Dynamic Routing and Wavelength Assignment Using Learning Automata Technique Anwar Alyatama Kuwait University
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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. I NTRODUCTION 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 [1]. 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 [1]. 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 IEEE Communications Society Globecom 2004
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 route1 . 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 1 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].
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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 [10], [11] and [12]. 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 LR−L 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, [13] 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 1000 wavelengths per link already made [14]). 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 IEEE Communications Society Globecom 2004
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 = 1 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 Pr(s,d) . If the selected route r(s,d) fails; the source will choose another route r´(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: Pr(s,d) ← Pr(s,d) + a[1 − Pr(s,d) ] r´ = r Pr´(s,d) ← (1 − a)Pr´(s,d)
(1)
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: Pr(s,d) ← (1 − )Pr(s,d) Pr´(s,d) ← R(s,d) −1 + (1 − )Pr´(s,d)
r´ = r
(2)
Where a and are the convergence parameters and 0 < a < 1, 0 < < 1 with being small compared with a, and a is itself usually small. Values of a = 0.01 and = 0.0001 are used in our simulation. The effect of different values of a and 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 [15]. 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) w for short. The total number of is given by Prw(s,d) or P(s,d)
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T continuing (common) wavelengths on route r(s, d) is W(s,d) . If the selected wavelength is unavailable, the source will T . Therefore, choose another wavelength up to W ≤ W(s,d) the call is blocked if all W wavelengths are unavailable. As mentioned before, exhaustive algorithms must scan all T which produce longer continuing wavelengths, W = W(s,d) T setup delay. We propose a small value of W
