WAVELENGTH-DIVISION multiplexed (WDM) optical

Transcription

1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 22, NO. 9, NOVEMBER A Dynamic Routing Algorithm With Load Balancing Heuristics for Restorable Connections in WDM Networks Lu Ruan, Member, IEEE, Haibo Luo, and Chang Liu Abstract Dynamic routing of a restorable connection requires a pair of link-disjoint primary and backup lightpaths to be found online when a connection request arrives at the network. We present a distributed dynamic routing algorithm for restorable connections that uses load balancing heuristics in both primary and backup path computations to achieve low demand blocking. The key idea is to assign costs to links so that heavily loaded links will be avoided in the routing of the primary and backup paths and links with a high chance of including a sharable backup channel will be included in the backup path. Simulation results showed that the algorithm performs significantly better than a simple distributed algorithm and achieves comparable performance as a centralized algorithm. Index Terms Dynamic routing, load balancing heuristics, optical networks, restorable connections, wavelength-division multiplexed (WDM). I. INTRODUCTION WAVELENGTH-DIVISION multiplexed (WDM) optical networks are believed to be the backbone transport networks for the next-generation Internet [1]. A WDM network consists of optical cross-connects (OXCs) interconnected by multiwavelength optical fibers with each wavelength channel operating at gigabits-per-second speed. Connections in WDM networks are supported by lightpaths, where a lightpath is a circuit-switched communication pipe occupying one wavelength channel in each link along its route. If the OXCs are capable of wavelength conversion, different links on a lightpath can use different wavelengths; otherwise, the same wavelength must be used by all links on the lightpath. Since fiber cut is the predominant form of failures in WDM networks [2], it is important to support restorable connections that can survive any single fiber failure. A restorable connection can be realized by establishing two link-disjoint lightpaths. One lightpath is called primary lightpath, which is used to carry traffic under normal condition; the other lightpath is called backup lightpath, which is used to carry traffic when the primary lightpath fails. To reduce the spare capacity reservation for a backup lightpath, the technique of backup sharing can be used. In backup sharing, two backup lightpaths can share the Manuscript received March 27, 2003; revised May 27, This work was supported in part by the National Science Foundation (NSF) under CAREER Award ANI L. Ruan and C. Liu are with the Department of Computer Science, Iowa State University, Ames, IA USA ( ruan@cs.iastate.edu; liuc@cs.iastate.edu). H. Luo is with Microsoft Corporation, Redmond, WA USA ( haiboluo@microsoft.com). Digital Object Identifier /JSAC same wavelength on a common link if their primary lightpaths are link-disjoint. The sharing is possible since under the single link failure assumption two link-disjoint primary lightpaths cannot fail simultaneously, therefore their backup lightpaths will not be needed at the same time. The problem of restorable connection establishment has been studied under two traffic models: static traffic model and dynamic traffic model. Under the static traffic model, the set of connections to be established is given a priori and the problem is to find the primary and backup lightpaths for each connection so that the total wavelength consumption is minimized [3] [8]. Approaches to solve this problem include integer linear programming and combinatorial techniques such as simulated annealing and genetic algorithms. Under the dynamic traffic model, connection requests arrive at the network one by one and the problem is to compute a pair of primary and backup lightpaths online as a connection request arrives at the network with the goal of minimizing the connection blocking probability [9] [15]. In this paper, we consider the problem of restorable connection establishment under the dynamic traffic model. We propose a distributed online algorithm to compute primary and backup lightpaths for a given connection request based on the current network status. The algorithm uses load balancing heuristics to guide the routing of the primary and backup lightpaths and can achieve a blocking performance comparable to that of a centralized algorithm. We assume all network nodes have wavelength conversion capability so that a lightpath can use different wavelengths on its links. The rest of the paper is organized as follows. We introduce some terminologies in Section II. A review of previous work is given in Section III. In Section IV we present our distributed online routing algorithm for restorable connections. The control mechanism for establishing the primary and backup lightpaths is presented in Section V. We study the performance of the proposed algorithm in Section VI. Finally, a conclusion is given in Section VII. II. TERMINOLOGIES A wavelength channel in a link may be occupied by a primary lightpath, reserved by one or more backup lightpaths (backup sharing allows more than one backup lightpaths to share a wavelength channel), or free. We refer to these three types of channels as primary channel, backup channel, and free channel, respectively /04$ IEEE

2 1824 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 22, NO. 9, NOVEMBER 2004 Consider a backup channel and a satisfied demand. (In this paper we use demand and connection interchangeably.) s primary lightpath is said to be supported by if is reserved for s backup lightpath. The graph consisting of all nodes in the network and those links in the primary lightpaths supported by is called s supported graph. The complement of s supported graph is called s supportable graph. If an incoming demand s primary path is contained in s supportable graph, then it must be link-disjoint with the existing primary lightpaths supported by. Thus, the backup lightpath for can share with other backup lightpaths that have reserved.wedefine the ratio of the number of links in the s supported graph to the total number of links in the network as s supported ratio. We call a link P-only if it contains only primary channels. Clearly, neither the primary lightpath nor the backup lightpath of an incoming demand can use a P-only link. A primary lightpath can use a link only if the link contains a free channel. A backup lightpath can use a link if the link contains either a free channel or a sharable backup channel. III. PREVIOUS WORK We first describe two routing algorithms for restorable connection establishment that will be compared with our proposed algorithm later for the purpose of performance evaluation. Other related work is then reviewed. A. Centralized Algorithm (CA) In centralized scenario, when a demand arrives at the source node, the node sends the demand information to a network management system (NMS), which runs a centralized routing algorithm to compute a primary/backup path pair for the demand. The NMS then sends the computed routes back to the source node and the source node performs a signaling procedure to set up the primary lightpath and reserve backup channels along the backup path. A centralized routing algorithm is proposed in [16]. The algorithm requires the NMS to maintain a complete view of the current network status, including channel types (primary, backup, or free) in each network link and the supportable graph of each backup channel. To compute the primary path, the algorithm removes all links without a free channel and then finds the shortest path between the source and the destination nodes as the primary path. To compute the backup path, the algorithm removes all links used by the primary path and all P-only links, then set the cost of the remaining links as follows: if a link contains a backup channel that can support the primary path (i.e., the primary path is contained in the channel s supportable graph), set the link cost to ; else if the link contains a free channel, set the cost to 1; else set the cost to infinity. The least-cost path is then computed as the backup path. Here, provides a tradeoff between capacity efficiency and backup path length. When is set to 0, the backup path uses the least number of free channels at the expense of taking more hops. Since the algorithm computes the primary path and the backup path in separate steps, although the backup path is optimal with respect to the primary path, it is not necessarily true that the total cost of the primary/backup path pair is minimum. An integer linear program (ILP) formulation was given in [10] to compute the minimum cost primary/backup path pair. However, the computation time of the ILP is on the order of minutes for medium sized networks and therefore is not suitable for online routing of dynamic demands. B. Simple Distributed Algorithm (SDA) In distributed scenario, the source node is responsible for computing the primary and backup paths for an arriving demand. Since it is not feasible for each node to maintain the complete network status information, each node only maintains a limited network status information and uses this limited information for path computation. In the simple distributed algorithm (SDA) presented here, each node only knows whether each link has a free channel. The primary path computation is the same as that of the centralized algorithm. In backup path computation, the algorithm excludes the links along the chosen primary path and the links with no free channels, and then find the shortest path in the graph as the backup path. Although the source node does not have enough information to exploit backup sharing in backup path computation, a technique proposed in [12] can be used to determine the shareability of backup channels and reserve a channel for the backup path accordingly during the signaling of the backup path. The technique requires each OXC to maintain a sharing database that contains the supportable graphs for each backup channel in each link that is adjacent to the node. During the signaling of the backup path, each node along the path determines, using the sharing database, whether the backup path can share a backup channel in the link connecting itself and the next node. If so, a sharable backup channel is reserved for the backup path; otherwise, a free channel is reserved. In both cases, the sharing database should be updated. Although SDA is not as capacity efficient as CA, it is more scalable and practical to implement since the algorithm is distributed and the required network status information (i.e. whether each link contains a free channel) can be disseminated to every network node with little overhead. A drawback of SDA is that it may cause unnecessary blocking, i.e., it may reject a demand because it can t find a feasible backup path for it even though such a path exists in the network. To see why, recall that SDA only allows the backup path to use links that have a free channel. However, a backup path does not have to use a free channel in every link because it sometimes can share a backup channel with existing backup paths. To overcome this problem, we can exclude P-only links instead of excluding links with no free channels in backup path computation. This allows a backup path to use a link that has backup channels but no free channels. However, a backup path found this way may be blocked during the signaling of the backup path if a link in the path has no free channels and none of the backup channels in the link can support the primary path. In this case, a retry scheme [12] could be used to try to find another backup path at the cost of longer demand admission latency.

3 RUAN et al.: A DYNAMIC ROUTING ALGORITHM WITH LOAD BALANCING HEURISTICS 1825 C. Other Related Work Many dynamic routing algorithms for restorable connections have been proposed in recent years [9] [14]. The algorithms can be classified into two categories: alternate routing and adaptive routing. In alternate routing, a set of candidate primary/backup path pairs are precomputed and the pair with the minimum cost is chosen [13], [14]. In adaptive routing, a pair of primary/backup paths are computed online based on the current network status [9] [12]. A commonly used approach for backup path computation is to assign each link a cost that is an estimate of the additional bandwidth needs to be reserved on the link if the link is included in the backup path and then compute the least-cost path as the backup path [9] [11]. Either complete network status information or aggregate network status information can be used to compute the link costs; they provide a tradeoff between the performance of the routing algorithm and the amount of network status information needs to be maintained by the network nodes. In [12], the authors proposed to set the cost of a link for backup path computation to be the estimate of the probability that the link contains a sharable backup channel. To compute the cost of a link, a random sample of source-destination pairs is chosen first. For each pair in the sample, a set of shortest paths are computed as the potential primary paths, and the fraction of these paths that the link can support is determined. The average is then taken over all pairs in the sample to obtain the probability that this link contains a sharable backup channel. As mentioned in the simulation results, the method does not lead to significant savings in backup capacity. What s more, the computation time is rather long when a large sample is used. In this paper, we propose a new distributed dynamic routing algorithm for restorable connections. The algorithm uses adaptive routing method, i.e., it computes a pair of primary/backup paths online based on the current network status as a connection request arrives at the network. Unlike existing algorithms, we use load balancing heuristics in path computation. The key idea is to avoid using heavily loaded links in both primary and backup paths to achieve low connection blocking. Load balancing heuristics have been proposed previously for routing nonrestorable connections to achieve low connection blocking. In [17], a dynamic routing algorithm called least congested path (LCP) routing was proposed. LCP uses alternate routing method where a set of routes is precomputed for each pair of source-destination nodes. The number of free channels of a path is defined as the minimum number of free channels of all links in the path. When a demand arrives at the network, the numbers of free channels of all precomputed paths for this demand are collected and the path with the maximum number of free channels is chosen as the least congested path to accommodate the demand. A variant of LCP is proposed in [18] to reduce its computation time. Instead of searching all the links on the precomputed paths to obtain the number of free channels of the paths, only the first (a parameter to the algorithm) links on each path are searched to decide which path to select. In [19], an adaptive routing strategy called weighted-shortest path (WSP) was proposed. WSP seeks to find a path that minimizes Fig. 1. Assume links b-e and c-f have no free channels and all other links have 2 free channels. (a) Without considering load balancing, demand (c, d) is blocked. (b) Demand (c, d) can be satisfied if load balancing is considered. the resource cost while keeping the traffic load among the links as balanced as possible. To our best knowledge, the algorithm to be presented in the next section is the first to include load balancing heuristics in the routing of restorable connections. IV. ROUTING RESTORABLE CONNECTIONS WITH LOAD-BALANCING HEURISTICS The goal of dynamic routing algorithm is to accept as many demands as possible under the network resource constraint. CA can achieve this goal by finding a primary/backup lightpath pair that uses the minimum number of free channels for the current demand so that more network resources are left for the future demands. However, due to its centralized nature, CA is not scalable to large networks and the failure of the NMS can bring down the entire network. On the other hand, although SDA does not have the scalability problem and the single point of failure problem of CA, its performance in terms of the number of demand blocking is much worse than that of CA (as will be shown in Section VI). In this section, we present a new distributed routing algorithm that can achieve a performance close to that of CA. The key idea of the algorithm is to consider load balancing in path computation, i.e., lighter-loaded links are preferred over heavier-loaded links when routing the primary and backup paths. The benefit of considering load balancing in path computation can be seen from the example shown in Fig. 1. Here, we assume links - and - currently have no free channels and all other links have two free channels. Now suppose three demands (, ), (, ), (, ) arrive at the network sequentially. Without considering load balancing, we may route the first two demands as shown in Fig. 1(a), which will cause the third demand to be blocked. If we consider load balancing, we would route the second demand over the path since this path has lighter load than the path In this case, the third demand can be routed over link -, as shown in Fig. 1(b). Thus, considering load balancing in demand routing can improve the demand blocking performance. In the next section, we describe our routing algorithm, called Routing with Load Balancing Heuristics (RLBH). RLBH computes primary path and backup path for a demand in two separate steps. In each step, a cost is assigned to very network link and the least-cost path is chosen. A. Primary Path Computation in RLBH The link cost function for primary path computation is designed based on the following two rules. 1) The primary path should use the shortest path as long as every link along the path

4 1826 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 22, NO. 9, NOVEMBER 2004 has plenty of free channels. 2) When the number of free channels in a link is less than or equal to a threshold, the link becomes critical and we take precautionary step to avoid using it. To these ends, we assign a cost of 1 to every link with more than free channels and a cost greater than 1 to every link with no more than free channels, where is a constant called critical index. Formally, given a link, we define its link cost for primary path computation as follows: cost if has no free channels if has and 0 free channels if has free channels where is a constant and. After we assign each link a cost using the above formula, Dijkstra s algorithm is then used to compute the least-cost path as the primary path. If the least-cost path has a cost of infinity, then the demand is blocked; otherwise a backup path is computed using the method given in the next subsection. Note that when, primary path computation in RLBH becomes the same as that of CA and SDA. B. Backup Path Computation in RLBH In backup path computation, it is desirable not only to avoid using heavily loaded links as in primary path computation but also to use links that have high chance of containing a sharable backup channel. Both goals can be achieved by using a properly designed link cost function that allows us to use the number of free channels in every link as well as the usage of backup channels in every link to guide the backup path computation. In our algorithm, a backup channel with supported ratio larger than (called venture index) is considered not able to support any more primary paths; therefore such a backup channel is not considered as a backup channel candidate for new demands. Based on this, we define a link s backup channel candidates for new demands to contain those backup channels with supported ratio less than or equal to and all the free channels in the link. Clearly, links with more backup channel candidates would be preferred over links with less backup channel candidates when routing the backup path. Thus, we let the link cost function for backup path computation to be inversely related to the number of the link s backup channel candidates. Given a link, we let cand denote the number of s backup channel candidates. The link cost function for backup path computation is defined as follows: cost cand if cand or is on the primary path otherwise where is an integer greater than 1. After we assign each link a cost using the above formula, Dijkstra s algorithm is then used to compute the least-cost path as the backup path. If the least-cost path has a cost of infinity, then the demand is blocked; otherwise, the demand is admitted. The reason we include an exponent in the cost function is that when the difference between two link costs Fig. 2. r s effect on backup path computation. may be too small to reflect the preference in backup path computation even though a notable difference exists between the number of backup channel candidates in those two links. For example, consider Fig. 2, which shows part of a network with 16 wavelengths per link. We want to find the backup path for demand (, ), which will pass through and. Suppose both link and link currently have seven free channels and two backup channels with supported ratio less than or equal to,so cand cand. As for link, cand with only three free channels left. When, cost of,, and are 0.111, 0.111, and 0.2, respectively, and the algorithm will include link in the backup path. Consequently, will have only two free channels left (or still three left if a sharable backup channel for the demand exists in the link), aggravating the imbalance of wavelength consumption among,, and. On the other hand, if, cost of,, and will be 0.012, 0.012, and 0.04, respectively, so and will be chosen for the backup path. In this case, will have three free channels left, and each will have six or seven free channels left, giving more balanced wavelength consumption. V. CONTROL MECHANISM After a pair of primary and backup paths is computed by RLBH, signaling procedures need to be carried out to setup the primary lightpath and reserve wavelength channels for the backup lightpath. For primary lightpath setup, a reservation message is sent along the primary path. Each intermediate node reserves one free channel using first-fit wavelength assignment (i.e., the first free channel is reserved). After the destination receives the reservation message, it sends an acknowledgment message (ACK) back to the source node. Each intermediate node configures its cross-connect upon receiving the ACK and forward the message to the next node toward the source. In parallel with primary lightpath setup, a similar procedure is carried out for backup lightpath reservation. For each link on the backup path, first-fit wavelength assignment is used to choose a backup channel or a free channel for the backup lightpath. That is, the first backup channel that can support the primary lightpath is chosen if such a channel exists; else, the first free channel is chosen if such a channel exists; if neither a sharable backup channel nor a free channel exists, the demand cannot be admitted and a REJECT message is send back toward the source. Each intermediate node will cancel the channel reservation already made for the backup lightpath upon receiving the REJECT message. If channel reservation is successful, then the following update is performed: If a backup channel is chosen, the primary path is added to the channel s supported graph; if a free channel is chosen, the channel status is changed to backup

5 RUAN et al.: A DYNAMIC ROUTING ALGORITHM WITH LOAD BALANCING HEURISTICS 1827 TABLE I NUMBER OF BLOCKED DEMANDS UNDER DIFFERENT VALUES AND LOADS TABLE II NUMBER OF BLOCKED DEMANDS UNDER DIFFERENT r, AND LOADS Fig node 51-link network. and its supported graph contains only the primary path. Note that this requires the primary path information to be included in the reservation message. Unlike primary lightpath setup, the cross-connects in the nodes along the backup path cannot be configured at this time due to backup sharing. The configurations are done when the backup lightpath needs to be activated to restore traffic after the primary lightpath fails. The RLBH algorithm needs to know the number of free channels and the number of candidate backup channels in every link in order to perform the primary and backup path computations. This information can be disseminated to all nodes in the network using an augmented Interior Gateway Protocol (IGP) with appropriate extensions to its link state advertisement messages [20]. VI. NUMERICAL RESULTS To evaluate the performance of RLBH, we conducted simulations on a network topology with 32 nodes and 51 links used in [21], which is shown in Fig. 3. Dynamic traffic is used in the simulations. The arrival of traffic follows Poisson distribution with demands per second. The demand holding time is exponentially distributed with a mean of. The traffic load measured in erlangs is. The same set of random demands is loaded to the network for each simulation run and the number of blocked demands is recorded. Note that in RLBH, demand blocking can occur during either path computation or backup lightpath reservation. During path computation, a demand will be blocked if a finite-cost primary path or a finite-cost backup path cannot be found. During the reservation of the backup lightpath, the demand will be blocked if a link on the backup path has no free channels and no backup channel in the link can support the primary lightpath. Results presented in this section are obtained with link capacity set to 16 (i.e., there are 16 wavelength channels in every link). Although not shown due to space limitation, similar results are also obtained with link capacity set to 8. A. On Primary Path Computation The first set of simulations is aimed to study the impact of the link cost function for primary path computation in RLBH. To this end, we use the backup path computation procedure of SDA to compute the backup path in this set of simulations. For primary path computation, is set to 1.5. The number of blocked demands for different values and loads are shown in Table I. The bold number in each column is the smallest value of that column, so the corresponding value is the best choice for the load of that column. Note that when is 0, the algorithm becomes SDA. As shown in the table, for a fixed load, the number of blocked demands tends to first decrease and then increase as increases. Under all loads, proper choice can reduce the number of blocked demands compared with SDA (i.e., ) and the reduction is significant under light and medium loads. In general, or gives the best performance. B. On Backup Path Computation The second set of simulations is aimed to study the impact of the link cost function for backup path computation in RLBH. To this end, we do not adopt the precautionary step in the primary path computation, i.e., is set to 0 in this set of simulations. Table II shows the number of blocked demands for different values and loads under two different values ( and ). For comparison, the number of blocked demands by CA and SDA

6 1828 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 22, NO. 9, NOVEMBER 2004 TABLE III NUMBER OF BLOCKED DEMANDS BY SDA, RLBH, AND CA are also listed in the table. Note that primary path computation is the same in CA, SDA, and RLBH, the difference lies only in the backup path computation. The bold numbers in the table stand for the smallest number of blocked demands under different values for a fixed load and value. The results showed that increasing value can reduce the number of blocked demands. However, increasing to 4 and 5 (results not shown in the table) does not bring considerable reductions. As shown in the table, CA has much better blocking performance than SDA. When a proper value for is chosen, the performance gap between RLBH and CA is much smaller than the performance gap between SDA and CA, which shows the effectiveness of our backup path computation algorithm. Another finding from the table is that as the load increases, the value corresponds to the bold number tends to increase. This indicates that in order to achieve good performance, backup channels with higher supported ratio should be considered as backup channel candidates as the traffic load increases. C. Overall Comparison We now evaluate the complete RLBH, which includes load balancing heuristics in both primary and backup path computations. In the simulations, we set for primary path computation and for backup path computation. We also set the value of based on the traffic load as follows: for the traffic load ranges of [40, 70], [80, 90], and 100, is set to 10%, 20%, and 30%, respectively. The number of blocked demands by SDA, RLBH, and CA are shown in Table III. The results showed that the performance of RLBH is very close to that of CA under all traffic loads and RLBH performs significantly better than SDA. In summary, RLBH is a scalable and efficient algorithm for routing restorable connections since it requires very limited information (i.e., the number of free channels and the number of candidate backup channels in every link) for path computation while achieving comparable performance as the centralized algorithm that requires complete network status information for path computation. VII. CONCLUSION In this paper, we presented a distributed routing algorithm called RLBH for computing a pair of primary and backup paths for a restorable connection in WDM networks. The algorithm aims to achieve low demand blocking by including load balancing heuristics in both primary and backup path computations. RLBH assigns link cost based on the link channel usage information to guide the computation of the primary and backup paths. For primary path computation, a link is assigned a higher cost if the number of free channels in the link is smaller than or equal to a threshold. For backup path computation, the link cost is a function of the estimated number of backup channel candidates in the link. Simulation results show that the blocking performance of RLBH is very close to that of CA. However, RLBH requires much less network status information for path computation compared with CA. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their valuable comments that greatly helped improve the quality of the paper. REFERENCES [1] B. Mukherjee, WDM optical communication networks: progress and challenges, IEEE J. Select. Areas Commun., vol. 18, pp , Oct [2] L. Sahasrabuddhe, S. Ramamurthy, and B. Mukherjee, Fault management in IP-over-WDM networks: WDM protection versus IP restoration, IEEE J. Select. Areas Commun., vol. 20, pp , Jan [3] M. Herzberg, S. J. Bye, and A. Utano, The hop-limit approach for spare-capacity assignment in survivable networks, IEEE/ACM Trans. Networking, vol. 3, pp , Dec [4] B. Van Caenegem, N. Wauters, and P. Demeester, Spare capacity assignment for different restoration strategies in mesh survivable networks, in Proc. Int. Conf. Communications, 1997, pp [5] Y. Liu, D. Tipper, and P. Siripongwutikorn, Approximating optimal spare capacity allocation by successive survivable routing, in Proc. IEEE INFOCOM, 2001, pp [6] B. Van Caenegem, W. Van Parys, F. De Turck, and P. M. Demeester, Dimensioning of survivable WDM networks, IEEE J. Select. Areas Commun., vol. 16, pp , Sept [7] M. Alanyali and E. Ayanoglu, Provisioning algorithms for WDM optical networks, IEEE/ACM Trans. Networking, vol. 7, pp , Oct [8] Y. Miyao and H. Saito, Optimal design and evaluation of survivable WDM transport networks, IEEE J. Select. Areas Commun., vol. 16, pp , Sept [9] C. Qiao and D. Xu, Distributed partial information management (DPIM) schemes for survivable networks part I, in Proc. IEEE INFOCOM, 2002, pp [10] M. Kodialam and T. V. Lakshman, Dynamic routing of bandwidth guaranteed tunnels with restoration, in Proc. IEEE INFOCOM, 2000, pp [11] G. Li, D. Wang, C. Kalmanek, and R. Doverspike, Efficient distributed path selection for shared restoration connections, in Proc. IEEE IN- FOCOM, 2002, pp [12] S. Sengupta and R. Ramamurthy, Capacity efficient distributed routing of mesh-restored lightpaths in optical networks, in Proc. IEEE GLOBECOM, 2001, pp [13] G. Mohan and C. Murthy, Routing and wavelength assignment for establishing dependable connections in WDM networks, in Proc. IEEE Int. Symp. Fault-Tolerant Computing, 1999, pp [14] C. Xin, Y. Ye, S. Dixit, and C. Qiao, A joint working and protection path selection approach in WDM optical networks, in Proc. IEEE GLOBECOM, 2001, pp [15] G. Mohan, C. S. R. Murthy, and A. K. Somani, Efficient algorithms for routing dependable connections in WDM optical networks, IEEE/ACM Trans. Networking, vol. 9, pp , Oct [16] L. Ruan and H. Luo, Dynamic routing of restorable lightpaths: a tradeoff between capacity efficiency and resource information requirement, in Proc. Conf. Optical Network Design and Modelling (ONDM), 2003, pp [17] K. Chan and T. P. Yum, Analysis of least congested path routing in WDM lightwave networks, in Proc. IEEE INFOCOM, 1994, pp [18] L. Li and A. K. Somani, Dynamic wavelength routing using congestion and neighborhood information, IEEE/ACM Trans. Networking, vol. 7, pp , Oct [19] C.-F. Hsu, T.-L. Liu, and N.-F. Huang, Performance of adaptive routing strategies in wavelength-routed networks, in Proc. IEEE Int. Performance, Computing, And Communications Conf. (IPCCC), 2001, pp

7 RUAN et al.: A DYNAMIC ROUTING ALGORITHM WITH LOAD BALANCING HEURISTICS 1829 [20] D. Katz, K. Kompella, and D. Yeung, Traffic engineering (TE) extensions to OSPF version 2, RFC 3630, Sept [21] W. D. Grover and J. Doucette, Design of a meta-mesh of chain subnetworks: enhancing the attractiveness of mesh-restorable WDM networking on low connectivity graphs, IEEE J. Select. Areas Commun., vol. 20, pp , Jan Haibo Luo received the B.E. degree from Beijing University of Aeronautics and Astronautics, Beijing, China, in 1996, the M.E. degree from Zhejiang University, Hangzhou, China, in 1999, and the M.S. degree in computer science from Iowa State University, Ames, in He is currently with Microsoft Corporation, Redmond, WA. His research interests included restoration in optical networks. Lu Ruan (M 02) received the B.E. degree in computer science from Tsinghua University, Beijing, China, in 1996, and the M.S. and Ph.D. degrees in computer science from the University of Minnesota, Twin Cities, in 1999 and 2001, respectively. She is currently an Assistant Professor of Computer Science at Iowa State University, Ames. Her research interests include next-generation Internet, optical networks, and wireless networks. Dr. Ruan is a recipient of a CAREER Award from the National Science Foundation. Chang Liu received the B.E. degree in computer science and engineering from Beijing Institute of Technology, Beijing, China, in 1994, the M.S. degree in computer science from Peking University, Beijing, China, in 1999, and the M.S. degree in computer science from Iowa State University, Ames, in He is currently working toward the Ph.D. degree in the Department of Computer Science, Iowa State University. His research interests include optical networks, wireless networks, and distributed systems.