Dynamic Routing and Wavelength Assignment Using Learning Automata Technique

Transcription

1 Dynamic Routing and Wavelength Assignment Using Learning Automata Technique Anwar Alyatama Kuwait University Abstract Dynamic Routing and Wavelength Assignment RWA is one of the most important issues in wavelength routed all optical networks. We introduce the learning automata technique for the dynamic RWA in WDM networks without conversion under different load conditions. Learning automata will be used to choose a shortest route from the source to the destination if more than one shortest route exist. Furthermore, learning automata will be used to select which wavelength to be used on the chosen route. We compare our wavelength assignment technique with some exhaustive wavelength assignment algorithms that scan all wavelengths on a predetermined shortest route. The use of learning automata wavelength assignment technique reduces the call setup time by pursuing a small number of wavelengths. In addition, the technique is used to achieve fairness among different source/destination pairs. Simulation results are presented which indicate the benefits of using learning automata technique for the dynamic routing and wavelength assignment in WDM networks. I. INTRODUCTION Optical networks seem to have the answers for all problems in long haul and metro networking. They provide circuitswitched end-to-end optical channel or lightpath to the users. Using WDM,up to 80(and more) separate wavelengths of data can be multiplexed into a light stream transmitted on a single optical fiber between network nodes. Communication via switching circuit in WDM implies that there is a dedicated lightpath between the source and the destination. This lightpath is a connected sequence of dedicated wavelengths on each link between the source and the destination nodes. Since we assume the network does not have conversion capabilities, the same wavelength must be available on all links belonging to the selected route. Routing and wavelength assignment RWA algorithms usually include a description of a procedure for finding a route and for selecting a wavelength to be used from the set of available wavelengths along that route. The objective of the RWA problem depends on the type of network traffic. The network traffic is either static or dynamic. Even in simpler static traffic, the optimal static RWA problem without wavelength conversion was proven to be NPcomplete []. Thus, heuristic methods were introduced to solve the RWA problem. A common approach, is to decouple the RWA steps by first selecting a route from a predetermined set of candidate paths (dynamic routing) and then searching for an appropriate wavelength (dynamic wavelength assignment) on the selected route []. Dynamic Routing means the lightpath from the source to the destination is determined when the two end-nodes want to communicate. Thus, routing is not fixed and any feasible route from the source node to the destination node can be a candidate. Several dynamic routing algorithms have been proposed to solve the dynamic routing. Some of the proposed algorithms have longer setup delay and higher control overhead (e.g., the least-loaded routing and the fixed paths least congestion) [2][3]. Others, use the state information or neighborhood information. In an exhaustive dynamic wavelength assignment procedure, the source locks out all available wavelengths on the first link belonging to the selected route. These wavelengths are assigned temporary locks making them unavailable to other setup requests, which might be received for other intended communication. Then, the setup request will progress towards the destination along the selected route. Other intermediate nodes along the selected route will follow by temporary locking out all available common wavelengths. Wavelengths that are not common with upstream links are not locked. Once a wavelength is chosen or a lightpath cannot be constructed all temporary locked wavelengths are released [5]. Many heuristic approaches have been proposed in the literature of the exhaustive dynamic wavelength assignment once a route is selected. These include Random Wavelength Assignment, First-Fit, Least-Used (SPREAD), Most-Used (PACK), Min-product, Least Loaded, MAX-SUM, Relative Capacity Loss, Distributed Relative Capacity Loss, Wavelength Reservation and Protecting Threshold [6]. The rest of the paper is organized as follows: Next section introduces the proposed solution and motivation. Section III discusses fairness in terms of end-to-end blocking probabilities. Section IV presents numerical results of the dynamic routing and wavelength assignment using learning automata. Lastly, we present our conclusion. II. PROPOSED SOLUTION In this paper, we introduce an exhaustive dynamic routing and wavelength assignment RWA algorithm based on the learning automata concept. The concept of learning automata for circuit switched network was first reported by [7] and [8]. Many researchers had used the learning automata concept in This is called Forward reservation protocol. Other researchers suggest delaying the locking process until reserving the whole path. This approach increases the network performance by consuming the unoccupied bandwidth during the reservation phase. However, the results come at the price of extending the capacity of storage devices and perhaps the number of control channels [4]. Globecom /04/$ IEEE

2 solving different network problems. For example, [9] uses the concept of learning automata to implement a receiver conflict avoidance algorithm in a broadcast-and-select WDM star networks. Other examples are found in [0], [] and [2]. In this proposed RWA technique, the utilization of links (and hence, wavelengths) of the network is not measured directly, but rather relied on indirect information. The source node continually selects a route, a wavelength or both according to a probability distribution, which is updated at discrete time stages according to reactions regarding call completion or rejection. Source nodes reward a route, a wavelength or both when a call succeeds and punish a route, a wavelength or both when a call fails. A favored scheme is so called L R ɛl scheme, in which the punishment for a failure (decrease in route/wavelength selection probability) is small compared with the reward for a success (increase in route/wavelength selection probability). However, [3] had investigated other schemes which may be explored in the future. The motivation behind using learning automata is to cut down the duration of call setup phase. Our proposed algorithm consumes the least delay during call setup by pursuing a small number of route/wavelength combinations. Long setup delay reduces network efficiency especially when the traffic is generated by IP applications. The burstiness nature of IP traffic requires large capacity for a short time. In this case, the call setup delay must be very short compared to call duration. We first apply the learning automata concept for the dynamic routing step only. Secondly, we use the learning automata technique for the dynamic wavelength assignment step assuming predetermined fixed routing. The proposed dynamic wavelength assignment technique pursues a small number of wavelengths during call setup phase. We will compare our learning automata dynamic wavelength assignment with Random, First-Fit, and Most-Used (PACK) Wavelength Assignment algorithms. As mentioned before, these dynamic wavelength assignment algorithms are exhaustive and rely on exploring all wavelengths in the call setup phase. Thus, increasing call setup time and reducing network efficiency, especially when the number of wavelengths is large. For example, the number of wavelengths per link has reached recently more than 300 channels and is expected to increase substantially (with experiments approaching 000 wavelengths per link already made [4]). Finally, we apply the learning automata technique to the joint routing and wavelength assignment problem. It has been established in [6] that the best wavelength assignment algorithm is the one that is compatible with the routing protocol while routing is more significant. It will be shown that this simple isolated RWA technique using learning automata is efficient and robust. A. Traffic Model A call is considered the basic unit of WDM traffic. Each call originating from a source node s is directed to a destination node d. The call requires one wavelength (channel) from each link along the route from the source s to the destination d. Since no conversion capability is assumed the same wavelength w must be used in all links belonging to the route. The call arrival process for the source-destination pair (s, d) is assumed to be Poisson with rate λ (s,d) calls/unit time. We also assume that blocked calls at the source are lost and do not attempt to re-enter the system. The call holding time has an exponential distribution with rate µ =calls/unit time. We also assume that the time it takes for temporarily locking and releasing wavelengths is very small hence, it is neglected. Therefore, the call connection and disconnection times are assumed very short compared to the call holding time and as such zero values are assumed for them. The most important network performance measurement in circuit switched networks is the end-to-end blocking probabilities eebp (s,d) for each source/destination pair (s, d). Other factors, like fairness and robustness are also considered. B. Dynamic Routing Using Learning Automata The set of shortest paths R (s,d) is computed for each source/destination pair (s, d) by Dijkstra s algorithm and stored at each source node. Upon the arrival of a call to destination d, the source s will choose a route r (s,d) R (s,d) with probability P r(s,d). If the selected route r (s,d) fails; the source will choose another route ŕ (s,d) R (s,d) up to R (s,d). Hence, if all route selections are unavailable, then the call is blocked. Even though we have limited the routing to the shortest path, calls with longer routes may have many selections of shortest paths. In the case of a call success, the selected route r (s,d) will have a continuing free channel selected at random (or using other wavelength assignment techniques). Hence, the source s will update all route selection probabilities for destination d as follows: P r(s,d) P r(s,d) + a[ P r(s,d) ] Pŕ(s,d) ( a)pŕ(s,d) ŕ r However, if the selected route does not have a continuing free channel, after exhaustively searching all channels (call failure), then the source s will update all route selection probabilities for destination d as follows: P r(s,d) ( ɛ)p r(s,d) Pŕ(s,d) ɛ R (s,d) +( ɛ)p ŕ (s,d) ŕ r Where a and ɛ are the convergence parameters and 0 <a<, 0 <ɛ< with ɛ being small compared with a, and a is itself usually small. Values of a =0.0 and ɛ =0.000 are used in our simulation. The effect of different values of a and ɛ will be demonstrated later. C. Dynamic Wavelength Assignment Using Learning Automata In this case, routes are fixed predetermined shortest path selected by near-optimal offline computation [5]. Each source node maintains the routing table which is never assumed to change. The probability of selecting a wavelength w between source s and destination d on the predetermined route r(s, d) is given by Pr w (s,d) or P(s,d) w for short. The total number of () (2) Globecom /04/$ IEEE

3 continuing (common) wavelengths on route r(s, d) is W(s,d) T. If the selected wavelength is unavailable, the source will choose another wavelength up to W W(s,d) T. Therefore, the call is blocked if all W wavelengths are unavailable. As mentioned before, exhaustive algorithms must scan all continuing wavelengths, W = W(s,d) T which produce longer setup delay. We propose a small value of W<<W(s,d) T in our wavelength assignment learning automata technique. Once a wavelength w is selected and turns out to be unavailable on the route, then the source s will update all wavelength selection probabilities for destination d as follows: P(s,d) w ( ɛ)p (s,d) w P ẃ(s,d) ɛ +( ɛ)p ẃ(s,d) ẃ W T (s,d) w However, if wavelength w is available on all links belonging to the predetermined route, then the source s will update all wavelength selection probabilities for destination d as follows: P w (s,d) P w (s,d) + a[ P w (s,d) ] P ẃ(s,d) ( a)p ẃ(s,d) ẃ w To further improve our learning automata wavelength assignment algorithms, the source s will exclude all wavelengths that are busy on the first link of the predetermined route. This information is available to the source. Hence, the source will only select W wavelengths according to the wavelength selection probabilities P(s,d) w that are free on the first link. The Random wavelength assignment algorithm is closely related to the learning automata technique in which the wavelength selection probabilities are uniform and fixed a =0,ɛ = 0. On the other hand, the Most-Used (PACK) wavelength assignment algorithm uses the same concept of rewarding a wavelength on which a call is successful. Hence, learning automata WA is a general case for both the random wavelength assignment and Most-Used wavelength assignment algorithms. Furthermore, learning automata wavelength assignment algorithm can be deterministic in addition to the stochastic definition presented in this paper. D. Dynamic Routing and Wavelength Assignment Using Learning Automata In the case in which more than one shortest route exist between source s and destination d, the probability of selecting a wavelength w on route r is given by Pr w (s,d). If the selected wavelength is unavailable on the selected shortest route, the source s will choose another wavelength ẃ and/or another route ŕ up to RW RW(s,d) T, where RW (s,d) T is the total number of continuing wavelengths on all shortest routes between source s and destination d. Therefore, if RW combination of route/wavelength selections are unavailable, then the call is blocked. Similar to what we did before, if the call is successful the route/wavelength selection probabilities are updated as follows: P w r (s,d) P w r (s,d) + a[ P w r (s,d) ] P ẃŕ (s,d) ( a)p ẃŕ (s,d) ẃ w and/or ŕ r (5) (3) (4) Whereas, if the call is unsuccessful the route/wavelength selection probabilities are updated as follows: Pr w (s,d) ( ɛ)pr w (s,d) P ẃŕ ɛ (s,d) RW T (s,d) +( ɛ)pẃŕ (s,d) III. FAIRNESS ẃ w and/or ŕ r Since the quality of service of all calls must be very low to achieve customers satisfaction, the RWA algorithms have to reduce the blocking probabilities for calls that travel more than one link. To illustrate the fairness problem in WDM, we present the following simple formula for the end-to-end blocking probability eebp l for a route with l links from [6]: eebp l = [ ( π) l] C Assuming links are independent, π is the probability that a wavelength is used on a link, l is the call length and C is the link capacity. Consequently, the end-to-end blocking probability ratio between calls that travel l links to calls that travel only one link R(l) =eebp l /eebp grows exponentially. For example, if π<<then the ratio R(l) =l C.Thisis unacceptable and not fair. Although the preceding example is highly simplified, ignores several important effects, it does show that the end-to-end blocking probability is more sensitive to the call length l when wavelength converters are not used [6]. There are many ways to reduce the end-to-end blocking probabilities for calls that travel longer routes. However, all come with a price on the overall network performance. One way is to discourage calls that use fewer hops from using the same wavelengths used by calls using longer routes. Each node in the network will monitor all wavelengths on all outgoing links. New calls that request a wavelength can be denied if that wavelength is mostly used by other calls with longer routes. For example, let n l i be the number of wavelengths used by all source/destination pairs of length l over link i. Consequently, n i = l nl i is the sum of all wavelengths used by all source/destination pairs over link i. Hence, if a new call of length l requests a free wavelength w, then { allowed blocked if if (6) (7) l F l nl i n i l F l nl i n i < eebp l eebp l Where F l is the fairness constant for a call of length l and eebp l is the average end-to-end blocking probability of all calls of length l. Theeebp l s can be set as fixed thresholds or calculated and distributed for all the nodes in the network. In this case, moving averages are used for updating the eebp l s. IV. NUMERICAL RESULTS Our test vehicle is the 4 nodes NSFNET as shown in Fig.. Two versions of network traffic and network dimensioning are used as shown in table I. The first case is similar to a realistic network with realistic traffic, and has been dimensioned using the shortest path method [5]. Case two has a uniform load between each source/destination pair and uniform link capacity. Thus, the second case had not been (optimally) dimensioned. (8) Globecom /04/$ IEEE

4 TABLE II NETWORK CAPACITY FOR NON UNIFORM CASE WITH SHORTEST ROUTE DIMENSIONING 4 Fig.. The 4-Nodes NSFNET network topology TABLE I TWO CASES OF NETWORK CAPACITY AND NETWORK TRAFFIC Network Capacity Network Traffic Case Non uniform Non uniform (Table II) (Table III) Case 2 Uniform Uniform (link capacity =4 wavelengths) (load = 0.4 * load factor) Different load conditions are considered, and the load factor ranges from to 2. For each of the two considered cases and for each load factor =,...,2 we ran the simulation 0 times. Each run starts with a different random seed where, each seed simulation runs for 0,000 holding times. The overall average result is obtained with 95% confidence. Fig. 2, 3 show the learning automata wavelength assignment technique for the two cases where W =3, 5, 0. The learning automata wavelength assignment performs significantly well even for small values of W. The case where W =0performs as well as the exhaustive case whereas small values (e.g., W =3) give respectable results. Fig. 4, 5 show the Random, First-Fit and Most-Used exhaustive wavelength assignment algorithms compared to the learning automata wavelength assignment with W = 0. The figures also show the case where the network is assumed to have a full conversion capability. It is presented as a benchmark for wavelength assignment techniques. In both cases, the learning automata wavelength assignment performs significantly well even for small values of W. Node TABLE III NETWORK TRAFFIC FOR NON UNIFORM CASE WITH LOAD FACTOR =2 Node W = 3 W = 5 W = 0 Exhaustive Fig. 2. Wavelength assignment using learning automata where W =3, 5, 0 and exhaustive for case W = 3 W = 5 W = 0 Exhaustive Fig. 3. Wavelength assignment using learning automata where W =3, 5, 0 and exhaustive for case 2 Globecom /04/$ IEEE

5 Full conversion case Learning Automata case Full conversion case 2 Learning Automata case 2 Full conversion First Fit Random Most Used L.A. W= Fig. 4. Exhaustive dynamic wavelength assignment algorithms compared to the learning automata WA Technique with (W = 0) for case Fig. 6. Wavelength assignment using learning automata where W =0, compared to full conversion capability for both case and 2 with a scale up factor =5 No fairness Fairness No fairness Fairness E E-3 Full conversion First Fit Random Most Used L.A. W=0 E Call Length (a) Case E Call Length (b) Case 2 Fig. 5. Exhaustive dynamic wavelength assignment algorithms compared to the learning automata WA Technique with (W = 0) for case 2 Fig. 7. The average blocking probabilities of calls with different lengths with and without fairness with load factor =2 Most surprisingly, if the network capacities and loads are scaled up, the algorithm performs exceptionally well. This will obvious apply to the future when the number of channels per link is expected to increase along with the traffic load. We have scaled up our network capacity and offered load by a factor of five. Fig. 6 shows that the learning automata wavelength assignment with W =0performs well even though the link capacity reaches more than 350 wavelengths for case and more than 200 wavelengths for case 2. Fairness is an important part of a good wavelength assignment algorithm. Fig. 7 shows the huge differences in the average end-to-end blocking probabilities between calls that travel short routes (length=, 2) versus calls that travel long routes (length= 3, 4) for load factor =2 and no fairness. However, after applying our fairness technique the differences in the end-to-end blocking probabilities are minimal. As mentioned earlier the network total performance is degraded when fairness is considered. The average end-to-end blocking probabilities are given in Fig. 8 and 9 for the joint dynamic routing and wavelength assignment problem using the learning automata concept. The average end-to-end blocking probabilities are similar for both the learning automata RWA with small RW and for the fixed predetermined routing with exhaustive Most-Used wavelength assignment. However, the average end-to-end blocking probabilities for longer routes are lower in learning automata RWA. Hence, learning automata RWA achieves the same network performance with less RW and more fairness. For networks that are not dimensioned (case 2), the learning automata RWA also performs well indicating the robustness of the algorithm. Hence, RWA impleminting learning automata is suitable for poorly dimensioned networks or unpredictable traffic. The values of the route/wavelength selection probabilities Pr w (s,d) may start with a uniform distribution similar to the Most-Used (PACK) wavelength assignment. As calls being accepted/rejected, learning automata RWA starts updating the route/wavelength selection probabilities Pr w (s,d) using formulas 5 and 6. Then, the route/wavelength selection probabilities will converge within a minimal range. The convergence time depends on the convergence parameters a, ɛ. The convergence parameters are critical to balance between traffic trends and instant surge. Small values are preferred when the network experiences instant traffic surges. However, relatively large values mean the network can respond faster to network failure or traffic changes. Unlike other RWA, learning automata RWA can control the response behavior when the traffic or the network changes. Fig. 0 shows the total difference in wavelength Globecom /04/$ IEEE

6 L.A. RW=5 L.A. RW=0 L.A. RW=0 per path Most Used WA The Sum of Absolute Differences a=0.0, ε=0.000 a=0., ε= x x x x0 5 Time Fig. 8. The average blocking probabilities of RWA using learning automata with limited selection RW = 5, 0 and 0 per route compared with fixed predetermined routing with Most-Used wavelength assignment for case Fig. 0. The sum of absolute differences in wavelength selection probabilities P w r (s,d) over time in which the convergence parameters a =0.0,ɛ=0.000 and a =0.,ɛ=0.00 for load factor =2 L.A. RW=5 L.A. RW=0 L.A. RW=0 per path Most Used WA Fig. 9. The average blocking probabilities of RWA using learning automata with limited selection RW = 5, 0 and 0 per route compared with fixed predetermined routing with Most-Used wavelength assignment for case 2 selection probabilities for a case where a =0 2,ɛ =0 4 and the case where a = 0,ɛ = 0 3. The first case produces better overall performance and less fluctuation. More studies are needed to optimize the convergence factors a, ɛ. V. CONCLUSION In this paper, we presented an isolated dynamic routing and wavelength assignment technique using learning automata concept for optical networks without conversion. In the automaton approach, knowledge about the environment is gained only through the responses received by the automaton after each of its actions. Good selections are rewarded and bad ones are penalized. The learning automata concept is used to solve the online routing problem, the online wavelength assignment problem or the joint online routing and wavelength assignment problem. The proposed online RWA reduces the call set up time through limiting the number of wavelengths pursued by the source node without the need for state information or feedback messages. Furthermore, learning automata RWA can react faster to traffic or network changes, when relatively larger values for the convergence parameters a, ɛ are used. We also showed that fairness could be accomplished between calls that travel long distances versus calls that travel short distances. Moreover, we have shown the robustness of learning automata RWA by applying different loads and network conditions. REFERENCES [] A. Ozdaglar and D. Berteskas. Routing and wavelength assignment in optical networks, IEEE/ACM Trans. on Networking, Vol., No. 2, April [2] L. Li and A. Somani, Dynamic wavelength routing using congestion and neighborhood information, IEEE/ACM Trans. on Networking, Vol.7,No. 5, October 999. [3] H. Zang, J. Jue, L. Sahasrabuddhe, R. Ramamurthy and B. Mukherjee, Dynamic lightpath establishment in wavelength-routed WDM networks, IEEE Communications Magazine, No. 39(9), September, 200. [4] A. Sichani and H. Mouftah, A nested path reservation protocol for multiplexed all-optical netwoks. Proceedings of ONDM [5] A. Stocia and A. Sengupta, On a dynamic wavelength assignment for wavelength routed all-optical networks, Optical Networks Magazine, January/February [6] H. Zang, J. Jue, and B. Mukherjee, A review of routing and wavelength assignment approaches for wavelength-routed optical WDM network. Optical Networks Magazine, August, 999. [7] K. Narendra and M. Thathachar, Learning automata a survey, IEEE Trans. on Systems, Man and Cybernetics, SMC-4, 974. [8] K. Narendra, E. Wright and L. Mason, Application of learning automata to telephone traffic routing, IEEE Trans. on System, Man and Cybernetics, SMC-7, 977. [9] G. Papadimitriou and D. Maritsas, Learning automata based receiver conflict avoidance algorithms for WDM broadcast-and-select star networks, IEEE/ACM Trans. on Networking, Vol. 4, No. 3, June 996. [0] A. Economides, P. Ioannou and J. Silvester, Decentralized adaptive routing for virtual circuit networks using stochastic learning automata, Proceedings of INFOCOM 88, March 988. [] G. Papadimitriou and A. Pomportsis, A., Learning automata based scheduling algorithms for input queued ATM switches, Neurocomputing, Elsevier, Vol. 3, No.-4, March [2] G. Papadimitriou and A. Pomportsis, On the use of learning automata in medium access control of single-hop lightwave networks, Computer Communications, Vol. 23, No. 9, April 5, [3] B. Oommen and D. Ma, Deterministic Learning Automata Solutions to the Equipartitioning Problem, IEEE Trans. on Computers, Vol. 37, January, 988. [4] B. Collings, W. Knox and M. Mitchell, Bell Labs Uses Ultra- Dense WDM to Transmit,022 Channels over Fiber. [5] R. Hulsermann, et al., Dynamic routing algorithms in transparent optical networks, Proceedings of ONDM [6] R. Ramaswami and K. Sivarajan, Optical Networks: A practical Perspective, second Edition Morgan Kaufmann. Globecom /04/$ IEEE