Dynamic routing and assignment of wavelength ... - Semantic Scholar

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 18, NO. 10, OCTOBER 2000

Dynamic Routing and Assignment of Wavelength Algorithms in Multifiber Wavelength Division Multiplexing Networks Shizhong Xu, Lemin Li, and Sheng Wang

Abstract—This paper studies multihop optical networks in which nodes employ wavelength routing switches that enable the establishment of wavelength division multiplexed (WDM) channels, called lightpaths, between node pairs. In fact, most optical networks are multifiber networks. The problem of dynamical routing and assignment of wavelength (RAW) in such networks is studied in this paper. Two resource assignment strategies, PACK and SPREAD, are proposed. By virtue of layered-graph, routing and assignment of wavelength subproblems can be considered simultaneously. These two strategies can be used to solve the RAW problem in networks with even links as well as that in networks with uneven links. Simulation shows that layered-graph-based RAW algorithms perform better than the existing ones. It also shows that SPREAD with distributive use of network resources can achieve better performance than PACK with collective use of resources in multifiber networks. The layered-graph-based algorithms can effectively deal with the failure of fiber/link and node. By making use of the special structure of layered-graph, we propose a shortest path algorithm, whose complexity is lower than that of the standard shortest path algorithm. Index Terms—Dynamic traffic, layered-graph-based RAW algorithm, multifiber WDM networks. Fig. 1. Wavelength-routing node with nodal degree and four wavelengths per fiber.

I. INTRODUCTION

W

ITH THE development of an information-oriented society and the explosive growth of the Internet, the requirements of network capacity have increased dramatically, which is promoting the construction of a broadband trunk network [1]–[3]. Wavelength division multiplexing (WDM) is a promising approach that can use the enormous bandwidth of the optical fiber. A single fiber can be employed for multiple data streams simultaneously. All-optical networks employing the concept of WDM and wavelength routing are considered as the transport networks for the future [1]–[3]. In such networks, two adjacent nodes are connected by one or multiple fibers. Each node has a dynamically configurable optical switch which supports fiber switching and wavelength switching, i.e., the data on a specified input fiber and wavelength can be switched to a specified output fiber on the same wavelength [4]. In order

Manuscript received October 15, 1999; revised May 15, 2000. This work was supported by the Natural Science Foundation of China under Contract 69990540. This paper was presented in part at IEEE ICCCN99, Boston, MA, Oct. 11–13,1999. The authors are with the National Key Lab of Broadband Optical Fiber Transmission and Communication Networks, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China (e-mail: {xsz, lml, wsh_keylab}@uestc.edu.cn). Publisher Item Identifier S 0733-8716(00)09024-7.

= 4, two fibers per link,

to transfer data between source–destination node pairs, a lightpath needs to be established by allocating the same wavelength throughout the route of the transmitted data. Benefiting from the development of all-optical amplifier such as EDFA, lightpaths may span more than one fiber link and remain entirely optical from end to end. It is demonstrated that the introduction of wavelength-routing networks not only offers the advantages of higher transmission capacity and routing node throughput, but also satisfies the growing demand for protocol transparency and simplified operation and management [1]–[3]. A wavelength-routing node with nodal degree four (four input optical cables and four output optical cables), two fibers per link (cable), and four wavelengths per fiber is shown in Fig. 1. We assume that the switches are incapable of converting the data on one wavelength to another wavelength (wavelength conversion) [5]–[7]. Eliminating wavelength conversion significantly reduces the cost of the switch; however, it may lead to reduced network efficiency because the same wavelength must be available on each link of the route for a call to be established. For example, there may be a route which has a wavelength available on each of its links but they may not be the same wavelength, thereby causing the call to be rejected (i.e., wavelength blocking).

0733–8716/00$10.00 © 2000 IEEE

XU et al.: DYNAMIC ROUTING AND ASSIGNMENT OF WAVELENGTH ALGORITHMS

Most of the previous works on routing and wavelength assignment focus on single-fiber networks. There has been an increasing interest in studying the performance improvement due to the deployment of multiple fibers between node pairs [4], [8], [10], [12]–[14]. This interest is motivated by the economic advantage of installing bundles of fibers for the purposes of fault tolerance and future network growth. Two kinds of multifiber networks are studied in this paper. One is the network with even links, i.e., the number of fibers on each link is the same. The other is the network with uneven links, i.e., the number of fibers on different links may be different. In a real network, it is not always true that the number of fibers in any link is the same. Note that the multifiber network has partial wavelength conversion capability [4]. An -fiber -wavelength netwavelengths work (i.e., there are fibers in each link and on each fiber) is functionally equivalent to an -wavelength single-fiber network with limited wavelength conversion of degree [4], [6]. The benefits of wavelength conversion at the wavelength-routing nodes have been studied extensively [6], [7]. As mentioned in [7], limited wavelength conversion can obtain most of the performance advantage of full wavelength conversion. Multifiber links are also found to reduce the gain obtained due to wavelength conversion, and the number of fibers is found more important than the number of wavelengths for a network [8]. Therefore, multifiber networks can provide a viable and economical alternative to wavelength conversion [4], [6], [7]. Routing and assignment of wavelength (RAW) is an important problem in WDM networks. Given a set of calls or lightpaths (i.e., wavelength continuous paths without intermediate processing) to be established between the node pairs, the problem is to find routes from the source nodes to the destination nodes, and assign wavelengths to those routes. Several RAW algorithms that differ in the traffic assumptions and the performance metric used have been proposed. The traffic assumptions generally fall into one of two categories [3]: 1) static traffic, where a set of call requests is given and routes as well as wavelengths have to be assigned to calls so that some metric is optimized [9]; and 2) dynamic traffic, where calls arrive to and depart from the network randomly [10], [11]. The performance metric in the latter case is typically the call blocking probability. Analysis of the call blocking probability in multifiber networks has been studied in [4], [8], and [13]. The problem of dynamically establishing and terminating lightpaths may occur in several circumstances. For example, it may become necessary to reconfigure the network in response to changing traffic pattern or link/node failures [3]. Since the RAW problem is NP-complete [3], heuristics is necessary. It is often decoupled into routing subproblem and wavelength assignment subproblem in most algorithms proposed. In fixed routing (FR), every source–destination (s–d) pair is assigned a single route [4], [10]. A new call is blocked if its associated route is not available. If the route is available, i.e., at least one wavelength is idle on all of the fiber links along the route, wavelength assignment algorithm is needed to choose one denote the set of available available wavelength. Let wavelengths on path . RANDOM algorithm chooses one

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available wavelength from randomly [4]. First-fit (FF) [4] which has the lowest index. While chooses the choosing wavelength, RANDOM and FF ignore the network state. By taking the network state into consideration, maxsum (MS) [10] and relative capacity loss (RCL) [12] try to establish the new call on a wavelength which has the least influence on the whole network. In alternate routing (AR), each s–d pair is assigned a set of routes. The set is searched in a fixed [4], [12] or adaptive order [14] to find an available route for a new call. The fixed-paths least-congestion (FPLC) algorithm selects the route with the maximum number of idle wavelengths. If a call request cannot be accommodated by any of the routes, it is blocked. Based on the so-called layered-graph model, the RAW problem in single-fiber networks is solved with routing and wavelength assignment steps tightly coupled [11]. In this paper, we consider the dynamic RAW problem in multifiber networks without wavelength conversion. In Section II, we extend the layered-graph model to multifiber networks. In Section III, two resource assignment strategies for dynamic RAW problem and one shortest path algorithm are proposed. Simulation results and conclusions are presented in Sections IV and V, respectively. II. LAYERED-GRAPH MODEL FOR MULTIFIBER NETWORKS Define a network topology for a given WDM optical networks, where N is the set of nodes, L is the set of bidirectional links, and W is the set of available wavelengths per fiber. The set of wavelengths on each fiber is the same, . For any link is the set of i.e., pairs of fibers on it, i.e., is assumed to be composed of is the set of . unidirectional fibers. The layered-graph model LG(V, E) is a directed graph, which can be obtained from a given network topology G as follows. in G is replicated times in LG. These Each node . If link vertices are denoted by connects node to , then vertices and are for all connected by a couple of directed edges, . Edges and can accommodate equivalent channels, respectively. The number of vertices in LG is , and the number of directed edges is . Fig. 2(b) shows an example of layered-graph, which is obtained from the physical network topology shown in Fig. 2(a). The subgraph induced by the vertex s and edges s in the layered-graph is called the wth layer (wavelength plane). Assume that all the lightpaths (calls) are bidirectional. A lightpath in G corresponds to a pair of paths in LG. For example, as shown in Fig. 2(a), nodes 2 and 4 are connected by a , and on wavelength , lightpath consisting of links which corresponds to a pair of paths in Fig. 2(b). One consists , , and . Another consists of , , and of edges . We add two new vertices , to the LG. is connected to , , via zero-weight edges, and is connected to via zero-weight edges, too. When a new call from node to arrives, the RAW problem can be further reduced to finding to . a shortest path from

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If the resources on one edge are used up, the cost associated with the edge will be infinite. The routing and wavelength assignment for the new call can be simply realized by applying a shortest path algorithm (e.g., the Dijkstra algorithm [15]) in the layered-graph. In multifiber networks, the definition of cost function for each edge is much more complex. A good dynamic algorithm could use the network resources (wavelengths and fibers) effectively. In layered-graph, different cost functions correspond to different resource assignment strategy. We propose two strategies as follows. As shown in Section IV, they can be used to solve the RAW problem in multifiber networks with even links as well as that in networks with uneven links. 1) PACK Strategy: In PACK strategy, the cost functions of edges and , , and , are defined as follows: if

(1)

if

Fig. 2. (a) Physical network

G and (b) layered-graph LG.

III. DYNAMIC RAW ALGORITHMS IN MULTIFIBER NETWORKS Consider a WDM network at a certain state in which a set of lightpaths has been established and wavelengths are assigned to those lightpaths. Lightpath requests are assumed to arrive at the network according to a Poisson process with exponentially distributed holding time. The dynamic RAW problem can be solved by simply applying a shortest path algorithm in the layered-graph. A formal description of this formulation and two resource assignment strategies are given in Subsection A. The layered-graph-based RAW algorithms are given in Subsection . A modified shortest path algorithm is proposed based on the special structure of the layered-graph in Subsection . A. Mathematical Formulation for Multifiber Networks In single-fiber networks, each wavelength on one link can support one lightpath at the most. Lightpaths using the same wavelength cannot share any link. However, in multifiber networks, lightpaths using the same wavelength can share common links, as long as they can be accommodated on different fibers, i.e., the wavelength on the corresponding link can provide adequate free channels. Mapped into the layered-graph, the difference between the RAW problem in single-fiber networks and that in multifiber networks is significant. In single-fiber networks, the layeredgraph-based algorithm [11] attempts to find a path with lowest cost, which is edge-disjoint with the existing calls, for the new call. As mentioned in [11], the cost of one edge may be a function of physical length of the corresponding link if propagation delay is a concern. It also may be a function of the implementation cost associated with it. The cost can be set to 1 for all edges if the number of nodes in a lightpath is to be minimized.

is the number of occupied channels where at present. If there is any free channel on the on edge edge, the cost will be a constant, i.e., . Otherwise, the cost is the basic cost associated with link . will be infinite. It may be a function of physical length of the corresponding link, the installation cost of the fiber link, the number of optical amplifiers deployed along the link, and the cost of the OXC’s at the both ends of the link. This strategy attempts to pack the existing calls on as fewer edges and fewer layers as possible. The calls are routed on the most utilized wavelength and link first, in order to maximize the utilization of available wavelengths with more network resources reserved for accepting the calls arriving in the future. 2) SPREAD Strategy: In SPREAD strategy, the cost funcand are defined as follows: tions of edges

if if (2) is a constant associated with link . The cost of where as well as that of edge will increase by , if the edge there is any free channel after a new call is accommodated on it. Otherwise, the cost will be infinite. After a call is released, , if there is only one the cost will be . It is free channel left. Otherwise, the cost will decrease by obvious that the more the free channels are left on one edge, the lower the cost is. Depending on the quantity of , this strategy can spread the existing calls over all the edges and layers as even as possible by using any shortest path algorithm. In order to achieve a near-uniform distribution of the load over the wavelength set and link set, the calls are routed on the least utilized wavelength and link first. A simple example is given to show the difference between PACK and SPREAD. Assume that the last call (from node to ) is accommodated along path on the th layer, and there is still available channel along the . In PACK the cost of every


edge along has no change, but in SPREAD the cost of edge will increase by for any edge along . If the next arriving call is still from node and , PACK will still establish it on , but SPREAD will choose one suitable path on a suitable layer based on the whole network state. Now the dynamic RAW problem can be formulated as follows. Suppose that the arriving call is from node to in a denote the set of all the paths from physical network G. Let to in the corresponding LG. If edge is in path , the , otherwise, . If the new call is index function , otherwise, accommodated on , then the index function . , of a path from vertex to Then, the minimal cost, can be formulated as follows: (3) , where

subject to .

B. The Dynamic RAW Algorithms for Multifiber Networks The problem mentioned above can be solved by using any shortest path algorithm, e.g., Dijkstra. If the cost of the shortest , is found to be finite, the call will be accepted and path, accommodated on the route and the wavelength corresponding to the shortest path. otherwise the call will be blocked. Note that, the cost on the edges have to be updated according to (1) or (2) whenever a call is established or released. A formal description of the algorithms based on these strategies is given below. into the Step 1: Map a network topology G( corresponding layered-graph LG(V, E). . Set the cost of edge in LG according to (1) or (2), for all Step 2: Wait for a lightpath request. If it is a lightpath connection request, go to Step 3. If it is a lightpath release request, go to Step 4. Step 3: As described in Section II, according to the source node and destination node of the new call (e.g., and , add and to LG. Find a shortest path two additional vertices in LG from to (e.g., by Dijkstra algorithm). 1) If , the cost of the path, is infinite, block the call. 2) If the cost is finite, accept the call and map the shortest path in LG into the corresponding lightpath in G: a) Map the directed edges and vertices along the shortest path in LG into the links and nodes in G respectively, i.e., map the shortest path into a route in G. b) If the shortest path is on the th layer, assign to the route. wavelength c) Update the cost of the edges on path according to (1) or (2). Note that the lightpath is bidirectional, the cost and must be updated simultaneously. Go to of Step 2. Step 4: Update the cost of the edges corresponding to the route and wavelength of the lightpath according to (1) or (2). Release the lightpath and go to Step 2.

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As mentioned in [11], the computational complexity of the dynamic RAW algorithms is dominated by the point-to-point shortest path algorithm. In the next section, we show how to make use of the special structure of the LG to obtain the solution faster than by simply using a standard shortest path algorithm. C. Modified Dijkstra Algorithm: M_Dijkstra Chlamtac et al. propose a shortest path algorithm, SPAWG, by making use of the special structure of the so-called wavelength graph (WG) to obtain optimal speed [16]. Based on the similar idea we propose a shortest path algorithm, M_Dijkstra. It yields complexity , which is lower than that of the standard Dijkstra algorithm, . Suppose that we need find the shortest path from vertex to . For easy notation, we label the vertices in LG simply by . and are labeled as the numbers 0, 1, , respectively. The vertices in the th layer are 0, , . An exlabeled as of edge is determined ample is shown in Fig. 2. The cost by (1) or (2). The shortest path from vertex 0 to is denoted by , and the cost of is denoted by . The set of vertices is . S is the set of the permanently labeled vertices, i.e., the shortest path from vertex 0 to has . been found, if Step 1 (Initialization): ; 1) S , ; if , then 2) else ; : ,I 3) is the vertex number corresponding to , ; Step 2 (Designation of a New Permanent Label): , I is the vertex 1) ; number corresponding to , ; else return “cannot 2) If find a shortest path with finite cost,” STOP; , return “ is the solution,” STOP. 3) If I ): Step 3 (Update , , then If , else , Step 4 (Update If then

and ,

, Vertex is on the Layer): , and . Go to Step 2.

, the number The complexity of step 1 is linear with of edges in LG. Also the running time of steps 3 and 4 is , the number of nodes in G. In at most proportional to the worst case, the times of repeating steps 2, 3, and 4 is . Thus, the overall complexity of algorithm M_Dijkstra . is O IV. SIMULATION RESULTS In this paper, the dynamic RAW algorithms using PACK strategy are called PACK, and those using SPREAD strategy

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Fig. 4.

Fig. 3.

Benefits of multiple fibers for the 2

2 3 mesh network with jW j = 4.

Networks used in simulation.

are called SPREAD. We study the performance of these algorithms on two regular network topologies and two irregular topologies, which are shown in Fig. 3. The first network is a 3 mesh topology with 6 nodes and 7 links. The second 2 network is a 5 5 mesh_torus network, which has 25 nodes and 50 links. The third network is a modified CERNET (China Education and Research NETwork) topology [17] with 10 nodes and 16 links. The last one is the NSFNET T1 backbone network, which has 14 nodes and 21 links. In our simulation, call (lightpath) requests are assumed to arrive at the network according to an independent Poisson process with arrival rate . The s–d nodes are randomly chosen according to a uniform distribution. The call holding time is exponentially distributed with mean 1/ . Thus, the load per s–d node . Note that a node may engage in pair is multiple calls and several calls may be accommodated simultaneously between one s–d node pair. In our simulation, 10 calls are generated to ensure that steady state has been reached. The blocking performance of two kinds of networks is studied in this paper. One is the network with even links, i.e., the number of fibers on each link is the same. The other is the network with uneven links, i.e., the number of fibers on different links may be different. The heuristic RAW algorithms used in simulation are fixed routing with first-fit wavelength assignment heuristic (FR/FF) [4], fixed routing with maxsum heuristic (FR/MS) [10], alternate routing with RANDOM heuristic (AR2) [4], alternate routing with relative capacity loss heuristic (AR/RCL [12]), and fixed-path least-congestion (FPLC) [14]. A. Network with Even Links and Unit Basic Cost for any The network with even links means that . Suppose that the basic cost of each edge is unit, link

jW j =

2

Fig. 5. Blocking probabilities for the 2 3 mesh network, e.g., 1_16_FR/FF means FR/FF algorithm with 1 and F 16.

j j=

i.e., 1 for any link . In our simulation, is set . to 1 for any link First, we consider the benefits of using multiple fibers in conjunction with PACK. Fig. 4 shows the call blocking probability as a function of the load with one, two, and four fibers per link for the 2 3 mesh network. As expected, the blocking performance improves dramatically with the use of multiple fibers. The throughput increases significantly, too. For example, at a blocking probability of 0.01, using two fibers can achieve more than 200% increase in the network throughput related to using single fiber. And the increase associated with four fibers is more than 700%. Fig. 5 compares the call blocking probabilities for FR/FF, AR2, FPLC, and SPREAD for the 2 3 mesh network. In the AR2 algorithm, two routes are prepared for each source–destination node pair. The total number of channels on each link, deand , is 16. Two cases are studied, fined as the product of 4 with 4 and 1 with 16. i.e., Results show that in any case, SPREAD performs much better than FR, and outperforms AR2 and FPLC too in the regular topology. For example, at a blocking probability of 0.01, the network throughput can be increased by 70% over FR/FF and 4, by 27% over AR2 in both cases. In the case of


Fig. 6. Blocking probability versus number of fibers in a 5 network, F W 32.

j k j=

2 5 Mesh_Torus

4 and the total load 35 Erlang, the blocking probability for SPREAD is only 1.3 10 compared to 7.2 10 for FR/FF, 1.6 10 for AR2, and 3.8 10 for FPLC. Fig. 6 compares the call blocking probabilities for different 5 mesh-torus network under a fixed algorithms for the 5 load. The number of channels on each link is fixed at 32, i.e., 32. We vary the number of fibers on each link, , from 1 to 32. These results indicate that performance of FR/FF is very close to that of FR/MS. It is obvious that performance of alternate routing algorithms, AR/RCL and FPLC, is much better than that of fixed routing algorithms. The SPREAD can improve is larger than 4. the blocking probability significantly when Next, we examine the relative performance of layered-graphbased algorithms versus fixed and alternate routing algorithms for irregular networks. Fig. 7 compares the performance of different algorithms for CERNET_Like network. The total number of channels on each link is 16. We get the similar results: SPREAD performs much better than FR/FF, and outperforms AR2 and FPLC, too. At a blocking probability of 0.01, the throughput can be increased by 70% over FR/FF and 4 with 4, when by 38% over AR2. In the case of load is 80 Erlang, the blocking probability for SPREAD is only 1.4 10 compared to 9.9 10 for FR/FF, 3.6 10 for AR2, and 6.9 10 for FPLC. Fig. 8 depicts the performance of PACK and SPREAD along with FR/MS, AR/RCL, and FPLC for the NSFNET T1 back= 4 and = 8. It is clear that layeredbone network with graph-based routing algorithms are superior to fixed routing algorithms and alternate routing algorithms in the load range of interest. = 1 is functionally equivalent Note that the network with to a single-fiber network with full wavelength conversion capability [4]. Figs. 5–7 show that compared to SPREAD, the performance of fixed routing algorithms and alternate routing algorithms is poor even with full wavelength conversion. When routing and wavelength assignment subproblems are considered simultaneously (e.g., SPREAD algorithm) in multi-

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Fig. 7. Blocking probabilities for the CERNET_Like network, e.g., 1_16_AR2 means AR2 algorithm with W 1 and F 16.

j j=

j j=

Fig. 8. Blocking probabilities for the NSFNET network.

fiber networks, the performance advantage of full wavelength conversion is not significant. In single-fiber networks, it was shown in [4] that the algorithm with collective use of network resource can achieve better performance than that with distributive use of resource. We see here that the situation in multifiber networks is quite the opposite. We compare PACK and SPREAD in CERNET_Like network with 16 channels per link. Fig. 9 shows that SPREAD performs better than PACK. Furthermore, the performance gap in, the number of fibers per link. For example, creases with 8 and at a blocking probability of 0.001, with 2, the throughput ratio between SPREAD and PACK is 1.041; 4 and 4, the ratio is 1.053; with with 2 and 8, the ratio is 1.092. Packing the existing calls on as fewer edges and layers as possible may result in the resources on some edges of some layers being used up soon. It may become more difficult to find a suitable path to support the forthcoming calls in those layers, even if there were a lot of free resources on the other edges. The path chosen by SPREAD for a new call may be longer than that chosen by PACK. However,

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Fig. 10. Blocking probabilities for the CERNET_Like network with even links and different cost.

W=

Fig. 9. Blocking probabilities for the CERNET_Like network, e.g., 8 and jF j 2. 8_2_PACK means PACK algorithm with j j

BASIC COST MATRIX B

=

TABLE II

fjF jg, THE MATRIX OF THE NUMBER OF FIBERS ON EACH LINK

TABLE I

= (b

)

OF

CERNET_LIKE NETWORK

AR/RCL, and FR/FF. That means SPREAD can significantly improve the blocking performance in such networks. C. Network with Uneven Links and Different Cost at light loads, there is no need to pack the existing calls since the network resources are underutilized, and using longer paths will not lead to congestion [4]. B. Network with Even Links and Different Cost In Subsection A, we have assumed that the basic cost of each link is 1. As mentioned in Section III, the basic cost of one link is based on several factors. For simplicity, we define the cost based on the physical length of the link. The basic cost of link is defined as follows: if the physical length of link than 500 km

In Subsections A and B, we have assumed that the number of fibers on each link is the same. But in a real network, the number is more likely different due to the geographical limitation and economical reasons. The number of fibers on each link of CERNET_Like network is given in Table II. The matrix is . The basic cost matrix B is given in denoted by Table I. Note that both A and B are symmetrical. It is because all the links are supposed to be bidirectional. In SPREAD, is set to 8/ . In our simulation, is set to 4. As shown in Fig. 11, SPREAD still outperforms the other algorithms in such networks.

is less

if the length is larger than 500 km and less than 1000 km

V. CONCLUSION (4)

if the length is larger than 1000 km. of the CERNET_Like The basic cost matrix is set to 4 and network is shown in Table I. In our simulation, is set to 4. For any link , . As shown in Fig. 10, SPREAD performs much better than other algorithms. When the total load is 70 Erlang, the blocking probability for SPREAD is only 3 10 , which is much lower than that for PACK, FPLC,

The dynamic RAW problem in multifiber networks is studied in this paper. Based on the layered-graph model, the RAW problem is reduced to the problem of finding a shortest path with finite cost in the corresponding layered-graph. The routing and wavelength assignment subproblems can be considered simultaneously to achieve better performance. We propose two strategies, PACK and SPREAD, for this problem. These strategies can be used to solve the RAW problem of network with even links as well as that of network with uneven links. Simulation results show that using multiple fibers can increase


Fig. 11. Blocking probabilities for the CERNET_Like network with uneven links and different cost.

the network throughput dramatically. In all the cases we studied, PACK and SPREAD outperform the traditional fixed routing and alternate routing algorithms significantly. In multifiber networks, it is shown that SPREAD with distributive use of network resource can achieve better performance than PACK with collective use of resource in multifiber network. By making use of the special structure of layered-graph, we propose a shortest path algorithm, M_Dijkstra, which yields complexity , which is lower than that of the . standard Dijkstra algorithm, Another thing we want to point out is that the layered-graph-based algorithms can effectively deal with the failure of fiber/link and node. For example, if any kind failure occurred on all the fibers or part of them on link lij, the only thing that we need to do is to adjust the cost of the edges corresponding to the link. Some time later, the network can reach steady state again automatically. As we have shown in this paper, the blocking performance in such circumstance will be the best one that any RAW algorithm can achieve. ACKNOWLEDGMENT The authors would like to thank Dr. J. Hu, T. Li, Dr. D. Xu, and M. Tam for many useful discussions during the course of this work, and the anonymous reviewers for their valuable comments. REFERENCES [1] B. Mukherjee, Optical Communication Networks. New York: McGraw-Hill, 1997. [2] P. E. Green, “Optical networking update,” IEEE J. Select. Areas Commun., vol. 14, pp. 764–779, June 1996. [3] E. Karasan and S. Banerjee, “Performance of WDM transport networks,” IEEE J. Select. Areas Commun., vol. 16, pp. 1081–1096, Sept. 1998. [4] A. Mokhtar and M. Azizoglu, “Adaptive wavelength routing in all-optical networks,” IEEE/ACM Trans. Networking, vol. 6, pp. 197–206, Apr. 1998. [5] B. Ramamurthy and B. Mukherjee, “Wavelength conversion in WDM networking,” IEEE J. Select. Areas Commun., vol. 16, pp. 1061–1073, Sept. 1998. [6] R. Ramaswami and G. H. Sasaki, “Multiwavelength optical networks with limited wavelength conversion,” in Proc. INFOCOM’97, pp. 490–499.

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[7] V. Sharma and E. A. Varvarigos, “Limited wavelength translation in alloptical WDM mesh networks,” in Proc. INFOCM’98, pp. 893–901. [8] G. Jeong and E. Ayanoglu, “Comparison of wavelength-interchanging and wavelength-selective cross-connects in multiwavelength all-optical networks,” in Proc. INFOCOM’96, pp. 156–163. [9] R. Ramaswami and K. N. Sivarajan, “Routing and wavelength assignment in all-optical networks,” IEEE/ACM Trans. Networking, vol. 3, pp. 489–500, Oct. 1995. [10] S. Subramaniam and R. A. Barry, “Wavelength assignment in fixedfouting WDM networks,” in Proc. IEEE ICC, Nov. 1997, pp. 406–410. [11] C. Chen and S. Banerjee, “A new model for optimal routing and wavelength assignment in wavelength division multiplexed optical networks,” in Proc. IEEE INFOCOM96, pp. 164–171. [12] X. Zhang and C. Qiao, “Wavelength assignment for dynamic traffic in multi-fiber WDM networks,” in Proc. ICCCN’98, vol. S18-2, Lafayette, LA. [13] L. Li and A. K. Somani, “Blocking performance analysis of fixed-paths least-congestion routing in multifiber WDM networks,” in Proc. SPIE Photonics East’99, Boston, MA, 1999. , “Dynamic wavelength routing using congestion and neighborhood [14] information,” IEEE/ACM Trans. Networking, vol. 7, pp. 779–786, Oct. 1999. [15] M. Gondran and M. Minoux, Graph and Algorithms. New York: Wiley, 1979, ch. 2. [16] I. Chlamtac, A. Farago, and T. Zhang, “Lightpath (wavelength) routing in large WDM networks,” IEEE J. Select. Areas Commun., vol. 14, pp. 909–913, June 1996. [17] http://www.edu.cn/cernet/structure/index.html.

Shizhong Xu received the B.S. and M.S. degrees in electrical engineering from University of Electronic Science and Technology of China, Chengdu, China,in 1994 and 1997, respectively. He is currently a Ph.D. candidate at the National Key Lab of Broadband Optical Fiber Transmission and Communication Networks in the same university. His research interests include broadband networks, all-optical network, and image processing.

Lemin Li was born in Zhejiang, China, on May 28, 1932. He graduated from Shanghai Jiaotong University, Shanghai, China, in 1952, majoring in electronic engineering. From 1952 to 1956, he was with the Department of Electrical Communications at Shanghai Jiaotong University. Since 1956, he has been with the Chengdu Institute of Radio Engineering (now the University of Electronic Science and Technology of China), where he is currently a Professor and the Director of the Academic of the National Key Lab of Broadband Optical Fiber Transmission and Communication Networks. From 1980 to 1982, he was a Visiting Scholar at the Department of Electrical Engineering and Computer Science, University of California at San Diego. His research work is in the area of digital information transmission and communication networks. Mr. Li is a member of CAE (Chinese Academy of Engineering).

Sheng Wang received the B.S., M.S., and Dr.E. degrees in electrical engineering from the University of Electronic Science and Technology of China, Chengdu, China, in 1992, 1995, and 1999, respectively. He was an honorable graduate of the former MEI and won an award for his Master degree paper on high-quality audio coding algorithm. His research interests include BISDN/ATM, all-optical networks, audio signal processing, and TCP/IP.