Dynamic Routing in WDM Grooming Networks - CiteSeerX

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Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ 85721 ... Dependable Computing and Networking Laboratory, Department of Electrical and Computer Engineering, ... electronic transmission speed and has been steadily ...... [1] J. Yates, J. Lacey, D. Everitt, Blocking in multiwavelength.
Photonic Network Communications, 5:2, 123±135, 2003 # 2003 Kluwer Academic Publishers. Manufactured in The Netherlands.

Dynamic Routing in WDM Grooming Networks R. Srinivasan Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ 85721 E-Mail: [email protected]

Arun K. Somani Dependable Computing and Networking Laboratory, Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 E-Mail: [email protected] Received April 18, 2002; Revised and Accepted August 28, 2002

Abstract. Traf®c grooming in optical networks has gained signi®cant importance in recent years due to the prevailing sub-wavelength traf®c requirement of end-users. In this paper, a methodology for dynamic routing of fractional-wavelength traf®c in WDM grooming networks is developed. To evaluate the performance of routing algorithms, a new performance metric that re¯ects the network utilization is also proposed. The performances of shortest-widest path, widest-shortest path, and available shortest path routing algorithms are evaluated on a class of WDM grooming networks by considering traf®c of different capacity requirements. The effect of dispersity routing, where higher capacity requests are broken into multiple unit capacity requests, is also investigated. The most interesting counter-intuitive result that is observed is that increasing the grooming capability in a network could result in degrading the performance of the widest-shortest path algorithm. Keywords: optical networks, traf®c grooming, dynamic routing, wavelength division multiplexing

1

Introduction

Optical communication employing wavelength division multiplexing (WDM) has emerged as the most viable infrastructure for wide-area backbone networks. WDM divides the available ®ber bandwidth into a set of wavelengths (WDM channels). The bandwidth on a wavelength is close to the peak electronic transmission speed and has been steadily increasing from OC-48 (2.5 Gbps) to OC-192 (10 Gbps), and is expected to increase up to OC-768 (40 Gbps) in the near future. However, this large granularity of wavelength capacity is too large for certain traf®c requirements. One approach to provisioning fractional wavelength capacity is to divide a wavelength into multiple time slots and multiplex traf®c on the wavelength. The resulting multiwavelength time-division multiplexed networks are referred to as WDM-TDM networks or WDM

grooming networks. Nodes in such networks are capable of multiplexing/de-multiplexing lower rate traf®c onto a wavelength and switching them from one lightpath to another, where a lightpath is de®ned as an all-optical connection between two nodes. Optical processing and buffer technologies are currently not mature enough to achieve runtime routing decisions at high-speeds. Therefore, WDM grooming networks are circuit-switched in nature. WDM grooming networks can be classi®ed into two categories [1]: dedicated-wavelength grooming (DWG) networks and shared-wavelength grooming (SWG) networks. In DWG networks, the sourcedestination pairs are connected by lightpaths. Connections between a source and destination are multiplexed onto the lightpath. If the bandwidth required by a new request at a node is not available on any of the existing lightpaths to the destination, a

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new lightpath to the destination is established. On the other hand, in SWG networks, if a request cannot be accommodated on an existing lightpath to the destination, it is multiplexed onto an existing lightpath to an intermediate node. The connection is then switched at the intermediate node to the ®nal destination either directly or through other nodes. The performance of WDM grooming networks depends on the ef®cient merging of the fractional wavelength requirements of the requests into full or almost-full wavelength requirements. Traf®c grooming in SWG networks can be either static or dynamic. In static grooming, the sourcedestination pairs whose traf®c requirements will be combined are pre-determined. In dynamic grooming, connections of different source-destination pairs are combined based on the existing lightpaths at the time of a request arrival. Nodes in a WDM grooming network can be classi®ed into various categories depending on the level of grooming capability available. If a node can multiplex and de-multiplex low-rate traf®c only on dropped wavelengths at an add-drop multiplexer (ADM), it is referred to as a constrained grooming (CG) node. Hence, grooming cannot be performed on wavelengths that are not dropped. CG nodes have fewer number of ADMs as compared to the total number of wavelengths in the links connected to the node. If a node can switch connections across different lightpaths but cannot convert from one wavelength to another, it is termed as a wavelengthlevel grooming (WG) node. WG nodes have dedicated ADMs for every wavelength on every link. Connections are dropped at these nodes even if they are not destined for them. If a node can switch connections in any permutation from one wavelength to another, then it is termed as a full grooming (FG) node. Routing and wavelength (and/or time-slot) assignment (RWA) is an important problem in WDM-based networks and has received extensive attention from the research community. Several RWA algorithms have been developed for routing static traf®c demands to optimize the network capacity by formulating them as integer linear programming (ILP) problems. While such an approach could produce the optimal solution for static traf®c demands, applying these techniques to dynamic traf®c is not practical due to their prohibitively large computation time. Dynamic routing in wavelength-routed WDM

networks has been studied extensively in the literature. Fixed alternate path routing (FAPR) has been studied in Lowe and Hunter [2] and Ramamurthy and Mukherjee [3]. Fixed-path least-congestion routing (FPLCR) has been analyzed in Li and Somani [4]. In these approaches, a path from a source to destination is selected from a set of precomputed paths. While FAPR attempts the paths in a speci®ed order, FPLCR selects the least loaded path. In Zang et al. [5], a wavelength-routed network with W wavelengths and no wavelength conversion is treated as W networks with one wavelength each. Shortest path algorithm is applied on each network. A request from a source to destination is assigned a connection on a wavelength that has the minimum path length. The impact of distributed routing on the connection setup time and stabilizing time for exchanging of network state has also been analyzed in Zang et al. [5]. In Jue and Xiao [6], alternate link routing (ALR) is proposed. In this approach, a precomputed set of preferred links to reach a destination is available at every node. A request is forwarded on any one of the preferred outgoing links to the destination. In Mokhtar and Azizoglu [7], an analytical model is developed for evaluating the blocking performance of various routing algorithms, including adaptive unconstrained routing which does not restrict the path selection to any pre-de®ned set of routes. Mechanisms for controlling setup and teardown of lightpaths and network update procedures for wavelength-routed networks are presented in Ramaswami and Segall [8]. The blocking performance of grooming networks with shortest-path routing has been studied in Thiagarajan and Somani [9]. Dynamic routing in WDM grooming networks has received very little attention thus far in the literature though it has been extensively studied in the context of qualityof-service routing for single-channel networks1 [10]. This motivates the research presented in this paper. The paper is organized as follows: Section 2 describes the steps involved in dynamic routing and different routing paradigms. Section 3 describes a WDM grooming network and the metrics of importance in such a network. Dynamic routing in WDM grooming networks is discussed in Section 4. The performances of different dynamic routing approaches are evaluated and compared in Section 5. Conclusions are presented in Section 6.

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2

Dynamic Routing

Dynamic routing in a network consists of two basic steps: (a) collection of network state information and (b) selection of a path using the gathered information. 2.1 Collection of State Information The ®rst step in dynamic routing is to collect information about the state of the network. The state of a network is de®ned by a set of link and node parameters. For example, available bandwidth, delay, etc. constitute link parameters. The grooming capability available at a node is an example of a node parameter. Consider the example network shown in Fig. 1. Assume that every link carries two wavelengths with four timeslots per wavelength. The ®gure shows the available wavelength capacity (in timeslots) on the two wavelengths on each of the links at some point of time during the network operation. The network state information can be obtained by using either link-state or distance-vector protocols [11]. In link-state protocol, every node transmits its node-speci®c and link-speci®c information to every other node in the network. Hence every node in the network is aware of the entire network topology. The information maintained by the nodes in this case is called global state information. In a distance-vector protocol, the network state is gradually updated at every node by exchanging the distance information with its neighbors. The information collected by a node about the state of its neighbors is called local state information. In this

Fig. 1. Representation of state information in a network with two wavelengths per link. The tuples denote the available capacity on the two wavelengths.

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approach, the nodes in the network are not aware of the network topology. Every node maintains a routing table that indicates the preferred neighbor to reach any other node. The two approaches for collecting network state information have their own merits and demerits. The advantage of the link-state protocol is that it allows centralized implementation of routing algorithms at every node. However, the drawback of this approach is that it is not scalable for large networks as the amount of global state information maintained at every node increases with increasing network size. Distance-vector protocol has the advantage of scalability. As the information is exchanged only among the neighbors, this approach scales well with increasing network size. However, it takes a certain amount of time for the nodes to reach a consistent view of the network state. The convergence of the routing tables maintained at each node depends on the path selection algorithm. 2.2 Path Selection The second step in dynamic routing is to identify a path from a source to destination using the collected network state information. The path selection depends on the amount of information collected and where the routing decisions are made. Based on this, the path selection strategies can be divided into two categories: source routing and distributed routing. 1. Source routing: In source routing, each node maintains the global network state. Upon a request arrival at a node, a path to the destination is selected from a set of feasible paths and a control message is sent along the path. If resources are available in all the links of the path, the connection is established and the linkstate information is updated accordingly. Otherwise, the connection is rejected. The advantage of source routing is its simplicity. The computation that is required to select a path is centralized at a node. It is easier to develop complex algorithms and sophisticated heuristics in a centralized manner rather than in a distributed manner. This approach avoids problems like deadlock (that occurs when resources are reserved along the path while the path is not fully established) and loop formation. Source routing does not allow intermediate nodes to make routing decisions during connec-

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tion establishment. Hence, the source has complete control over the path that is established. The main drawback of the source routing approach is its reliance on the up-to-date global state information. The global state information increases with increasing network size, hence the computational complexity of path selection algorithms also increase. Therefore, it is impractical to employ source routing for large networks. 2. Distributed routing: As the name suggests, the routing decision in this approach is made in a distributed manner. When a connection request arrives at a node, the preferred neighbor to reach the destination is identi®ed and the request is forwarded. This approach relies only on the neighborhood information. The intermediate nodes have the ¯exibility of re-routing a request depending on the network dynamics. The number of requests accepted can be increased if more than one preferred neighbor is maintained at every node to reach a destination. The performance of distributed routing algorithms is adversely affected by the inconsistency in the state information. The time taken for the nodes to reach a consistent view of the network increases with the size of the network. Hence, the information at the time of routing a request may not be up-to-date. Unlike source routing, distributed routing algorithms have the problem of loop formation as routing decisions are made independently at each node. Hence, detection and elimination of loop formation has to be an integral part of any distributed routing algorithm. The above mentioned two steps in dynamic routing, namely information collection and path selection, allow a path to be selected from the set of all-possible paths from a source to destination. However, if path selection is restricted to a ®xed set of pre-computed paths, it is not necessary to maintain the global state information, thus simplifying the routing procedures in the network. FAPR and FPLCR are examples of restricted-path routing schemes. Dynamic routing can be classi®ed into two categories based on the nature of the path selection technique employed [12]: destination-speci®c and request-speci®c. In the destination-speci®c approach,

the path selection algorithm selects the best possible route to reach a destination without the knowledge of the request. This technique is well-suited for networks where all the requests are of the same nature. The traditional shortest-path routing based on hop-length is an example of destination-speci®c heuristic. In the request-speci®c approach, a path is selected based on the characteristics of a request. The choice of the preferred neighbor for different requests to the same destination could be different. This approach is wellsuited for networks in which the characteristics of the requests vary signi®cantly. 3

WDM Grooming Networks

A WDM grooming network consists of switching nodes interconnected by one or more optical ®bers. Each ®ber carries a certain number of wavelengths. Each wavelength is divided into frames which are further sub-divided into time slots. Let L denote the number of links at a node, F denote the number of ®bers per link, W denote the number of wavelengths per ®ber, and T denote the number of time slots per frame on a wavelength. Every slot within a frame can be denoted by a 4tuple, …l; f ; w; t†, where 1  l  L, 1  f  F, 1  w  W, and 1  t  T. For example, the tuple …1; 1; 2; 1† (read from right to left) denotes the ®rst time slot in a frame on the second wavelength of the ®rst ®ber on the ®rst link. A channel on a link is de®ned as a collection of a particular time slot across successive frames. Hence, the number of channels in a link is the same as the number of slots in a frame, F6W6T. Each channel is also represented by a 4tuple, …l; f ; w; t†, similar to the representation of a slot. It can be observed that if a frame has only one time slot, T ˆ 1, a WDM grooming network reduces to a multi-®ber multi-wavelength wavelength-routed network. A switch at a node maps an input channel to an output channel. The constraints on the mapping of an input channel to an output channel is determined by the nature of the switch. For example, a WG node can switch an input channel …li ; fi ; wi ; ti † to an output …lo ; fo ; wo ; to †, if wi ˆ wo . An FG node can switch any input channel to any output channel. In this paper, a WDM grooming network with WG nodes is considered. The choice of studying this node type is due to the increasing interest in developing all-optical solutions for traf®c grooming.

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It is well understood that all-optical wavelength conversion is an expensive proposition, hence is not likely to be employed in the networks in the near future. Hence, the ®rst generation technology in alloptical grooming is expected to obey wavelength continuity constraint. It is assumed that a fullpermutation switching capability is available in the time domain for each wavelength. 3.1 Metrics in WDM Grooming Networks Every link in the network is denoted by a link-state vector. The vector consists of a set of properties associated with a link, e.g., available bandwidth on individual wavelengths, hop-length, ®ber length etc. Each entity in the vector is referred to as a metric. Every path from a source to destination has a pathvector that is obtained by combining the link-state vectors of the links in the path. Note that the link vector is a special case of a path vector when the path has only one link. In WDM grooming networks, the metrics can be classi®ed either as path-speci®c or wavelengthspeci®c. Path-speci®c metrics are those metrics that depend only on the route from a source to destination and are independent of the wavelength used. One example of path metric is the hop-length. However, in networks where wavelength conversion is not allowed, a network with W wavelengths can be treated as W networks with one wavelength each. In such a case, hop-length can be treated as a wavelength-speci®c metric. Available wavelength capacity is a trivial example of a wavelength-speci®c metric. A metric is said to be concave if its value in a path vector is the minimum among the corresponding metrics on the individual links of the path, e.g., available bandwidth on a wavelength. A metric is said to be additive if its value in a path vector is the sum of the corresponding metrics of the individual links in the path, e.g., hop count. If reliability of the links are considered, then the reliability of a path is obtained as a product of link reliabilities. In such a case, the metric is referred to as a multiplicative metric.2 A wavelength-speci®c additive metric that is of signi®cance for a WDM-TDM network is an indicator variable for each wavelength which denotes whether the wavelength is occupied by any connection or not. The value of this metric in a path vector indicates the number of links in which the wavelength is not used, hence requiring a new lightpath to be setup on those

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links. The metric on a link is set to 1 if the wavelength is not occupied by any connections, otherwise it is set to 0. Various dynamic path selection algorithms can be developed based on the above speci®ed metrics.

4 Dynamic Routing in WDM Grooming Networks Every node in the network is assumed to maintain the global state information through a link-state protocol. The information collection and path selection are based on two metrics: available wavelength capacity and hop length. A path with W wavelengths with C channels per wavelength is denoted by a vector f…A1 ; A2 ; . . . ; AW †; Hg, where each Aw …1  w  W† denotes the number of available channels on a wavelength and H denotes the hop-count. For a link vector, the value of H is 1. The available capacity on a wavelength w and hop length of a path p is denoted by Awp and Hp respectively. Dijkstra's shortest path algorithm is extended to the above link-state vector, referred to as extended Dijkstra's shortest path (EDSP) algorithm, and is employed at every node in the network. The EDSP algorithm uses the link-state vector as de®ned above instead of a single metric that is traditionally used. The EDSP algorithm has two important operations: (1) combining two path vectors and (2) selecting the best path vector. Let cik and ckj denote the path vectors from node i to k and from node k to j, respectively. The path vector from node i to j through k is obtained by combining the path vectors cik and ckj , denoted by cij ˆ cik +ckj. The vectors are combined in different ways depending on the grooming capability of the node k. The second operation of selecting the best path vector from a given set of path vectors is de®ned by a speci®c path selection policy. For example, the traditional shortest path algorithm selects a path with minimum hop length. 4.1 Wavelength-Level Grooming Networks In wavelength-level grooming networks, connections cannot be switched from one wavelength to another. Hence, wavelength continuity constraint is obeyed. Two paths vectors cik and ckj are combined at a WG node to obtain cij where Awij ˆ min…Awik ; Awkj † and Hij ˆ Hik ‡ Hkj .

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Consider the example network in Fig. 1. Assume that Node 4 can perform wavelength-level grooming. The path from Node 1 to 6 through 4 is described by the vector c16 ˆ f…0; 1†; 2g. 4.2 Sparse Full-Grooming Networks In sparse full-grooming networks, a few nodes in the network have full-grooming capability. Low-rate traf®c streams can be switched across wavelengths at these nodes. Hence, the maximum capacity of a connection that can be switched by an FG node corresponds to the maximum available capacity across different wavelengths on an output link. In such a scenario, the available capacity on a path Pij on a wavelength w is obtained by combining two path metrics Pik and Pkj as Awij ˆ min…Awik ; Amax kj † where Amax denotes the maximum available capacity across kj different wavelengths on the path from k to j. The hop length is computed as Hij ˆ Hik ‡ Hkj . Consider the example network in Fig. 1. Assume that full-grooming is available at Node 4. The vector for the path from Node 1 to 6 through 4 is obtained as c16 ˆ f…0; 2†; 2g. 4.3 Constrained Grooming Networks In constrained grooming networks, grooming is accomplished only on the dropped wavelengths. Consider the example in Fig. 1. Let two connections exist between nodes 3 and 6 through 4. Assume that the ®rst connection occupies two channels on the ®rst wavelength while the second occupies three on the second wavelength. Although both the wavelengths have free channels, they cannot be used to reach Node 4 as the wavelengths are not dropped at Node 3. Hence, when a lightpath is setup between a source and destination, they can be treated as logical neighbors. The established lightpaths can then be used to route further connections by updating the link-state information. If the nodes in the network shown in Fig. 1 perform constrained grooming, then the network is viewed as shown in Fig. 2. The lightpaths that are established between nodes that are not physical neighbors are shown in dotted lines. Two path vectors in such networks are combined in a manner similar to that of wavelength-level grooming networks. 4.4 Path Selection Algorithms The path selection algorithms considered in this paper are restricted to destination-speci®c approaches. The

Fig. 2. Visualizing a constrained grooming network. The dotted lines denote virtual links.

different path selection algorithms speci®es the rule for selecting the best path vector in the EDSP algorithm. Four examples of path selection algorithms are listed below: Widest-shortest path routing (WSPR): In this approach, the available wavelength capacity vector on a path is ordered in descending values of the individual wavelength capacities. Thus an available wavelength capacity vector A0p ˆ …A01 ; A02 ; . . . ; A0W † is said to be ordered descending if A0i  A0j for i < j and 1  i; j  W. An ordered vector A0 ˆ …A01 ; A02 ; . . . ; A0W † is said to be smaller than another ordered vector B0 ˆ …B01 ; B02 ; . . . ; B0W † if for some i…1  i  W†; A0i < B0i and for all j < iA0j ˆ B0j . The vectors are said to be equal if A0i ˆ B0i , for all i, where 1  i  W. Otherwise, A is said to be larger than B. A path with the largest path-vector is said to be the widest path and is chosen for establishing a connection. In case of a tie, the path with the minimum hop length is chosen. Shortest-widest path routing (SWPR): This is the conventional shortest-path routing based on the hoplength. If more than one such path is available, the widest among them is chosen. Available shortest path routing (ASP): In this approach, the shortest path among those that can accommodate the request is chosen. The paths that can accommodate the request are those that have at

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least one wavelength that can accommodate the request. If two paths that can accommodate the request have same hop length, then one of them is chosen at random. WSPR and SWPR are examples of destinationspeci®c routing schemes while ASPR is an example of request-speci®c routing. In ASPR, the set of feasible paths is chosen based on the capacity requirement of the request. If two path vectors are equal by any of the above algorithms, one of the path vectors is chosen at random. Note that only the selection of the path vector is based on the ordered available capacity vector.

dispersity routing while SMSPR and MSSPR are used by networks that employ dispersity routing. 5.1 Experimental Setup The experimental setup for the simulation is based on the following assumptions. *

*

*

*

4.5 Dispersity Routing If the connection for a request of capacity b has to be established only on one wavelength, then SWP and WSP algorithms are used. If multiple wavelengths can be used to meet the capacity requirement, the request is split into b requests of unit capacity each. If the path from the source to the destination can accommodate the set of b requests, then the request is said to be accepted. Otherwise, it is blocked. Such an approach to routing a larger capacity requests by splitting into smaller capacity requests is called dispersity routing. In this paper, it is assumed that a request can be assigned channels that are dispersed over wavelengths of the same path, referred to as wavelength-level dispersity routing. When dispersity routing is employed, a path is said to be wider if the total available capacity on all the wavelengths in the path is higher. 5

Performance Evaluation

The performance of four path selection algorithms described in the previous section are evaluated on the NSFnet network. The 14-node 22-link NSFnet network is shown in Fig. 3. The performance results reported in this section are restricted to wavelengthlevel grooming employed at all nodes in the network. When a request arrives at a node, the path to the destination is chosen using one of the above mentioned path selection schemes. The wavelength allocated to establish the connection is the one that can just accommodate the capacity of the request (best-®t wavelength assignment). SWPR and WSPR algorithms are used in networks that do not allow

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The arrival of requests at a node follow a Poisson process with rate l and are equally likely to be destined to any other node. The holding time of the requests follow an exponential distribution with unit mean. The capacity requirement of a request is equally likely to take integer values from 1 to 8. Every link has 128 channel capacity divided over W wavelengths.

A network with links having 16 wavelengths and 8 channels per wavelength are referred to as 1668 network. Four different wavelength-channel combinations are considered: (1) 1668 (2) 8616 (3) 4632 and (4) 16128. The requests are generated independently at a rate of Nl, where N denotes the number of nodes in the network. The requests are equally likely to have any of the N nodes as its source. The generated requests are fed to the different networks running in parallel and their performances are measured. A total of 66105 requests were generated with performance metrics being measured in batches of 105 requests. The average of the performance metrics over observed six set of values are reported in the results. 5.2 Performance Metrics The performance metrics that are measured are the request blocking probability, average path length of an accepted connection …Z†, average shortest-path length of an accepted request …Zm †, and network utilization …Z†. The blocking probability is computed as the ratio of the number of blocked requests to the number of total requests generated. Z is computed as the average of the length of the paths assigned to the accepted requests by a speci®c routing algorithm. Zm is computed as the average of the shortest-path length of the requests accepted by the routing algorithm. It can be observed that SWPR would have Z ˆ Zm while other routing schemes could have Z  Zm . The network utilization is computed by assigning an effective network capacity requirement for a request. A request r for capacity b from source s to

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Fig. 3. The NSFNET network.

destination d has an effective capacity requirement of b6hs , where hs is the shortest path length from the source to the destination. This effective capacity requirement of a request is the minimum capacity that is required in the network to support the request, irrespective of the routing algorithm. If a routing algorithm selects a path of length h for the connection, b…h hs † denotes the additional capacity used by the network to support the connection. The effective network capacity utilized at an instant of time, denoted by U, is de®ned as the sum of the effective network capacity requirement of all the connections that are active at that instant. The value of U at any instant of time is bounded by L6C, where L is the total number of links in the network and C is the capacity on each link. The network utilization is then computed as the ratio of the effective used capacity to the maximum capacity of the network as Z ˆ U=…L6C†.

5.3 Effect of Routing Algorithms Fig. 4 shows the blocking performance of different routing algorithms on 1668 and 16128 NSFnet networks. It is observed that ASPR performs better than SWPR and WSPR. It is also observed that as the network load is increased, the blocking performance of WSPR worsens as it routes connection over wider but longer paths resulting in wastage of bandwidth. Fig. 5 shows the network utilization under different routing algorithms on 1668 and 16128 NSFnet

Fig. 4. Blocking performance of different routing algorithms on a 1668 and 16128 NSFnet networks.

Fig. 5. Network utilization of different routing algorithms on a 1668 and 16128 NSFnet networks.

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networks. It is observed that ASPR achieves the maximum utilization compared to WSPR and SWPR. More insights into the working of the algorithms are obtained by observing the average path length of the connections established. Fig. 6 shows the average path length of connections established in the networks by different routing algorithms. It is observed that WSPR selects longer paths for establishing connections as compared to ASPR and SWPR. This difference is signi®cant when the grooming capability in the network is increased. This indicates that increasing the grooming capability helps dynamic routing algorithms in ®nding more paths but at the expense of longer path lengths. SWPR has the least value for this metric as it selects only shortest paths. The average path length for a connection established under WSPR remains almost a constant with load as the preference is given to distributing the load in the entire network. On the other hand, SWPR attempts only on the shortest path. As network load increases, more longer path requests are blocked, hence results in a decrease in the average path length. ASPR behaves similar to SWPR under low loads. However, as the offered load to the network is increased, ASPR attempts to route connections on the longer paths, hence the trend of increasing average path length with increasing offered network load. The average path length of all the routing algorithms for 16128 network is higher than that of 1668 network because more requests are accepted, but along longer paths in the former network due to the increased grooming capability. Increasing the grooming capability improves the chances of ®nding a path between nodes, though it would result in wastage of network resources.

Fig. 6. Average length of connections established by different routing algorithms on a 1668 and 16128 NSFnet networks.

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Fig. 7 shows the average shortest path length of accepted requests for different routing schemes. At low loads, very few requests are rejected. Hence, the average shortest path length of accepted requests is the same for different routing schemes. When the offered load to the network is increased, requests with longer shortest path length experience more blocking resulting in a bias in favor of requests with smaller shortest path length. The lower the value of this metric for a routing algorithm, the stronger is the bias in favor requests with smaller path length. ASPR performs the best with respect to this fairness metric. It is observed that increasing the grooming capability enhances the performance of the routing schemes with respect to this metric. The routing schemes also exhibit a bias in favor of smaller capacity connections when the offered load to the network is increased. Requests for larger capacity experience more blocking than the ones for smaller capacity. Such a behavior is pronounced in networks that have lesser grooming capability. Fig. 8 shows the average capacity of accepted requests for different routing schemes. It is observed that increasing the grooming capability enhances the fairness of the routing algorithms with respect to requests of different capacity requirement. The average shortest path length of and average capacity of accepted requests quantify the fairness property of the routing algorithms. An ideal routing algorithm would have a constant value for these metrics at all network loads. It is observed that ASPR offer better performance over SWPR and WSPR algorithms with respect to various performance metrics. Similar performance

Fig. 7. Average shortest path length of connections established by different routing algorithms on a 1668 and 16128 NSFnet networks.

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Fig. 8. Average capacity of accepted requests for different routing algorithms on a 1668 and 16128 NSFnet networks.

results were obtained for 8616 and 4632 NSFnet networks. 5.4 Effect of Dispersity Routing In order to improve the network performance under different routing algorithms, dispersity routing is also employed. Dispersity routing removes the constraint of routing a connection entirely on a wavelength, hence provides greater ¯exibility in assigning connections. Figs. 9 and 10 show the performance of different routing algorithms on a 1668 NSFnet network. It is observed that ASPR performs the best when dispersity routing is employed. From the results it is clear that employing dispersity routing signi®cantly improves network performance. At offered load of 0.7, a network employing ASPR with dispersity routing achieves an utilization of 0.62 while the utilization achieved by emplying ASPR without dispersity routing is 0.526, a 17.9% improvement. Under dispersity routing, only the end nodes need to maintain the information regarding how the connection is split, while the intermediate nodes would route the connection as if they were unit capacity connections. 5.5 Effect of Dispersity vs. Grooming Capability While wavelength-level dispersity routing is one mechanism to achieve increased network performance, alternatives to improve grooming capability can also be considered as a solution. For example, instead of employing 16 wavelengths with eight time slots, one could employ eight wavelengths and 16 time slots. As call requirements still vary only between one and eight time slots, the latter wavelength and time slot combination would result in

Fig. 9. Performance of different routing algorithms on 1668 NSFnet network with and without dispersity routing. (a) Blocking probability; (b) Network utilization.

reduced blocking. However, such a change increases the transmission speed on a wavelength, requiring faster switches at the nodes. On the extreme, one could consider one wavelength with 128 time slots. In this case, the switching speed has to be 16 times faster as compared to that in a 16-wavelength eight-time slot network. Another approach to achieve improved performance is to employ multiple wavelengths, but include wavelength conversion capability. This would eliminate the need for faster switches. For example, consider a network with eight wavelengths and 16 time slots in each wavelength. If limited wavelength conversion capability is provided at a node where wavelength W1 and W2 , W3 and W4 , W5 and W6 , and W7 and W8 can be interchanged, then this is similar to a network employing four wavelengths and 32 time slots in each wavelength. In such an architecture, the network cost is higher due to the wavelength conversion capability at every node in the network.

R. Srinivasan, A. K. Somani/Dynamic Routing in WDM Grooming Networks

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Fig. 11. Blocking performance of different routing algorithms on NSFnet network with different levels of grooming capability and dispersity routing.

It can be concluded from the extensive simulation results shown in this paper that a signi®cant performance improvement can be achieved with dispersity routing while having lesser grooming capability.

Fig. 10. Performance of different routing algorithms on 1668 NSFnet network with and without dispersity routing. (a) Average shortest path length; (b) Average accepted request capacity.

We study the performance of dispersity routing and varying grooming capability to evalute the trade-off. We evalute four different wavelength and time slot combinations: 1668, 8616, 4632, and 16128. In the case of 16128 there is no distinction between routing a connection with or without dispersity. Fig. 11 shows the blocking performance of ASPR with dispersity routing for the four different wavelength and time slot combinations. It is observed that the blocking performance is reduced with increasing grooming capability. This performance improvement is observed to be a gradual. It is observed that at offered loads of 0.5 and above, the blocking performance under various grooming capabilities within the same order of magintude. The performance with respect to other metrics such as network utilization, average shortest path length, and average accepted call capacity were very close, hence not reported in the paper.

5.6 Improvements and Future Work The selection of a path vector at random when more than one path vectors are equivalent under a speci®ed path selection policy that is employed in the EDSP algorithm deserves a closer look. For example, assume that Node i can reach Node k along two different paths on wavelengths w1 and w2 on the ®rst and the second path, respectively, having the same capacity. Assume that one of the paths is chosen at random, say the path with wavelength w1 being free. Assume that a path from Node k to j is available only on wavelength w2 . This results in a scenario when the path selected from Node i to j through k does not have any capacity available. Although such a scenario affects all the routing algorithms presented in this paper, their impact on the performance still needs to be quanti®ed and is currently under investigation. The routing algorithms presented in this paper are based on the availability of up-to-date global state information. Distributed implementation of the proposed algorithms poses a signi®cant challenge as the routing table entries may not converge. This effect can be observed when a node can be reached through two different paths that are equivalent with respect to a speci®c path selection algorithm and one of the paths is chosen at random.

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R. Srinivasan, A. K. Somani/Dynamic Routing in WDM Grooming Networks

The dispersity routing considered in this paper is restricted to wavelengths. Dispersity routing across different paths can also be considered for improving performance. Issues relating to establishing primary and backup paths to tolerate single link and node failures and fairness among requests of different source-destination pairs, path length, and capacity requirement are also important in such networks.

[2] [3]

[4]

6

Conclusion

In this paper, a methodology for dynamic routing of fractional-wavelength traf®c in WDM grooming networks is proposed. Three routing algorithms have been studied using simulation and their performances are evaluated on wavelength-level grooming networks. A new metric to evaluate routing algorithms that re¯ects the network utilization is also proposed. We show that routing connections based on the shortest available path is a preferred approach. We quantify the bene®t of routing larger capacity connections by breaking them into multiple smaller capacity streams, referred to as dispersity routing. It is shown that employing dispersity routing is an attractive alternative compared to increasing the grooming capability at nodes in the network in order to reduce the network cost.

[5]

[6]

[7] [8] [9]

[10]

Acknowledgment The research reported in this paper is funded in part by the National Science Foundation under grant ANI9973102, Defense Advanced Research Projects Agency and National Security Agency under grant N66001-00-1-8949. Notes 1. A single-channel network is equivalent of an optical network with one wavelength. 2. A multiplicative metric can be converted into an additive metric using logarithm of the metric.

References [1] J. Yates, J. Lacey, D. Everitt, Blocking in multiwavelength TDM networks, in: 4th International Conference on

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Telecommunication Systems, Modeling, and Analysis, (Nashville, Tennessee, USA, March 1996), pp. 535±541. E. D. Lowe, D. K. Hunter, Performance of dynamic path optical networks, in: IEE Proceedings of Optoelectronics, vol. 144, no. 4, (August 1997), pp. 235±239. S. Ramamurthy, B. Mukherjee, Fixed alternate routing and wavelength conversion in wavelength-routed optical networks, in: Proceedings of the Global Telecommunications Conference, GLOBECOM'98, (Sydney, Australia, November 1998), pp. 2295±2303. L. Li, A. K. Somani, Dynamic wavelength routing using congestion and neighborhood information, IEEE Transactions on Networking, vol. 7, no. 5, (October 1999), pp. 779±786. H. Zang, L. Shasrabuddhe, J. P. Jue, S. Ramamurthy, B. Mukherjee, Connection management for wavelength-routed WDM networks, in: Global Telecommunications Conference, GLOBECOM'99, vol. 2, (Rio de Janeiro, Brazil, 1999), pp. 1428±1432. J. Jue, G. Xiao, An adaptive routing algorithm for wavelengthrouted optical networks with a distributed control scheme, in: Proceedings of the Nineth International Conference on Computer Communications and Networks, (Las Vegas, Nevada, USA, October 2000), pp. 192±197. A. Mokhtar, M. Azizoglu, Adaptive wavelength routing alloptical networks, IEEE Transactions on Networking, vol. 6, no. 2, (April 1998), pp. 197±206. R. Ramaswami, A. Segall, Distributed network control for wavelength routed optical networks, IEEE Transactions on Networking, vol. 5, no. 6, (December 1996), pp. 936±943. S. Thiagarajan, A. K. Somani, Performance analysis of WDM networks with grooming capabilities, in: Proceedings of the SPIE Technical Conference on Terabit Optical Networking: Architecture, Control, and Management Issues, (Boston, Massachusetts, USA, 2000), pp. 253±262. S. Chen, K. Nahrstedt, An overview of quality-of-service routing for the next generation high-speed networks: Problems and solutions IEEE Network, Special Issue on Transmission and Distribution of Digital Video, vol. 12, no. 6, (November/ December 1998), pp. 64±79. R. Perlman, Interconnections: Bridges, Routers, Switches, and Internetworking Protocols, Second ed. (Addison-Wesley, 1999). R. Sriram, G. Manimaran, C. S. R. Murthy, Preferred link based delay-constrained least-cost routing in wide area networks, Computer Communications, vol. 21, no. 18, (November 1998), pp. 1655±1669.

R. Srinivasan is currently an Assistant Professor in the Department of Electrical and Computer Engineering at University of Arizona. He received his B.E. (Hons) degree in Electrical and Electronics Engineering from Birla Institute of Technology and Science (BITS), Pilani, India, in 1997 and Ph.D. in Computer Engineering from Iowa State University, Ames, in 2002. He is a codeveloper of the Hierarchical Modeling and Analysis Package (HIMAP), a reliability modeling and analysis tool, which is currently being used at Boeing, Honeywell, and several other

R. Srinivasan, A. K. Somani/Dynamic Routing in WDM Grooming Networks companies and universities. His research interests include architectures and algorithms for optical networks, computer communication networks and protocols, fault tolerance, system modeling, and performance analysis. Arun K. Somani is currently the David C. Nicholas Professor of Electrical and Computer Engineering at Iowa State University. He earned his B.E. (Hons) degree in Electrical and Electronics Engineering from the Birla Institute of Technology and Science (BITS), Pilani, India, in 1973, M.Tech. in Computer Engineering from the Indian Institute of Technology, Delhi, India, in 1979, MSEE and Ph.D. degrees in Electrical Engineering from the McGill University, Montreal, Canada, in 1983 and 1985, respectively. He

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worked as Scienti®c Of®cer for the Government of India, New Delhi from 1974 to 1982. From 1985 to 1997, he was a faculty member at the University of Washington, Seattle, WA, where he was a Professor of EE and CSE from 1995 onwards. Professor Somani's research interests are in the area of fault tolerant computing, computer communication and networks, optical networking, computer architecture, and parallel computer systems. He has taught courses in these areas and published more than 150 technical papers. He has served on several program committees of various conferences in his research areas, was the General Chair of IEEE Fault Tolerant Computing Symposium and Technical Program Chair of IEEE Conference on Computer Communications and Networks. He is currently serving as an Associate Editor of IEEE Transactions on Computers and an Editor of a Microprocessors and Microsystems. He is a Fellow of the IEEE. He is also a distinguished lecturer and distinguished tutorial speaker of the IEEE.