ADAPTIVE LINK WEIGHT ASSIGNMENT AND RANDOM EARLY BLOCKING ALGORITHM FOR DYNAMIC ROUTING IN WDM NETWORKS

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1 ADAPTIVE LINK WEIGHT ASSIGNMENT AND RANDOM EARLY BLOCKING ALGORITHM FOR DYNAMIC ROUTING IN WDM NETWORKS Ching-Lung Chang, Yan-Ying, Lee, and Steven S. W. Lee* Department of Electronic Engineering, National Yunlin University of Science & Technology, Taiwan, R.O.C. * Optical Communications & Networking Technologies Department, Computer & Communications Research Laboratories Industrial Technology Research Institute, Taiwan, R.O.C. ABSTRACT In order to use WDM networks efficiently, a lightpath is dynamically established upon the arrival of a connection request. Dynamic routing is usually determined by conventional shortest path algorithm. Different link weight assignment results in different routing and network performance. In this work, we propose a new weight assignment scheme in which link weights are proportional to the exponential of link utilization. It is used to differentiate network in different traffic loads so as to arrive load balanced routing. Based on the assignments, one adaptive routing algorithm referred to as Exponential Weighted Shortest Feasible Path () is presented. Furthermore, to avoid consuming too much network resources by a path with large hop count, a new call control algorithm named Random Early Blocking (REB) is proposed. By randomly rejecting calls with long routing path in heavy load, the whole network blocking probability can be greatly improved. Moreover, to balance the favor of short distance calls, a fair version of REB (called FREB) is presented in the paper. Extensive simulations are performed to evaluate the performance among different schemes. Compared to well-known shortest feasible path routing and weighted feasible shortest path routing, achieves lowest call blocking probability. In cooperation with REB, all of the three adaptive routing approaches can significantly improve their performance. Among them the EWSCP+REB scheme outperforms all of the others. Simulation results also reveal that the FREB can obtain fairness among calls with different distances by only sacrificing a little blocking performance. KEY WORDS WDM Network, Dynamic Routing, Blocking Probability, Fairness Routine, Exponential Weighted Shortest Feasible Path Routing, Random Early Blocking 1. Introduction Thanks to the advances in Wavelength Division Multiplexing (WDM) technology [1], optical networks are now capable to provide tremendous bandwidth economically. In WDM, the bandwidth of an optical fibre is divided into many individual wavelength channels. By concatenating the wavelength channels in a WDM network, a lightpath can be set up to provide a circuitswitched connection between two nodes. It is believed that the on demanded lightpath establishment is much more efficient in using WDM networks. To provide such function, it is essential for a network to be able to dynamically find out a route and assign wavelengths upon the arrival of a connection request. Therefore, there have been many researches focusing on dynamic routing and wavelength assignment (RWA) problems with targets to utilize network resources efficiently and maximize the number of establishment lightpaths [4][5][6][7][8]. Dynamic routing is usually determined by conventional shortest path algorithm. However, by assigning different link weight, it results in different network performance especially in call blocking probability. In this work, we propose a new weight assignment scheme that proportions to exponential of link utilization. The new weight function can differentiate network in different loads so as to facilitate load balanced routing. Based on the weight assignments, one adaptive routing algorithm referred to as Exponential Weighted Shortest Feasible Path () is presented. We compare the performance of different adaptive routing schemes in WDM networks and demonstrate that the has best performance in different traffic loading distribution. To reduce network resources consumed by a long-hop path, a scheme called Random Early Blocking (REB) is presented. The concept of REB is that lightpaths with large hop counts will be randomly blocked when the network is in heavy load. The simulation results show that the blocking probability can be significantly improved when dynamical routing strategy embedding the REB scheme. Finally, to balance the favour of short distance paths in REB, a fair version of REB (called FREB) is also presented in the paper. Only sacrificing a little network blocking probability, connections with different distances can be fairly treated. The rest of this paper is organized as follows. Section 2 presents conventional adaptive routing and the proposed routing. Section 3 describes the algorithms of

2 Link Weight (0,1) Wavelength in Use Fig. 1. Link Weight Assignment REB and FREB. The simulation results are shown in Section 4. We make a concluding remark in Section Adaptive Link Weight Assignment and Dynamic Routing Strategies In adaptive routing, the routing path is dynamically determined upon the arrival of a connection request. The routing computation is based on global network states that can be obtained from communication protocols [9][10]. The routing is usually based on shortest path algorithm. However, with different link cost assignment, different routes are selected.. In this section, we compare different weight assignments schemes for a wavelength routed WDM network. Routing policies include traditional equal-weighted link cost assignment [3], linear-weighted link cost assignment [2], and the proposed exponential-weighted cost assignment. Herein, we assume optical switches with the capability of performing full-range wavelength conversion. For the traditional Shortest Feasible Path routing denoted as, an equal-weighted link cost assignment is applied to obtain a least-cost routing path. The selection of a route is to minimize the number of hop count for the purpose of consuming as least resources as possible. The link weight is determined by the following function. 1, if Ui ( ) < 1 ; where U(i) is the utilization on link i,, if Ui ( ) = 1 that is the ratio of wavelengths in use to the total wavelengths on the link. The link weight on link i is assigned to 1 if there is at least one free wavelength; otherwise, the weight is set to to avoid path selection on the link. In the scheme, only paths with minimum number of hop count are considered. It doesn t care loading on each link along the path. Therefore, some links may be in heavy load while the others remain light load. By equally distributing traffic, lower call blocking probability can be obtained. To achieve load balancing, Hsu el al. proposed a Weighted Shortest-Feasible Path routing () [2]. The weight to link i is defined as: 1 + Ui ( ) ω, if Ui ( ) < 1, where ω is balance factor., if Ui ( ) = 1 In, the usage of link resources is reflected on the term U(i). Since the weight change is equally proportional to 1/W (W is the number of total wavelengths on the link), it does not distinguish the difference of network in heavy load and light load. It means no matter how congested the network is, the performs route selection with the same strategy. Different from the, we propose a new load balancing routing scheme named Exponential Weighted Shortest Feasible Path (). By applying nonlinear link weight function, the algorithm is able to adopt different routing strategies under different network load. Since minimum hop count path consumes least network resources, for network with light load, it is the best strategy However, while the network status changed from light load to heavy load, the traffic should be balanced distributed into the network. Finally, once the network load is very heavy, the routing strategy should avoid to exhausting all wavelengths on a link so as to reduce the blocking for the future calls. To achieve the above objective, the link cost function C i of for link i is chosen as: au 4 () i + 1, if U() i < 1, where a is a constant value to, if Ui ( ) = 1 limit the maximum link cost. Figure 1 depicts link weights for,, and. The values in are similar to in light load. When load is in the middle, the cost function is approximately linear. It makes act like. When load is heavy, the link cost of grows up very quickly so as to avoid using all of the wavelengths in congested links. 3. Random Early Blocking Algorithms 3.1 Random Early Blocking In this section, we present a new call setup control algorithm named Random Early Blocking (REB). The concept of REB is to reject an incoming call setup request even the network has enough resources to accommodate it. By rejecting few connections, it gains opportunity to accept more calls in the future. The acceptance or rejection of a call in REB is based on the network state and the geographical distance between the sd pair. Since a

3 begin find a lightpath p for the sd pair; if (a feasible lightpath p exists) then begin if (network in heavy load) then begin /*Activate Random Early Blocking */ find the associated group G k of the sd pair; if (H(p) > Th(G k )) then begin get a random value r from 0 to 99; if (EB(p)> r) then reject the connection else establish the connection; end else establish the connection; end end end. Figure 2. REB Algorithm call with a long path (i.e., large hop counts) consumes more network resources than a short one, to prevent the long call from exhausting the network resources, we impose the formal higher rejection probability than the latter. Before introducing the REB, we first define some terminologies. Link congestion index: the ratio of number of wavelength in use to the number of wavelengths on the link Congestion link: The link with congestion index greater than 0.5 Heavy load: the network is in heavy load if more than or equal to half of the network links are congestion Figure 2 shows the REB algorithm. First, we classify each source-destination (sd) pair into a group G k, where k is the minimum number of hop count between the sd pair. Each group is associated with a threshold value that determines if random blocking is activated. The threshold of G k is defined as Th(G k )= k + c; where the c is a constant value. Once a connection request arrives, the routing algorithm determines a lightpath p for the sd pair (s,d) if feasible; If the network state is not under heavy load, path p is accepted; otherwise, REB scheme is activated. In REB, if a random value r (ranged from 0 to 99) is smaller than the Early Blocking (EB) value of the given path p, the connection request will be rejected. The EB value is defined as EB(p)=(H 2 (p) α)/β; where H(p) is the number of hop count of path p, and α, β are two constant values. The detailed REB algorithm is shown in Fig Fair Random Early Blocking In REB, the sd pair with a long distance hop in physical network are discouraged by introducing higher blocking probabilities. In this section, we consider the fairness Early Blocking Value Group1 Group2 Group3 Group # Hop Count problem in REB and propose a Fair-REB (FREB) scheme to improve the imbalanced blocking probability. The proposed FREB scheme reduces the lightpath accepting rates for sd pairs with short hop distances while enlarging the success rate of those with long hop distances. The algorithm of FREB is same as REB except EB value. In the FREB scheme, we define the EB value to be EB(p)=(H(p) k) 2 /k;where the k is the index of the sd pair (i.e. the minimum hop count between the two termination nodes). The value of k distinguishes the blocking probability from different groups for fairness consideration. Figure 3 depicts the distribution of the blocking probability of each group. 4. Simulation Results and Performance Comparisons The NSFNET network shown in Fig. 4 was used in our simulation. It consists of 14 nodes and 42 bi-directional links. There are 32 wavelengths on each fiber link (i.e., W=32). The connection requests follow Poisson arrival and with exponential holding time. We considered networks with uniform traffic distribution between any node pair. The network load in (i.e., node call arrival rate mean call holding time) is given in the x- axis of all graphs. The considered performance is shown 1 0 Fig. 3. No. Hop Count versus ER value Fig. 4. NSFNET Network

4 Blocking Probability Fig. 5. Blocking Prob. of Different Routing Schemes in the y-axis. In REB, the parameters c, α, and β was set to 2, 16, and 1 respectively. 4.1 Dynamic Routing Algorithms We have carried out simulation study on,, and routing algorithms. We have drawn comparisons of blocking probability, average path hop count, and link congestion index among them. First we study the blocking probabilities and the results are shown in Fig. 5. We observe that the blocking probability goes up for the three schemes when traffic load increases. However, holds best blocking performance under all traffic loads. By involving both hop-count and residual bandwidth in the non-linear weight function, can avoid wavelength exhaust on congested link so as to reserve resources for future requests. The simulation results demonstrate that has 47% and 35 % (at 15) performance improvement comparing to and. Figure 6 plots the average number of hop count under different traffic loads. has the smallest average path hop count for traffic load smaller than 12. Refer to Fig. 5, the blocking probability is almost zero for loads smaller than 12 which means the network has enough capacity to serve all of the connection requests. Once the traffic load goes beyond 12, both blocking probability and average number of hop count increase fast in scheme. It indicates that some particular links may incur heavy traffic and exhaust the wavelengths on them. It prevented further lightpath setup on those congested links. Thus, it forced to select longer hop-distance routes and resulted in consuming more network resources and increasing call blocking probability. Unlike and using constant and linear weight function, adopts nonlinear weight assignment for Average Hop Count network under different traffic loads. Under very light load (e.g., 2 in Fig. 6), obtained a route with minimum hop count just like. As the traffic load increases, the weight increases gently that helps to distribute the traffic load in balance to the network. Although the average path hop-count is larger than the, leaves more network resources on the most congested links for future use. When the network load continues to increase, the average hop-count increases rapidly in three adaptive routing schemes. However, can maintain the lowest blocking probability in the three schemes. It reveals that the exponential linkweight helps to avoid exhausting link resources. As shown in Fig. 6, the drawback of linear link weight assignment in has two folds. First, it starts to lengthen the paths even when network is in light load. This results in the waste of network resources and the increase of blocking probability. Secondly, by applying linear weight increasing, cannot effectively distinguish network status. Therefore, link resources may be exhausted. It induces higher blocking probability in heavy load. Figure 7(a) shows the link congestion index and its variance for each link in different traffic loads. We observe that the relationship between variance of link congestion index and the blocking probability. If the routing scheme induces large variance of link congestion index, the traffic distribution is more imbalanced and the associated blocking probability is higher. As Fig. 7(b) plots, the holds a lowest variance in all traffic loads. It is because that the can distribute traffic load more equally. Therefore, derives much better blocking performance than the other schemes. 4.2 REB Performance Fig. 6. Average Hop Count under Different Loads We further draw performance comparisons of the proposed REB control. Simulation results for REB with

5 performance metrics of blocking probability and average hop count are shown in Fig. 8 and Fig. 9. In Fig. 8, both and are able to improve the blocking probability when REB is embedded. Comparing to pure and, the performance improvements in the two approaches can up to 26% and 38%, respectively. The effect of REB scheme on average hop count of a lightpath is revealed in Fig. 9. When the load is smaller than 13, the average hop path count of REB is similar to those without it. As netowrk load increases the acceptance of paths with large hop counts are suppressed by REB. The average hop count of lightpath in REB is clearly lower than the pure as network operated under heavy load. 4.3 FREB Performance To observe the unfairness issue in with REB, we have carried out numerical data shown in Fig. 10, 11, and 12. Figure 10 compares the blocking probability among, +REB, and +FREB. Although +FREB reaches larger blocking probability than +REB scheme, it still has 24% improvement than pure. We particularly compare the fairness among the three schemes, shown in Fig. 11, + FREB has the best fairness performance among different groups of geographical distances. Fig. 12 shows the average hop count of the accepted lightpaths. Unlike +REB, the average hop value goes up when network load increases. The results indicate that long paths have their chances to be accepted by the network. 5. Conclusion In this paper, we have proposed a new link weight assignment function for adaptive routing in WDM networks. The weight is a non-linear function of link utilization that can differentiate network under different Link Congestion Index =15 Blocking Probability REB +REB +REB Link ID (a) Average Link Congestion Index of Each Link Fig. 8. Blocking Prob. w/wo REB Variance of Congestion Index Average Hop Count REB (b) Variance of Link Congestion Index Fig. 7. Link Congestion Index Fig. 9. Average Hop Count under w/wo REB

6 Blocking Probability REB +FREB Fig. 10. Blocking Probability of in call blocking probability. also maintains the smallest variance of both path hop count and link congestion index. Additionally, to reduce network resources consumed by long paths, we have proposed REB control algorithm. By randomly rejecting requests under heavy network load, the whole network blocking probability can be greatly improved. Simulation results reveal that not only but also and can significantly improve their call blocking probability in cooperation with REB mechanism. To improve the favor of short paths in REB, the fairness issue has been studied and the FREB scheme has been proposed to achieve fairness routing. Simulation results shown that FREB can achieve fairness blocking probability among different connection groups with different geographical distances. References: Blocking Probability Average Hop Count REB +FREB = Group ID Fig. 11. Blocking Prob. of Different Groups +REB +FREB Fig. 12. versus Average Hop Count traffic loads so as to arrive load balanced routing. We have drawn comparisons of blocking probability, average path hop count, and link congestion index among,, and the proposed under benchmark NSFNET network. Simulation results demonstrated that approach outperforms the other two approaches [1] J. Harry and R. Dutton, Understanding optical communications, Prentice Hall, [2] C. F. Hsu, T. L. Liu, and N. F. Huang, An Adaptive Routing Strategy for Wavelength-Routed Networks with Wavelength Conversion Capability, in Proc. IEEE ICC 2002, vol. 5, pp , [3] R. Ramamurthy and B. Mukherjee, Fixed-alternate Routing and Wavelength Conversion in Wavelengthrouted Optical Networks, IEEE/ACM Transactions on Networking, vol. 10, pp , June [4] M. H. Park, J. S. Choi, S. H. Choi, and Y. H. Jeong, Load Balanced Wavelength Routing Algorithm for the Layered-Graph Model, in Proc. COIN/ACOFT 2003, pp , [5] H. Harai, M. Murata, and H. Miyahara, Performance of Alternaterouting Methods in All-optical Switching Networks, in Proc. IEEE INFOCOM'97, pp , [6] A. Birman and A. Kershenbaum, Routing and Wavelength Assignment Methods in Single-hop Alloptical Networks with Blocking, in Proc. IEEE INFOCOM '95, vol. 2, pp , [7] Hui Zang, J. P. Jue, L. Sahasrabuddhe, R. Ramamurthy, and B. Mukherjee, Dynamic Lightpath Establishment in Wavelength Routed WDM networks, IEEE Communications Magazine, vol. 39, pp , Sept [8] K. M. Chan and T. Yum, Anslysis of least congested Path Routing in WDM Lightwave Networks, in Proc. IEEE INFOCOM, vol. 2, pp , [9] X. Yuan, R. Gupta, and R. Melhem, Distributed Control in Optical WDM Networks, in Proc. IEEE MILCOM, vol. 1, pp , Oct [10]H. Zang, L. Sahasrabuddhe, J. P. Jue, S. Ramamurthy, and B. Mukherjee, Connection Management for Wavelength-routed WDM Networks, in Proc. IEEE GLOBECOM, vol. 2, pp , 1999.

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