Dynamic routing and wavelength assignment in the ... - IEEE Xplore

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IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 13, NO. 3, JUNE 2005

Dynamic Routing and Wavelength Assignment in the Presence of Wavelength Conversion for All-Optical Networks Xiaowen Chu, Member, IEEE, and Bo Li, Senior Member, IEEE

Abstract—Blocking probability has been one of the key performance indexes in the design of wavelength-routed all-optical WDM networks. Existing research has demonstrated that an effective Routing and Wavelength Assignment (RWA) algorithm and wavelength conversion are two primary vehicles for improving the blocking performance. However, these two issues have largely been investigated separately; in particular the existing RWA algorithms have seldom considered the presence of wavelength conversion. In this paper, we firstly demonstrate that the existing dynamic RWA algorithms do not work well in the presence of wavelength conversion as they usually only take into account the current traffic, and do not explicitly consider the route lengths. We then propose a weighted least-congestion routing and first-fit wavelength assignment (WLCR-FF) algorithm that considers both the current traffic load and the route lengths jointly. We further introduce an analytical model that can evaluate the blocking performance for WLCR algorithm. We carry out extensive numerical studies over typical topologies including ring, mesh-torus, and the 14-node NSFNET; and compare the performance of WLCR-FF with a wide variety of existing routing algorithms including static routing, fixed-alternate routing and least-loaded routing. The results conclusively demonstrate that the proposed WLCR-FF algorithm can achieve much better blocking performance in the presence of sparse or/and full wavelength conversion. Index Terms—Routing and wavelength assignment (RWA), wavelength conversion, wavelength division multiplexing (WDM).

I. INTRODUCTION

W

AVELENGTH-ROUTED all-optical WDM networks are considered to be candidates for the next generation of wide-area backbone networks [21]. A wavelength-routed all-optical WDM network comprises optical wavelength routing nodes (i.e., wavelength routers) interconnected by optical fiber links. A lightpath has to be established before the communication between any two wavelength routers [5]. To establish a lightpath, it is normally required that the same wavelength channel should be allocated on all the links along the route. This limitation is known as the wavelength continuity constraint, which makes the wavelength-routed networks different from

Manuscript received June 21, 2002; revised April 17, 2004, approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor C. Qiao. This work was supported in part by grants from RGC under Contracts HKBU2159/04E, HKUST6204/03E and HKUST6104/04E, a grant from NSF China under Contract 60429202, a NSFC/RGC joint grant under Contract N_HKUST605/02, and a grant from Microsoft Research under Contract MCCL02/03.EG01. X.-W. Chu is with the Department of Computer Science, Hong Kong Baptist University, Hong Kong, China (e-mail: [email protected]). B. Li is with the Department of Computer Science, Hong Kong University of Science and Technology, Hong Kong, China (e-mail: [email protected]). Digital Object Identifier 10.1109/TNET.2005.850226

the traditional circuit-switched telephone networks. Lightpath connection requests arrive over time and each lightpath may have a random holding period. These lightpaths need to be set up dynamically by determining a route across the network connecting the source to the destination, and allocating a free wavelength channel on each fiber link along the chosen route. In this paper, we assume that existing lightpaths cannot be re-routed to accommodate new lightpath requests until they are released. Some of the lightpath requests could be blocked if there is currently no common free wavelength along any route. One of the primary design objectives of wavelength-routed all-optical WDM networks is to minimize the blocking probability, i.e., the probability that a lightpath connection request cannot be accepted. Wavelength conversion can eliminate the wavelength continuity constraint and thus improve the blocking performance [14], [17]. A wavelength router with wavelength conversion capability is called a wavelength convertible router (WCR). If all the wavelength routers can support wavelength conversion, this is referred to as full wavelength conversion. Because wavelength converters are still very expensive at the current stage, much research work focuses on sparse wavelength conversion, in which only part of the wavelength routers have the capability of wavelength conversion. Subramaniam et al. have shown that, by using sparse wavelength conversion, a relatively small number of WCRs can achieve satisfactory performance [24]. The key issue in sparse wavelength conversion architecture is the wavelength converter placement problem, i.e., given a network topology, a certain number of WCRs, and the traffic statistics, how can the WCRs be placed so as to minimize the overall blocking probability? The algorithms for optimal converter placement for simple topologies, such as bus and ring, have been shown in [25]. However, optimal converter placement for arbitrary mesh is considered to be very hard. An efficient algorithm for optimal converter placement has been proposed in [26], which is more efficient than exhausted search solution. A large number of heuristic algorithms also exist in the literature [1], [8], [10], [12], [27]. The existing research demonstrates that an effective routing and wavelength assignment (RWA) strategy and wavelength conversion are the two primary vehicles for improving the blocking performance [6], [13], [20]. However, these two issues have largely been investigated separately in that existing RWA algorithms have seldom considered the presence of wavelength conversion, whilst the wavelength converter placement algorithms have largely assumed that a static routing and

1063-6692/$20.00 © 2005 IEEE

CHU AND LI: DYNAMIC ROUTING AND WAVELENGTH ASSIGNMENT IN THE PRESENCE OF WAVELENGTH CONVERSION

random wavelength assignment algorithm is employed. Our study in this paper is mainly motivated by the observation that conventional dynamic routing algorithms may not work well in the environment with sparse or/and full wavelength conversion. The main reason is that the existing dynamic routing algorithms only consider the distribution of free wavelengths, i.e., they usually select a route with more free wavelengths, and do not explicitly consider the route hop lengths. Evidently, without wavelength conversion, the route with more free wavelengths usually has shorter hop length, as the probability that a longer route has more free wavelengths is much smaller as compared with that of a shorter route [2]. However, with the presence of wavelength conversion, the above property no longer holds. Consider an example in ring network with full wavelength conversion, least-loaded routing algorithm [3], [4] actually achieves very poor performance as compared with the fixed-alternate routing algorithm (Further elaboration will be given in Section IV). In this paper, we propose a new dynamic RWA algorithm, called weighted least-congestion routing and first-fit wavelength assignment (WLCR-FF), which considers the distribution of free wavelengths and the hop length of each route jointly. We carry out extensive performance studies of the proposed WLCR-FF algorithm over a variety of topologies. The results conclusively demonstrate that the proposed WLCR-FF algorithm can achieve much better performance than static routing, fixed-alternate routing and least-loaded routing, especially in the environment with sparse or/and full wavelength conversion. It is worth pointing out that it is not the objective of this paper to design the best possible RWA in the presence of wavelength conversion, which is subject to further research. The primary objective in this paper is to present a convincing argument and strong evidences that RWA and wavelength conversion need to be considered jointly. This is highlighted by the significant performance gain in term of blocking probability observed from extensive numerical studies in using the proposed WLCR-FF algorithm. In addition, our contribution lies in the development of WLCR algorithm and the analysis of WLCR with random wavelength assignment. The rest of the paper is organized as follows. Section II introduces some related work. In Section III, we present the WLCR algorithm and an analytical model for deriving its performance. In Section IV, we evaluate the blocking performance of the WLCR-FF algorithm for different topologies, followed by the discussion of performance measures in terms of the average route hop length and the average link utilization. Finally, Section V concludes the paper. II. RELATED WORK RWA algorithms play a key role in improving the blocking performance of all-optical WDM networks [20]. Shortest path routing (SPR) strategy has been widely used in telephone networks and Internet mainly because it consumes fewer resources. Many variations of SPR have also been investigated in the domain of optical networks. Generally these routing strategies can be classified into two categories: static routing, and dynamic (or adaptive) routing. In static routing, the routes are determined

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under a prior-given traffic matrix without considering the ongoing network status (e.g., the current traffic load distribution); while in dynamic routing, the route selection is based on the current network status. Birman introduced a generalized reduced load approximation scheme to calculate the blocking probabilities for SPR [3], which shows that the blocking probabilities grow with the number of hops much faster than for circuit-switched telephone network due to the wavelength continuity constraint. This result has also been exposed by Barry and Hamblet [2]. The performance of SPR is, however, very limited because the traffic is likely to be distributed to the links that belong to some short paths. These links are heavily loaded whilst the other links are comparatively lightly loaded, resulting in a low link utilization on average. To alleviate this problem, Harai et al. proposed the fixed-alternate routing (FAR) algorithm [9] and investigated its performance by extending Birman’s analytical model. FAR algorithm can improve the blocking performance by considering more candidate routes between each pair of nodes. If there is no available wavelength on the primary route, an alternative route will be considered. Thus the traffic can be distributed to more fiber links, and the overall blocking performance can be improved. A new analytical technique for the analysis of all-optical networks without wavelength conversion has been proposed in [23], which is based on the inclusion-exclusion principle from combinatorics and has a lower computational complexity. The main weakness of static routing strategies is that the route decision does not consider the current network status. Thus static routing strategies do not have the capability of traffic engineering, which is very important in the dimensioning of backbone networks. On the contrary, dynamic routing algorithms are good candidates for traffic engineering and generally they can improve the blocking performance significantly [3], [4], [11], [15], [16]. In dynamic routing, the route decision is based on the current network status which can be managed in either a distributed manner or a centralized manner. Distributed management is often preferred for scalability reasons [19]. Least-loaded routing (LLR) is an early-proposed dynamic routing strategy [3]. The main idea of LLR is borrowed from telephone networks: the route with the largest number of free wavelengths is chosen to setup the lightpath. Li and Somani proposed a dynamic routing algorithm named fixed-paths least-congestion routing (FPLC), based on path and neighborhood link congestion [16]. Their results showed that FPLC algorithm can improve the performance significantly as compared with FAR algorithm. However, in the presence of wavelength conversion, the conventional dynamic routing algorithms do not work well because they only take into account the distribution of free wavelengths and do not consider the route hop length explicitly. Recently, another two dynamic routing strategies for full wavelength conversion have been proposed [11], [15]. Lang et al. presented an analysis for dynamic routing in regular torus network with full wavelength conversion [15]. Hsu et al. proposed a weighted-shortest path strategy, which looks for the path that minimizes the resource cost while maintaining the traffic load among the links as balanced as possible [11]. Both works have shown the importance of re-examination

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among all the segments in route

of

, i.e.,

. is the offered traffic and is the real 7. For node pair , carried traffic. is the lightpath connection blocking probability of 8. Fig. 1.

A route and its segments.

of RWA problem in the presence of wavelength conversion. However, only the case of full wavelength conversion has been investigated.

III. WEIGHTED LEAST-CONGESTION ROUTING AND FIRST-FIT WAVELENGTH ASSIGNMENT ALGORITHM In this section, we introduce a new dynamic RWA algorithm called weighted least-congestion routing and first-fit wavelength assignment (WLCR-FF). The routing algorithm considers the distribution of free wavelengths and the hop length of each route jointly, and the wavelength assignment algorithm chooses the first-fit strategy because of its simplicity and excellent performance [28]. A. System Parameters, Assumptions, and Notations 1. The network consists of nodes and links. For simplicity, we consider bi-directional links. Each link can support bi-directional wavelength channels. The wavelength channels are labeled from 1 to 2. Following the convention, we assume that lightpath connection requests arrive at end-to-end node pair following a Poisson process with rate . We also assume that the connection holding time is exponentially distributed with a unit time. . The hop 3. A route is a subset of the link set . length of route is denoted by 4. The number of free wavelength channels on link is denoted by . is the set of routes pre-com5. puted for node pair . These routes are required to be edge-disjoint such that the blocking events on these routes can be approximately considered as independent with each other. is denoted 6. The number of free wavelengths on route as . Without wavelength conversion, is simply defined as the number of common free wavelengths on all the links of the route. In the case of full wavelength conversion, is defined as where link belongs to route . In the case of sparse wavelength conversion, assume there are wavelength convertible routers in route (excluding the two end nodes), we can divide the route into segments, as illustrated in Fig. 1. The th segment is denoted by . The number of free wavelengths for segment is represented as . The number of free wavelengths of route

is then defined as the minimum value

route

.

B. WLCR-FF RWA Algorithm In WLCR-FF algorithm, a set of routes have been pre-computed for each source-destination pair. These routes will be re-computed if the network topology is changed. If a lightpath connection request comes to a node pair, the system should make a decision to select a route from the pre-computed set of routes, and then assign wavelength(s) to the selected route. The design objective of RWA algorithms is to carry more traffic while keeping the blocking probability at a low level. is the set of routes preAssume computed for node pair . Upon arrival of a connection request for node pair , the WLCR-FF algorithm will make a route selection decision as follows: for each candidate route First, associate a weight value . The weight function is defined as follows:

After the calculation of all the weight values, we choose the route with the maximum weight value to setup the lightpath. If no wavelength is available on any of the routes, i.e., for all the routes, the connection request has to be blocked. Once a lightpath is setup, the first-fit wavelength assignment scheme will be employed on each segment in the selected route, i.e., for each segment, the free wavelength channel with the smallest label will be allocated on all the links in that segment. is based on the folThe design of weight function lowing observations: When selecting a route, two important factors should be considered: (1) the number of free wavelengths; (2) the hop length of each route. Intuitively, the route with more free wavelengths should be preferred, and at the same time the hop length of that route should not be very long. If there is no wavelength conversion, these two factors are correlated, i.e., a route with shorter length is likely to have more free wavelengths than the routes with longer length. Therefore conventional dynamic RWA algorithms work very well by selecting the route with more free wavelengths if there is no wavelength conversion. However, if the network has the capability of wavelength conversion, the correlation between the number of free wavelengths and the route hop length is weakened, in the sense that a route with longer length is possible to have more free wavelengths than the routes with shorter length. Thus if we always select the route with more free wavelengths, it is possible that such routes have longer route lengths, which can result in a low wavelength utilization and high blocking probability. In principle, the weight function should be proportional to the number of free wavelengths, and be inversely proportional to the hop length of the route. However, the blocking performance seems


to be very sensitive to the weight functions. We have tried different weighted functions, and square root works the best. More details including comparisons are presented in Section IV-B. C. Analytical Model of the WLCR Algorithm In this subsection, we present an analytical model to estimate the blocking probability when using WLCR algorithm and random wavelength assignment. Random wavelength assignment is assumed to simplify the analytical model. The model consists of routing analysis and route-blocking analysis. The routing analysis determines link-offered traffic from the route-blocking probabilities, and the route-blocking analysis determines the route blocking probabilities from the link-offered traffic. This will result in a set of fixed-point nonlinear equations, which can then be solved by numerical iterative substitutions. To simplify the analysis, we assume that only two link-disjoint routes are provided for each node pair , denoted by and . Without loss of generality, we also assume that . In fact, the maximum number of link-disjoint routes between a node pair depends on the network topology. Some researchers found that having more than two candidate routes cannot improve the performance significantly [15], [17]. Nevertheless, our analytical model can be extended to the case of more than two routes. The overall blocking probability is the ratio of the blocked lightpath requests to the total number of lightpath requests in a stable long term. That is,

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where

(4) The traffic carried on link is the sum of the carried traffic and be the of all the routes that contain link . Let probabilities that a connection for node pair is setup on the first and second route respectively. Then we can approximately have

(5) where

is the link-route incidence matrix defined as .

We introduce

for representing the probability that

wavelengths are available on segment . We also introduce for representing the probability that when wavelengths are available on link , wavelengths are available on segment that contains link . Then we have (6)

(1)

A route can be setup if each segment in that route has its own available wavelengths. With an approximate assumption that the blocking events of all the segments are independent, we by can derive the blocking probability of any route

The lightpath connection request between node pair will be blocked only if both candidate routes cannot accommodate the new connection. Since the blocking events of the two routes are assumed to be independent, we have

(7)

To determine two notations: Let (2) To obtain the steady-state probability of the number of available wavelengths on each link, we use the reduced load approximation method presented in [3]. Let denote the random variable representing the number of free wavelengths on link . We , are indeassume that the random variables pendent, and the aggregated connection requests arrive at link following a Poisson process with rate . Let denote wavelengths are free on link . We can the probability that derive

and

, we need to introduce another and be the probabilities

that wavelengths are available on route tively, i.e., . Therefore, for both

and and and

respec, we

have

(8) (3)

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According to the WLCR routing algorithm, we can have where

(9)

and where Fig. 2.

(10)

Suppose

the

links ,

of then

segment

are

the

probability

is given by (11), shown at the bottom of the page, where denotes the probability that there exist available wavelengths on the -hop segment, given the numbers of free wavelengths of all its links. It can be determined by the recursive relation shown in (12) and (13) at the bottom of the page. is the probability that The conditional probability there exist available wavelengths under the condition that and wavelengths are available on successive two links. From is given by [3],

8-node ring network.

1) Initialize as 0 for all routes. Initialize as 0 for and as 1/2. all links. Initialize using (5) for all links. 2) Calculate using (3) and (4) for all links. 3) Calculate 4) Calculate and for all the segments using (6), (11)–(14). Then calculate and using (8)–(10). for all routes using (7). If new values of 5) Calculate are converged to the older ones,1 the iteration is terminated and we can go to Step 6). Otherwise go to Step 2) for next iteration. 6) Finally, calculate the overall blocking probability using (1) and (2). IV. NUMERICAL RESULTS AND ANALYSIS

D. Numerical Algorithm

In this section, we carry out extensive simulations to investigate the performance of WLCR-FF algorithm over the 8-node ring topology (Fig. 2), 25-node mesh-torus topology (Fig. 3), and 14-node NSFNET topology (Fig. 4). In all simulations, the lightpath connection requests are generated as a Poisson process, and the connection holding time is exponentially distributed. We assume that all the source-destination node pairs have the same traffic load in Erlangs. Each fiber link is assumed

In summary, we can determine the overall blocking probability as follows:

1The convergence here means that the difference between the new value and old value is less than some pre-defined small value.

(14)

(11)

(12) , , otherwise.

, ,

(13)


Fig. 3.

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25-node mesh-torus network. Fig. 5. Overall blocking probability versus total traffic load in NSFNET, random wavelength assignment, sparse wavelength conversion.

Fig. 4.

14-node NSFNET network.

to support 40 bidirectional wavelength channels. Two edge-disjoint shortest paths are provided for each source-destination pair. We compare the performances of WLCR-FF, shortest path routing (SPR-FF), fixed-alternate routing (FAR-FF) and least-loaded routing (LLR-FF) algorithms under three different scenarios: no wavelength conversion, sparse wavelength conversion, and full wavelength conversion. For sparse wavelength conversion, we use a well-known heuristic converter placement algorithm called Minimum Blocking Probability First (MBPF) to place a given number of WCRs [8]. MBPF simply inserts WCRs into the network one by one such that each time the overall blocking probability can be minimized. In MBPF, the analytical model presented in previous section is used to calculate the approximate blocking probabilities. In all of our simulations, every single data is obtained by conducting 30 independent replications of the same simulation and then calculating the mean results. The simulation time is controlled such that the relative error is within 5% at 95% confidence level. A. Performance of WLCR Algorithm With Random Wavelength Assignment We use NSFNET as an example to compare the analytical results of WLCR with simulation results. Fig. 5 depicts the

blocking probabilities of sparse wavelength conversion using five WCRs. In these set of simulations, random wavelength assignment is used because it is an assumption of the analytical model. From the figure, we observe that the analytical model overestimates the blocking probabilities; however, the analytical results still follow the trend of simulation results, and it will be more accurate if more WCRs are installed. We will use this model to solve the wavelength converter placement problem for sparse wavelength conversion. We also show the simulation results of SPR and FFR algorithms for comparison. The results show that, under light traffic load, WLCR algorithm can decrease the blocking probability by one to two orders of magnitude; when the traffic load grows, the benefit of WLCR will decrease. In real wavelength-routed WDM networks, the blocking probability is likely to be controlled at a low level since each lightpath can carry huge amount of data; therefore WLCR algorithm is a good candidate for WDM networks which demand a small blocking probability (e.g., below 5%). B. Performance Comparison of Different Weight Functions In our proposed WLCR algorithm, the weight func. It is very tion is chosen as challenging to design an optimal weight function suitable for all kinds of topologies mathematically. We obtain ours by trying different weight functions and analyzing from extensive simulation results. In this subsection, we present the blocking performances of another two inand tuitive weight functions: . Both of them are designed to be proportional to the number of free wavelengths, is a very and inversely proportional to the route hop length. intuitive weight function which considers free wavelength distries to normalize tribution and route hop length explicitly. the traffic load factor by taking into consideration the total could be number of wavelengths. Note that the value of equal to positive infinity.

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Fig. 6. Overall blocking probability versus total traffic load in NSFNET, sparse wavelength conversion.


Fig. 7. Overall blocking probability versus total traffic load in 8-node ring network, without wavelength conversion.

Fig. 6 shows the simulation results of different weight functions under the NSFNET topology using five WCRs and first-fit wavelength assignment. In the figure, the curves of WLCR2-FF and WLCR3-FF represent the blocking perforand respectively. mance of WLCR with weight function The blocking performance of LLR-FF algorithm is also shown as a benchmark. Obviously the performances of WLCR2-FF and WLCR3-FF are worse than that of LLR algorithm. We also is very close to observe that the behavior of WLCR using takes too much FAR, and the reason turns out to be that account of the route hop length. In order to decrease the impact factor of route hop length, we designed the weight function , and its performance is the best among all those we have examined. C. Performance of WLCR-FF Algorithm In what follows, we investigate the performance of WLCR-FF algorithm by extensive simulation studies in two regular network topologies, i.e., ring and mesh-torus, and one real network topology NSFNET. Ring topology is widely used in today’s backbone networks, and it is a typical loosely-connected topology. On the contrary, mesh-torus is a typical densely-connected topology. Fig. 7 depicts the blocking performance of different RWA algorithms in an 8-node ring network without wavelength conversion. We can observe that FAR-FF, LLR-FF and WLCR-FF algorithms work much better than SPR-FF algorithm. This can be explained as follows: when the traffic load is light, the main reason of a lightpath blocking is the lack of common free wavelengths in the route. If two candidate routes are provided for each pair node, the blocking events of these two routes can be approximately considered as independent and hence the blocking probability can be decreased by a large margin. Dynamic routing algorithms can further improve the blocking performance because more wavelengths are left free for future connections and at the same time they can avoid using too many long routes.

Fig. 8. Overall blocking probability versus total traffic load in 8-node ring network, sparse wavelength conversion.

Fig. 8 shows the blocking performance of sparse wavelength conversion with four WCRs which are placed at nodes (1, 3, 5, 7). An important observation is that the blocking probability of LLR-FF algorithm increases much faster than other routing algorithms with the increase of traffic load. The main reason is that, the majority of the pair nodes in ring topology have one short route and one long route. LLR-FF algorithm uses lots of long routes (as compared with other routing algorithms) and therefore does not utilize the resources efficiently. On the contrary, WLCR-FF algorithm takes into account the length of each route and avoids using too many long routes; therefore it can achieve the best performance. This phenomenon is more obvious in the case of full wavelength conversion, as shown in Fig. 9. The performance of LLR-FF algorithm is even worse than SPR-FF algorithm when the total traffic loads are beyond 110 Erlangs. With the traffic load is low, WLCR-FF outperforms all other routing algorithms by a large margin.


Fig. 9. Overall blocking probability versus total traffic load in 8-node ring network, full wavelength conversion.

Fig. 10. Overall blocking probability versus total traffic load in 25-node mesh-torus network, without wavelength conversion.

Figs. 10–12 compare the performances of different RWA algorithms in the 25-node mesh-torus network for no wavelength conversion, sparse wavelength conversion and full wavelength conversion, respectively. The results show that both LLR-FF and WLCR-FF algorithms can improve the blocking performance significantly as compared with SPR-FF and FAR-FF algorithms. For FAR-FF algorithm, most of the traffic will be distributed to the shortest route between each pair node, resulting that some links are very lightly utilized. Dynamic routing algorithms can distribute the traffic more evenly among all the links. Thus they can decrease the blocking probability significantly. When there is no wavelength conversion or with sparse wavelength conversion, the performance of WLCR-FF is only slightly better than that of LLR-FF. But in the case of full wavelength conversion, we can see that WLCR-FF algorithm outperforms LLR-FF algorithm by a considerable margin.

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Fig. 11. Overall blocking probability versus total traffic load in 25-node mesh-torus network, sparse wavelength conversion.

Fig. 12. Overall blocking probability versus total traffic load in 25-node mesh-torus network, full wavelength conversion.

The simulation results in NSFNET topology is shown in Figs. 13–15. We can observer that there is a big gap between SPR-FF and FAR-FF, and there is another big gap between FAR-FF and LLR-FF/WLCR-FF. The gap between LLR-FF and WLCR-FF increases when more wavelength conversion can be done in the network. For sparse wavelength conversion and full wavelength conversion, WLCR-FF can improve the blocking performance significantly over LLR-FF. D. Analysis of the Average Route Hop Length and Average Link Utilization To best understand the behavior of WLCR-FF algorithm, we measure the average route hop lengths and average link utilizations. The average route hop lengths for different RWA algorithms in 8-node ring and NSFNET topologies are shown in Tables I and II, respectively. From the tables, we observe that SPR-FF algorithm always has the shortest average route

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Fig. 13. Overall blocking probability versus total traffic load in 14-node NSFNET, without wavelength conversion.


Fig. 15. Overall blocking probability versus total traffic load in 14-node NSFNET, full wavelength conversion. TABLE I AVERAGE ROUTE LENGTH IN 8-NODE RING NETWORK

TABLE II AVERAGE ROUTE LENGTH IN 14-NODE NSFNET

Fig. 14. Overall blocking probability versus total traffic load in 14-node NSFNET, sparse wavelength conversion.

lengths. The average route lengths of FAR-FF algorithm are a little longer. WLCR-FF has very close average route lengths as compared with FAR-FF. Finally, LLR-FF has the longest average route lengths. When there is no wavelength conversion, the average route lengths of FAR-FF, WLCR-FF and LLR-FF are very close. This is because without wavelength conversion, the probability that a long route has free wavelengths is smaller than that of a short route. So for both LLR-FF and WLCR-FF algorithms, the probability of choosing a long route is very small. However, in the case of sparse wavelength conversion and especially full wavelength conversion, LLR-FF algorithm will choose the longer route with a relatively high probability, and therefore the average route lengths of LLR-FF algorithm becomes much longer. WLCR-FF algorithm makes a good compromise between FAR-FF and LLR-FF. Since it considers the route

length explicitly in the route decision, the resulted average route lengths are only a litter longer than those of FAR-FF. This makes WLCR-FF algorithm consume less link resources as compared with LLR-FF, and therefore the blocking performance is improved. One advantage of dynamic routing algorithm is the capability of distributing the traffic load evenly to all the links. We use to denote the utilization ratio of link which is defined as , where is the holding time of lightpath , is the number of wavelengths per link, and is the counted simulation time.2 Using 8-node ring topology as an example, Figs. 16–18 show the average link utilization ratio versus the traffic load for different wavelength conversion capabilities. It is obvious that with the increase of 2We

only count the time after the system enters the steady state.


Fig. 16. Average link utilization in 8-node ring network, without wavelength conversion.

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Fig. 18. Average link utilization in 8-node ring network, full wavelength conversion. TABLE III STANDARD DEVIATION OF LINK UTILIZATION IN 8-NODE RING NETWORK

TABLE IV STANDARD DEVIATION OF LINK UTILIZATION IN 14-NODE NSFNET NETWORK

Fig. 17. Average link utilization in 8-node ring network, sparse wavelength conversion.

traffic load, the link utilization also increases. LLR-FF algorithm always has the highest link utilization. WLCR-FF algorithm also has higher link utilization than FAR-FF and SPR-FF. One reason is that dynamic routing algorithms can distribute the traffic to some light-loaded links and thus utilize the resource more efficiently. SPR-FF algorithm has the lowest link utilization because there is only one route provided for each pair nodes. FAR-FF algorithm is better than SPR-FF by providing some alternate routes. However, when the traffic load is low, these alternate routes are seldom chosen because the primary route is always considered first. We should also notice that the link utilization is correlated with the average route length. Long average route length inherently means high link utilization (according to our definition). This explains why the blocking performance of LLR-FF is poor in the presence of wavelength conversion, even though it has the highest link utilization ratio. Another important

observation is that in order to guarantee a low blocking probability, the average link utilization ratio cannot be very high. For example, in the 8-node ring topology without wavelength conversion, in order to guarantee a blocking probability of 2%, the average link utilization ratio for SPR-FF algorithm is only around 62%, and for FAR-FF, LLR-FF and WLCR-FF algorithms, the utilization ratio can reach 70%. To observe how the traffic loads distribute among the links, we also show the standard deviation of link utilization in Tables III and IV, for 8-node ring and NSFNET, respectively. From these two tables, we can observe that the standard deviations of LLR-FF and WLCR-FF algorithms are much less than those of FAR-FF and SPR-FF algorithms. In the ring network, since we assume all the pair nodes have the same traffic load, the standard deviations are very small because of the symmetry of the

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network topology. In the NSFNET network, the standard deviations are much higher because of the irregular topology. In summary, our study shows that LLR-FF algorithm can achieve high link utilization, but its average route length is too long; FAR-FF algorithm has a short average route length, but its link utilization is too low; WLCR-FF algorithm makes a good trade-off between the average route length and the link utilization so that it can achieve relatively high link utilization and keep the average route length at an acceptable level at the same time. Therefore the blocking performance of WLCR-FF algorithm is better than others, especially in the presence of wavelength conversion. V. CONCLUSIONS In this paper, we have examined the dynamic RWA problem in the presence of wavelength conversion. We proposed a new dynamic RWA algorithm, called WLCR-FF algorithm, in wavelength-routed all-optical WDM networks. WLCR-FF algorithm takes into account the distribution of free wavelengths and the hop lengths of each route jointly when it makes a route decision. An approximate analytical model has been introduced to estimate the lightpath connection blocking probability when using WLCR algorithm. The simulation results demonstrated that WLCR-FF algorithm could improve the blocking performance significantly compared with conventional dynamic RWA algorithms in the environment of sparse or/and full wavelength conversion. Through detailed analysis of average route length and link utilization, we illustrated that WLCR-FF algorithm makes a good trade-off between the average route length and the link utilization and thus improves the performance a lot. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their valuable comments and constructive suggestions. REFERENCES [1] A. S. Arora and S. Subramaniam, “Converter placement in wavelength routing mesh topologies,” Proc. of IEEE ICC 2000, pp. 1282–1288, Jun. 2000. [2] R. A. Barry and P. A. Humblet, “Models of blocking probability in alloptical networks with and without wavelength changers,” IEEE Journal on Selected Areas in Communications, vol. 14, pp. 858–867, Jun. 1996. [3] A. Birman, “Computing approximate blocking probabilities for a class of all-optical networks,” IEEE Journal on Selected Areas in Communications, vol. 14, pp. 852–857, Jun. 1996. [4] K. Chan and T. P. Yum, “Analysis of least congested path routing in WDM lightwave networks,” Proc. of IEEE INFOCOM ’94, pp. 962–969, 1994. [5] I. Chlamtac, A. Ganz, and G. Karmi, “Lightpath communications: An approach to high bandwidth optical WAN’s,” IEEE Transactions on Communications, vol. 40, pp. 1171–1182, Jul. 1992. [6] I. Chlamtac, A. Farago, and T. Zhang, “Lightpath (Wavelength) routing in large WDM networks,” IEEE Journal on Selected Areas in Communications, vol. 14, pp. 909–913, Jun. 1996. [7] X.-W. Chu, B. Li, and Z. Zhang, “A dynamic RWA algorithm in a wavelength-routed all-optical network with wavelength converters,” Proc. of IEEE INFOCOM ’03, pp. 1795–1804, Mar. 2003. [8] X.-W. Chu, B. Li, and I. Chlamtac, “Wavelength converter placement for different RWA algorithms in wavelength-routed all-optical networks,” IEEE Transactions on Communications, vol. 51, pp. 607–617, Apr. 2003.

[9] H. Harai, M. Murata, and H. Miyahara, “Performance of alternate routing methods in all-optical switching networks,” Proc. of IEEE INFOCOM ’97, pp. 517–525, Apr. 1997. [10] , “Heuristic algorithms of allocation of wavelength convertible nodes and routing coordination in all-optical networks,” IEEE/OSA Journal of Lightwave Technology, pp. 535–545, Apr. 1999. [11] C.-F. Hsu, T.-L. Liu, and N.-F. Huang, “On adaptive routing in wavelength-routed networks,” SPIE/Kluwer Optical Networks Magazine, vol. 3, no. 1, pp. 15–24, Jan. 2002. [12] J. Iness and B. Mukherjee, “Sparse wavelength conversion in wavelength-routed WDM optical networks,” Photonic Network Communications, Nov. 1999. [13] E. Karasan and E. Ayanoglu, “Effects of wavelength routing and selection algorithms on wavelength conversion gain in WDM optical networks,” IEEE/ACM Transactions on Networking, vol. 6, pp. 186–196, Apr. 1998. [14] M. Kovacevic and A. Acampora, “Benefits of wavelength translation in all-optical clear-channel networks,” IEEE Journal on Selected Areas in Communications, vol. 14, pp. 868–880, Jun. 1996. [15] J. P. Lang, V. Sharma, and E. A. Varvarigos, “An analysis of oblivious and adaptive routing in optical networks with wavelength translation,” IEEE/ACM Transactions on Networking, vol. 9, pp. 503–517, Aug. 2001. [16] L. Li and A. K. Somani, “Dynamic wavelength routing using congestion and neighborhood information,” IEEE/ACM Transactions on Networking, vol. 7, pp. 779–786, Oct. 1999. [17] B. Ramamurthy and B. Mukherjee, “Wavelength conversion in WDM networking,” IEEE Journal on Selected Areas in Communications, vol. 16, pp. 1061–1073, Sep. 1998. [18] S. Ramamurthy and B. Mukherjee, “Fixed-Alternate routing and wavelength conversion in wavelength-routed optical networks,” IEEE/ACM Transactions on Networking, vol. 10, pp. 351–367, Jun. 2002. [19] R. Ramaswami and A. Segall, “Distributed network control for optical networks,” IEEE Transactions on Communications, vol. 5, pp. 936–943, Dec. 1997. [20] R. Ramaswami and K. Sivarajan, “Routing and wavelength assignment in all-optical networks,” IEEE/ACM Transactions on Networking, vol. 3, pp. 489–500, Oct. 1995. , Optical Networks: A Practical Perspective. San Francisco, CA: [21] Morgan Kaufmann Publishers, 1998. [22] M. Sivakumar and S. Subramaniam, “On the performance impact of wavelength assignment and wavelength conversion architecture and placement algorithms,” SPIE/Kluwer Optical Networks Magazine, Mar./Apr. 2002. [23] A. Sridharan and K. N. Sivarajan, “Blocking in all-optical networks,” IEEE/ACM Transactions on Networking, vol. 12, pp. 384–397, Apr. 2004. [24] S. Subramaniam, M. Azizoglu, and A. K. Somani, “All-Optical networks with sparse wavelength conversion,” IEEE/ACM Transactions on Networking, vol. 4, pp. 544–557, Aug. 1996. [25] , “On optimal converter placement in wavelength-routed networks,” IEEE/ACM Transactions on Networking, vol. 7, pp. 754–767, Oct. 1999. [26] S. Thiagarajan and K. Somani, “An efficient algorithm for optimal wavelength converter placement on wavelength-routed networks with arbitrary topologies,” Proc. of IEEE INFOCOM ’99, pp. 916–923, Mar. 1999. [27] K. R. Venugopal, M. Shivakumar, and P. S. Kumar, “A heuristic for placement of limited range wavelength converters in all-optical networks,” Proc. of IEEE INFOCOM ’99, pp. 908–915, Mar. 1999. [28] Y. Zhu, G. N. Rouskas, and H. G. Perros, “A comparison of allocation policies in wavelength routing networks,” Photonic Networks Communication Journal, vol. 2, no. 3, pp. 265–293, Aug. 2000.

Xiaowen Chu (M’03) received the B.E. degree in computer science from Tsinghua University, Beijing, China, in 1999, and the Ph.D. degree in computer science from the Hong Kong University of Science and Technology, Hong Kong, China, in 2003. He is currently an Assistant Professor in the Department of Computer Science, Hong Kong Baptist University. His main research interests include optical WDM networks, multimedia networking, and internet security.


Bo Li (S’89–M’92–SM’99) received the B.E. (summa cum laude) and M.E. degrees in computer science from Tsinghua University, Beijing, China, in 1987 and 1989, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Massachusetts at Amherst in 1993. Between 1993 and 1996, he worked on high performance routers and ATM switches in IBM Networking System Division, Research Triangle Park, NC. Since 1996, he has been with the Department of Computer Science, Hong Kong University of Science and Technology, where he is now an associated professor and Co-Director for the ATM/IP Cooperate Research Centre, a government sponsored research center. Since 1999, he has also held an adjunct researcher position at the Microsoft Research Asia (MSRA), Beijing, China. He concurrently holds guest or adjunct professorship in several universities such as Huazhong University of Science and Technology (Wuhan), Beijing University of Post and Telecommunications (Beijing), Tongji University (Shanghai), Sun Yat-Sen University (Guangzhou). His current research interests are on adaptive video multicast, peer-to-peer communications, packet scheduling and dynamic routing in optical networks, resource management in mobile wireless systems, scheduling and energy efficient routing in ad hoc networks, across layer design for sensor networks, and content distribution and replication. He has published 80 journal papers and held several patents in above areas. He received the prestigious Oversea Outstanding Young Scientist Investigator Award from Natural Science Foundation of China in 2004. Dr. Li has been on the editorial board for IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, IEEE TRANSACTIONS ON MOBILE COMPUTING, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, ACM/Kluwer Journal of Wireless Networks (WINET), IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS (JSAC) - Wireless Communications Series, ACM Mobile Computing and Communications Review (MC2R), Elsevier Ad Hoc Networks, SPIE/Kluwer Optical Networking Magazine (ONM), KICS/IEEE Journal of Communications and Networks (JCN). He served as a guest editor for IEEE Communications Magazine Special Issue on Active, Programmable, and Mobile Code Networking (April 2000), ACM Performance Evaluation Review Special Issue on Mobile Computing (December 2000), and SPIE/Kluwer Optical Networks Magazine Special Issue in Wavelength Routed Networks: Architecture, Protocols and Experiments (January/February 2002), IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS Special Issue on Protocols for Next Generation Optical WDM Networks (October 2000), Special Issue on Recent Advances in Service-Overlay Network (January 2004), and Special Issue on Quality of Service Delivery in Variable Topology Networks (September 2004), and ACM/Kluwer Mobile Networks and Applications (MONET) Special Issue on Energy Constraints and Lifetime Performance in Wireless Sensor Networks (2nd Quarter of 2005). In addition, he has been involved in organizing over 40 conferences, especially IEEE INFOCOM since 1996. He was the Co-TPC Chair for IEEE INFOCOM 2004.

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