sharing Savings from Cross-Sharing Fig. 4. Comparison of the three multicast protection approaches. In this study, we proposed the use of a link-vector model for protecting several multicast sessions from any single link failure in a network by maximizing sharing among backup edges. We investigated cross-sharing approach for both small and large networks. Our cross-sharing approach produces significant savings in the cost of backup resources over existing self-sharing or arc-disjoint approaches, especially for large batches. These cost savings were observed to be 48% for a small network and 39% for a large nationwide network. This study focused on reducing the cost of backup resources using cross-sharing approach after primary light-trees have been provisioned. We are studying efficient formulations to reduce the total cost of provisioning both primary arid backup trees employing cross-sharing approach. Cross-sharing is well applicable to other contexts, such as in SONET or Gigabit Ethernet (GbE), for lower-speed multicast trees. References [1] N. Singhal, C. Ou, B. Mukherjee, Shared protection for multicast sessions in mesh networks, Technical Digest, OFC, Anaheim, CA, March 200. [2] L.H. Sahasrabuddhe, B. Mukherjee, Multicast routing algorithms and protocols: a tutorial, IEEE Network (January/February) (2000) [3] L.H. Sahasrabuddhe, B. Mukherjee, Light-trees: Optical multicasting for improved performance in wavelengthrouted networks, IEEE Communications Magazine 37 (2) (1999) [4] X. Zhang, J. Wei, C. Qiao, Constrained multicast routing in WDMnetworks with sparse light splitting, in: Proceedings of IEEE INFOCOM2000, Tel Aviv, Israel, vol. 3, March 2000, pp [] R. Malli, X. Zhang, C. Qiao, Benefit of multicasting in alloptical networks, in: Proceedings of SPIE Conference on All-optical Networking, vol. 231, November 1998, pp [6] J. Gu, X. Hu, X. Jia, M. Zhang, Routing algorithm for multicast under multi-tree model in optical networks, Theoretical Computer Science 314 (1) (2004) [7] J. He, S.H. Chan, D.H.K. Tsang, Routing and wavelength assignment for WDMmulticast networks, in: Proceedings of IEEE Globecom Õ01, San Antonio, Texas, November [8] N. Sreenath, C. Siva Ram Murthy, G. Mohan, Virtual source based multicast routing in WDMoptical networks, Photonic Network Communications 3 (3) (2001) (Special Issue on WDMTechnology in Core, Metro and Access Networks). [9] A.E. Kamal, R. Ul-Mustafa, Multicast traffic grooming in WDMnetworks, in: Proceedings of Opticomm, October 2003, pp

7 206 N.K. Singhal et al. / Computer Networks 0 (2006) [10] N. Singhal, B. Mukherjee, Protecting multicast sessions in WDMoptical mesh networks, IEEE/OSA Journal of Lightwave Technology 21 (4) (2003) [11] N.K. Singhal, L.H. Sahasrabuddhe, B. Mukherjee, Provisioning of survivable multicast sessions against single link failures in optical WDMmesh network, IEEE/OSA Journal of Lightwave Technology 21 (11) (2003) [12] M. Medard, S. Finn, R. Barry, R. Gallager, Redundant trees for preplanned recovery in arbitrary vertex-redundant or edge-redundant graphs, IEEE/ACMTransaction on Networking 7 () (1999) [13] G. Mohan, C.S.R. Murthy, A.K. Somani, Efficient algorithms for routing dependable connections in WDM optical networks, IEEE/ACMTransactions on Networking 9 () (2001) [14] S.L. Hakimi, SteinierÕs problem in graphs and its implications, Networks 1 (2) (1971) [1] N. Singhal, B. Mukherjee, Architectures and algorithm for multicasting in WDMoptical mesh networks using opaque and transparent optical cross-connects, Technical Digest, OFC, Anaheim, CA, paper TuG8, March Narendra K. Singhal (SÕ00) received the B.Tech. (Hons.) degree in computer science and engineering from the Indian Institute of Technology, Kharagpur, India, in May 1998 and the Ph.D. degree in computer science from the University of California, Davis in September From June 1998 to September 1999, he was with Verifone India Ltd., a fully owned subsidiary of Hewlett Packard. He is a recipient of Professors for the Future Fellow (PFTF) award at the University of California, Davis. He is now working at Microsoft Corp. His research interests include optical network design, multicasting, survivability, and network optimization. Biswanath Mukherjee (SÕ82 MÕ87) received the B.Tech. (Hons.) degree from Indian Institute of Technology, Kharagpur (India) in 1980 and the Ph.D. degree from University of Washington, Seattle, in June At Washington, he held a GTE Teaching Fellowship and a General Electric Foundation Fellowship. In July 1987, he joined the University of California, Davis, where he has been Professor of Computer Science since July 199, and served as Chairman of Computer Science during September 1997 to June He is a winner of the 2004 Distinguished Graduate Mentoring Award at UC Davis. Two PhD Dissertations (by Laxman Sahasrabuddhe and Keyao Zhu), which were supervised by Professor Mukherjee, were winners of the 2000 and 2004 UC Davis College of Engineering Distinguished Dissertation Awards. He is co-winner of paper awards presented at the 1991 and the 1994 National Computer Security Conferences. He serves or has served on the editorial boards of the IEEE/ACMTransactions on Networking, IEEE Network, ACM/Baltzer Wireless Information Networks (WINET), Journal of High-Speed Networks, Photonic Network Communications, and Optical Network Magazine. He also served as Editor-at-Large for optical networking and communications for the IEEE Communications Society. He served as the Technical Program Chair of the IEEE INFOCOM Õ96 conference. He also serves as Chairman of the IEEE Communication SocietyÕs Optical Networking Technical Committee (ONTC). He is author of the textbook Optical Communication Networks published by McGraw-Hill in 1997, a book which received the Association of American Publishers, Inc.Õs 1997 Honorable Mention in Computer Science. He is a Member of the Board of Directors of IPLocks, Inc., a Silicon Valley startup company. He has consulted for and served on the Technical Advisory Board of a number of startup companies in optical networking. His research interests include lightwave networks, network security, and wireless networks. Canhui (Sam) Ou (SÕ02) received the B.S. degree from Peking University, Beijing, China, in 2000, and the M.S. and Ph.D. degrees from the University of California, Davis, in 2001 and 2004, respectively. He is currently a Principal Member of Technical Staff at SBC Services, Inc., San Ramon, CA. His technical interests include WDMnetworks, MPLS, optical Ethernet, and FTTx.