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Backtrack routing and priority-based wavelength assignment in WDM networks
Computer Communications 22 (1999) 1–10
Backtrack routing and priority-based wavelength assignment in WDM networks Sheng-Tzong Cheng* Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan, ROC Received 13 February 1998; received in revised form 29 June 1998; accepted 29 June 1998
Abstract In this paper, we consider two key problems in the WDM networks: the wavelengh assignment and routing problems. The objective of the problems is to minimize the request blocking rate. We propose two priority-based methods for the wavelength assignment problem: static and dynamic strategies. Based on the priority of an incoming request, the proposed methods allocate a wavelength among the available wavelengths for the given priority. Analytic models and simulations are presented for the proposed wavelength assignment methods so as to analyse the link blocking rate. The simulation results show that the link blocking rate by the dynamic strategy is less than that by the assignment strategy. We also develop a routing algorithm that works together with the proposed wavelength assignment methods to reduce the overall blocking rates. The proposed routing method maintains a routing tree for a given connection request. Based on the routing tree, the algorithm finds a route with one available wavelength for each link along the route. We compare the proposed routing method with the fixed routing and fixed alternate routing algorithms. The experiments show that the proposed routing algorithm performs better than the fixed routing and the alternate routing methods. 䉷 1999 Elsevier Science BV. All rights reserved. Keywords: Backtrack Routing; Priority-based; WDM Networks; Wavelength assignment; Performance evaluation
1. Introduction One of the main issues of using communication networks is the availability of network bandwidth. As the number of network connections increases, the available bandwidth becomes inadequate and the quality of information service degrades. It is no doubt that new network techniques that support high-bandwidth requirements are essential. To solve the problem of the bandwidth shortage, the optical networks were advocated to be the choice for the networks of the next generation. The virtues of the optical networks are high bandwidth, high speed and reliability. Optical networks are able to provide high bandwidth in the range of terabits per second. Bandwidth of an optical link is divided into wavelengths. New components for optical networks, such as optical amplifiers, optical switches, optical wavelength (de)multiplexers and wavelength converters, are developed to exploit the available wavelengths in a link, as reported in the literature. In the context, the Wavelength Division Multiplexing (WDM) technology is proposed to utilize multiple wavelengths to establish
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connections concurrently and independently on a single optical fibre link. In this paper, we propose two wavelength assignment strategies and a routing method for WDM networks. The main objectives are to satisfy requirements of different types of quality of service (QoS) and to reduce the blocking rates. The connection requests are prioritized to support connections with different QoS requirements. Priorities are the index of assigning a wavelength to a given request. The proposed static wavelength assignment method pre-allocates a set of wavelengths for each priority class of requests and chooses one-wavelength for a given request based on its priority and the available wavelengths for the given priority. The dynamic wavelength assignment method selects a wavelength dynamically among the available wavelengths, but it controls the number of assigned wavelengths for a given priority class of requests according to a predefined quota. The proposed routing algorithm maintains a routing tree which includes possible paths for a given connection request. Based on the routing tree, it finds a non-blocked route in a fashion of backtracking. This paper consists of five sections. Section 2 surveys the background. In Section 3, we present our methods on the wavelength assignment and routing problem and the analytic models. In Section 4, we present a simulation model to
0140-3664/99/$ - see front matter 䉷 1999 Elsevier Science BV. All rights reserved. PII: S0140-366 4(98)00209-6
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Fig. 1. An example of the Static Assignment Scheme.
evaluate the performance and discuss the simulation results. The conclusion is drawn in Section 5. 2. Background In the literature, researchers propose various architectures for WDM networks. Two main kinds of networks reported are the single-hop and the multi-hop WDM networks. Single-hop WDM networks restrict a light-path connection to use the same wavelength on all links of the path without buffering or optical-to-electronic conversion [1–4]. The blocking rate increases dramatically as the number of links in a lightpath increases or the network complexity grows. Multi-hop WDM networks allow wavelength conversion to ease the restriction of wavelength continuity. Such networks scale well and block less traffic [5]. Huang et al. propose an architecture for interconnecting WDM-based start networks [6,7]. The star-coupler bridge (SCB) is used to interconnect two broadcast-and-selective networks, transmitting and receiving data through a dual bus between the two interconnected networks. Transmission is carried out by the time division multiplexing (TDM) technique. Each node in the interconnected networks either recieves data or transmits data via one wavelength at a given time slot. They consider the path assignment problem for isochronous and asynchronous requests and develop solutions based on the proposed architecture. The wavelength encoded multi-channel optical bus (WEMCOB) is proposed in Ref. [8]. They study a backbone network based on WEMCOB and show that such a network can offer the transmission rate of the order of gigabits per second. Ramaswami and Sasaki study the WDM networks with limited wavelengh conversion [9] and show that the throughput can be improved significantly for such networks. The WDM networks with wavelengh conversion are equivalent to circuit-switched networks. Hence, several papers on evaluating routing algorithms are based on circuit switching [10,11]. Fixed routing and fixed alternate routing methods [12] are studied. These two methods block a request if any
link in the pre-defined path(s) has no available wavelengh. The time complexity of the routing algorithm is O(兩E兩), where 兩E兩 is the number of links in the possible paths for a given request to find a non-blocking route. As stated previously, a WDM network with wavelengh conversion achieves a higher connection acceptance rate than one without wavelengh conversion does. The problem of wavelengh conversion can be solved by the wavelengh assignment. The simplest way of wavelengh assignment is the first-come-first-served (FCFS) method. Whenever a traffic request arrives, an attempt is made to reserve a wavelength from available bandwidth for this traffic request. The incoming traffic requests can only be accepted if an available wavelength is found. However, not much work was reported on the wavelength assignment with the QoS requirements. In this paper, we consider the wavelength assignment problem in which the priorities for the connection requests are given. The priority value of a request is obtained from its QoS requirement. The objective of our wavelengh assignment strategies is to minimize the blocking rates for different classes of requests. 3. Our approach 3.1. The proposed wavelength assignment methods The basic idea of the proposed methods is that the connection requests are treated differently according to their QoS requirements. The connection requests with higher QoS requirements, such as real-time video or sound, should have higher priority and, hence, should incur lower blocking probability. Two wavelength assignment methods are proposed: the static and dynamic wavelength assignment methods. 3.1.1. Static assignment method Assume that the network bandwidth contains m wavelengths, li, i 1,…,m, and the system have n priority values, p1, p2,…pn, where p1 is the highest priority. The proposed method pre-defines a preferred wavelength set for each priority class. Let WPi be the preferred wavelength set for a priority class pi. The static method chooses an available wavelength for a request of a priority class pi from its preferred wavelength set, WPi and WPj for j i ⫹ 1,…,n, if the wavelengths in WPi were assigned. The constraints on the preferred wavelength sets are listed as follows. 1. WPi 傽 WPj ⭋, ᭙ i 苷 j. Each wavelength can only be included once in a preferred wavelength set. 2. 傼i WPi {li 兩i 1; …; m}. All wavelengths are used. 3. 兩WP1兩 ⱖ 兩WP2兩 ⱖ … ⱖ 兩WPn兩, where 兩WPi兩 is the number of wavelengths in the preferred wavelength set of priority class pi. The number of available wavelengths for a higher priority class is not less than that of a lower priority one.
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Fig. 2. An example of a WDM network with 6 nodes.
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For a request of priority pi, the proposed method starts with finding a wavelength from WPi. If no wavelength is available in WPi, then it checks from WPi⫹1 to WPn until an available wavelength is found. If no available wavelength is found in WPi through WPn, the request is considered to be blocked. Fig. 1 illustrates an example. The illustrated system has three priority classes of connection requests (n 3) and three wavelengths (m 3). Suppose that, l1, is preferred to be assigned to priority p1, that l2 is preferred to be assigned to priority p2, and that l3 is preferred to being assigned to priority p3. The dash lines shown in Fig. 1 indicate the possible assignment for the higher priorities. We observe that l3 can be assigned to a connection of priority-p3 as well as one of higher priorities as indicated by dash lines. 3.1.2. Dynamic assignment method Unlike the static assignment method, the dynamic assignment method does not specify the preferred wavelength sets. A wavelength can be assigned to a connection request of any priority. To control the number of wavelengths assigned to a priority class, the dynamic method pre-sets a wavelength quota for each priority class. Assume that the network bandwidth contains m wavelengths, li,i 1,…,m, and the system has n priority values, p1, p2,…,pn, where p1, is the highest priority. Let qi denote the wavelength quota for priority class of pi or lower. The constraints on the quotas are stated as follows. 1. m q1 ⱖ q2 ⱖ …qn ⱖ 1. 2. qi29 ⫺ q2 ⱖ q2 ⫺ q3 ⱖ q3 ⫺ q4 ⱖ …qn⫺1 ⫺ q n ⱖ qn. The value of qi ⫺ qi⫹1 indicates the number of wavelengths initially reserved for the requests of priority pi and the value of qi ⫺ q2 indicates the number of wavelengths exclusively allocated for the requests of priority pi .
Fig. 3. (a) The routing table of Node 5; and (b) the route tree for a connection from Node 1 to Node 4.
The dynamic method can assign at most qi wavelengths to the requests with the priority pi or lower. A quota is specified for the requests of a given priority. In Constraint 2, the proposed method gives higher priority requests more wavelengths such that they have less chance to be blocked. To examine the used quota for each priority class, the wavelength assignment method keeps track of a counter for each priority class which records the number of wavelengths currently assigned to the requests of the priority class. Let w(pi) be the counter for priority class pi. Upon the arrival of method a new connection request of priority pi, the proposed P assigns a wavelength to it if the condition nxi w px ⬍ qi holds. For example, assume that the system has three priority classes and that the bandwidth contains three wavelengths. Suppose the dynamic method sets the quotas as follows: q1 3, q2 2 and q3 1. It means that at least one wavelength and at most three wavelengths can be assigned to the p1class requests, since q1 ⫺ q2 1 and q1 3. The method assigns at most two wavelengths to p2-class requests and at
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most one to p3. Note that p2-class and p3-class requests may get no wavelengths. Unlike the static scheme where each wavelength is ‘hardwired’ to a preferred wavelength set, the dynamic scheme has the flexibility of choosing a wavelength among all the available wavelengths. A simple solution to it is to pick up the next available wavelength in the system. 3.2. The backtrack routing algorithm The proposed routing algorithm requires the routing nodes to maintain their routing tables. A routing table records the information about the preferred outgoing ports for each destination. A routing node determines the outgoing ports for a given destination under various link conditions. The routing tables must be carefully maintained to avoid cyclic paths. The process of initializing the routing tables for all nodes is called the vectorization of the routing tables. Based on the network shown in Figs. 2, 3(a) illustrates an example of the routing table for Node 5. The proposed routing algorithm finds a route based on the depth first search (DFS) traverse and backtracking of a routing tree. A routing tree for a pair of source and destination contains the possible routes, where the source is the root of the routing tree and all leaf nodes indicate the destination. The information of routing trees is partially stored in the routing nodes in the network. During the traverse of a routing tree for a given pair of source and destination, the routing algorithm assigns the currently traversed node a wavelength, if there is one available and then it proceeds in the DFS order until a leaf node is reached. However, if any link during the traverse to a leaf cannot be assigned to a wavelength, the algorithm backtracks to the up-stream link and continues the route finding process. The connection request will be blocked, if the routing algorithm cannot find a route after the corresponding routing tree is completely traversed. Note that any link in the network will be visited at most once during the search of a feasible path. Therefore, the time complexity of the proposed routing algorithm is O(兩E兩), where E is the set of links in the network. Fig. 3(b) shows an example of the route tree for a connection from Node 1 to Node 4. Suppose the links (1,2) and (2,3) are assigned to a wavelength. The algorithm proceeds to the down-stream link (3,4). If the assignment fails, link (2,5) is visited. If the assignment for this link fails again, the algorithm backtracks to link (1,2) and then link (1,6). The algorithm for the backtrack routing performed by each node is shown below. 3.2.1. Procedure ROUTING (node, src, dest, req id, priority) top: Wait for a message; if (message REQUEST) {
if (dest node) /* check the address*/ Call CONNECTION_SETUP. Commit all the reserved resource for the connection req_id. Return to the top. else{ Look up the routing table; While there exists some unvisited link for the request req_id do Call WAVELENGTH_ASSIGNMENT(req_id, priority, link) if (successful) Reserve the wavelength and add the link to the path for this connection. Send a REQUEST message to NEXT_NODE Return to the top. end if. End while. Send a REJECT message to the previous node to cancel the wavelength reservation. Reclaim all resources for this connection. Return to the top. }/* End of the else part*/ }/* End of message REQUEST handling*/ if (message REJECT) { Look up the routing table. While there exists some unvisited link for the request req_id do Call WAVELENGTH_ASSIGNMENT(req_id, priority, link). if (successful) Reserve the wavelength and add the link to the path for this connection. Send a REQUEST message to NEXT_NODE. Return to the top. end if. End while if (src node) Return CONNECTION_REQUEST_FAILURE. else { Send a REJECT message to the previous node to cancel the wavelength reservation. Reclaim all resources for this connection. } Return to the top. }/* End of message REJECT handling*/ end Procedure. 3.3. Analytic models for the wavelength assignment methods 3.3.1. One priority class In this section, we consider the analytic model for the wavelength assignment strategies in a system with one
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Fig. 4. The state transition diagram for a system with one priority class.
priority class of requests. The analytic model will be extended to two-priority cases in the next section. For a system with only one priority class, the analytic model for the static and dynamic methods is the same as the FCFS method. The system is modelled as a continuous-parameter homogeneous Markov chain. We assume that the request arrivals form a Poisson process with rate r1 and the holding time for a connection request has the exponential distribution with mean 1/u1. Let N be the total number of wavelengths in the system. The system can be modelled as a birth–death process with finite states. A system state is characterized by the number of occupied wavelengths. The state transition diagram of the Markov chain model is shown in Fig. 4, this shows computing of the blocking rate. 3.3.2. Two priority classes Consider the following case in which a system has two wavelengths and two priority classes of connection requests. We assume the connections have the Poisson arrival rates and the exponential holding times. For the static assignment method to work, we set WP1 {l1} and WP2 {l2}. For the dynamic method to work, we set q1 2 and q2 1. We assume that the arrival rates for the first and the second priority requests have the Poisson distributions of r1 and r2, respectively. The holding times for them are exponential with means of 1/u1 and 1/u2, respectively. The state transition diagrams for the static and dynamic methods are shown in Figs. 5 and 6, respectively.
In Fig. 5 the interpretation of a state (x,y) is that x 0, if l1 is available; and x 1, if l1 is assigned to a request of the first priority. As for the value of y, y 0, if l2 is available; y 1, if l2 is assigned to a request of the first priority; and y 2, if l2 is assigned to a request of the second priority. Let r1 r1/u1 and r2 r2/u2. The blocking probability of the first priority requests can be computed by:
P 1; 2 ⫹ P 1; 1
r1 r2 ⫹
r21 rr 2 ⫹ r1 ⫹ 1 2 × 2 2 1 ⫹ r1 D
and the blocking probability of the second priority request is P 0; 1 ⫹ P 1; 1 ⫹ P 0; 2 ⫹ P 1; 2
r2
r1 r1 r2 rr 2 ⫹ r1 × ⫹ r1 r2 ⫹ 1 ⫹ 1 2 × 2 1 ⫹ r1 2 2 1 ⫹ r1 D
In Fig. 6 the, interpretation, of a state (x, y) is identical to that in Fig. 6. The blocking probability of the first priority requests is P(2,1) ⫹ P(1,1) ⫹ P(1,2), while that of the second priority requests is P(2,1) ⫹ P(2,0) ⫹ P(0,2) ⫹ P(1,1) ⫹ P(1,2). As for the general cases of analysis of the static and the dynamic assignments and the routing mechanism we apply the simulation modets to evaluate the performance and the blocking rates of them, as shown in the next section.
Fig. 5. The state diagram for the static assignments.
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Fig. 6. The state diagram for the dynamic assignment.
4. Simulations and results 4.1. Wavelength assignment We evaluate the performance of the proposed wavelength assignment methods by simulation. The wavelength assignment methods are evaluated on a simplified network with only one link. The simulated network has five priority classes and the bandwidth contains 80 wavelengths, l1 to l80. The related simulation parameters for the proposed wavelength assignment methods are listed later. WP2 {li 兩i 17; …; 32}, 1. WP1 {li 兩i 1; …; 16}, WP3 {li 兩i 33; …; 48}, WP4 {li 兩i 49; …; 64}, and WP5 {li 兩i 65; …; 80}. 2. q1 80, q2 64, q3 48, q4 32 and q5 16. We generate two traffic patterns: Binomial and Poisson. In the first traffic pattern, at each time unit, a decision is made about whether a request shall be generated. The probability of generating a request at each time unit is 0.1. If a request is to be generated, it has equal opportunity of being one of the five priority classes. Namely, the probability for a request to be of the ith priority is 0.2, ᭙ i 1…,5. The wavelength holding time for a request has the exponential distribution of mean 100 time units (i.e. u 0.01). If a request is generated and there is no available wavelength for it, it is considered to be blocked and removed from the system. For the previous traffic pattern, 20 runs are
generated and simulated to compute the averaged blocking probability for each priority class. The time taken to simulate each run is the time to simulate 10 000 requests. The blocking probability of each priority class is obtained by dividing the number of blocked requests over the total number of issued requests. The averaged blocking probability for a priority class is the averaged value of the blocking probability of each priority class over 20 runs. We present the comparison between the two assignment algorithms in Fig. 7. In the second traffic pattern, the arrivals of the requests follow the Poisson process with the rate of 0.07 (i.e. r 0.07). Given an arrival, the opportunity for it to be one of the five priority classes is 0.2. The wavelength holding time also has the exponential distribution of mean 100 time units. Altogether 20 runs are simulated, in which each run has 10 000 requests. The computation of the averaged blocking probability for a priority class is the same as that described in the last paragraph. The simulation results are given in Fig. 8. Figs. 7 and 8 plot the blocking rates and the averaged blocking rates for the two traffic patterns. The averaged blocking rate is computed by summing the blocking probabilities for the five priority classes and dividing it by 5. These two figures illustrate the point that the dynamic strategy has more balanced blocking rates than the static one has, since the discrepancy between the averaged blocking rate and the blocking rate of a priority class is smaller in the
Fig. 7. The blocking rates for Binomial traffic pattern.
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Fig. 8. The blocking rates for Poisson traffic pattern.
dynamic strategy. The static strategy has smaller blocking rates for high priority classes, but the blocking rates increases sharply as the priority becomes lower. Both figures show that the dynamic strategy performs better on the averaged blocking rate. 4.2. The fixed routing vs backtrack routing algorithms 4.2.1. Simulation design In this section, we present the simulation results about the proposed backtrack routing algorithm with the dynamic wavelength assignment method. We study a mesh network as shown in Fig. 9. The 9 × 9 mesh network contains 81 nodes and 144 links. Each link has 16 wavelengths. The regularity of mesh networks makes the vectorization of the routing tables easy. A node in the simulated network is identified by its X and Y-dimension coordinates. The vectorization of the routing table for a node (xr, yr) is performed by checking the relative position between the destination node (xd, yd) and the node (xr, yr). If xd ⬎ xr then the ‘right’ port of node (xr, yr) is
Fig. 9. The network structure for simulating the routing algorithms.
Fig. 10. The related network status for the connection from node N11 to node N54.
included in the routing table. If xd ⬍ xr the ‘left’ port is included instead. Similarly, if yd ⬎ yr the ‘down’ port is included, while if yd ⬍ yr, the ‘up’ port is included. Therefore, given a destination, there may be at most two outgoing ports for it. The example in Fig. 10 demonstrates how the backtrack routing algorithm works. Upon the arrival of a connection request from N11, to N54, the network contains several blocked links for the request represented by the bold line segments in Fig. 10. Fig. 11 represents the traversed tree nodes during the route finding. Note that, in Fig. 12, when N43 is visited at the second time, the algorithm backtracks to N33 without trying the outgoing ports (links) of N43. The reason is that the links X43 and Y43 were checked when N43 was visited the first time. It can be seen that the worst-case complexity of the algorithm is the number of links in the system. We evaluate our routing algorithm by comparing it with two base routing algorithms: the fixed routing (FR) and fixed alternate routing (FAR) algorithms. The FR algorithm follows the X-dimension first and then the Y-dimension until the destination is reached. FR only provides one route for every source-destination pair. The FAR algorithm gives an alternate route, beside the route provided by FR. The alternate route follows the Y-dimension first and then the Xdimension until the destination meets. If any link in the primary path cannot be assigned to a wavelength, the FAR algorithm tries the alternate route. An illustration for the two algorithms is given in Fig. 12. 4.2.2. Simulation results The simulated network system has four priority classes. The dynamic wavelength assignment method defines the following quota values: qi 16, q2 12, q3 8 and q4 4. The connection requests at a node have the Poisson arrival rates CR and the connection holding time has the exponential distribution with mean u 100. A connection request has an equal opportunity of being one of the four
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Fig. 11. The traversed routing tree for the connection from N11 to N54.
priorities (i.e. 0.25 for each priority class). The destination of a request is randomly decided. We simulate three traffic load situations: fight, medium and heavy load. The light-load situation has CR 0.0015, i.e. r 0.15; the medium-load situation has CR 0.015, i.e. r 1.5; and the heavy-load situation has CR 0.15, i.e. r 15. The shown results are the averaged values over 10 runs under the identical load situation. Each run generates 6000 requests. In each run, the simulation records the blocking rate for each routing algorithm at the time when 1000, 2000, 3000, 4000, 5000 and 6000 requests are served. The results for the light, middle and heavy load situations are shown in Figs. 13–15, respectively. The figures illustrate that the backtrack algorithm outperforms the other two algorithms. 4.3. Cost effectiveness evaluation The previous simulation assumes that the network bandwidth has 16 wavelengths. It is intuitive to claim that as the number of wavelengths in a link increases, the probability of a request being blocked is smaller and smaller. However, in the current optoelectronic technology, the number of wavelengths carried by an optical routing node is in the range of tens to one hundred. To explore an optical routing node with N wavelengths, N router switches and O(N 2) edges are required to connect the multiplexers and de-multiplexers between them. Therefore, even the availability of wavelengths from an optical fiber is abundant, the utilization of the wavelengths is limited. To evaluate the cost effectiveness of the proposed backtrack routing and dynamic wavelength assignment method, simulations are conducted to study the relationship between the number of wavelengths and the averaged blocking rate in a system under various load conditions. In the simulation design, the number of wavelengths in a link, N, is a parameter that has the possible values of 16, 32
and 64. Given a value N, the simulation program equally divides N wavelengths into 4 parts, and sets q1 N, q2 3N/ 4, q3 N/2 and q4 N/4. The holding time for each connection request has the exponential distribution of mean 100 time units (u 0.01). The arrival rate of each priority class has the Poisson distribution r such that r r/u 0.5, 1.0, 1.5,…,25, are the controlled values. For each combination of (N, r), 10 runs are generated and simulated. In each run, the time taken to simulate is the time when 10 000 requests are generated. The blocking probability is computed as well. The detailed results are shown in Fig. 16. From Fig. 16 we can see the proposed algorithm and the designed simulations provide a way for the optoelectronic engineers to evaluate the cost effectiveness of the whole system. Given a tolerable value of blocking rate, the designers have the options to choose the optical routing nodes with the most economic number of wavelengths under various predicted load traffic. 4.3.1. Evaluation of connection latency The time taken to find a path by the FR is 兩Ef兩*t1, in which 兩Ef兩 is the number of hops along the path and t1 indicates the time taken by the wavelength assignment to allocate a wave-
Fig. 12. The base routing algorithms.
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Fig. 13. The blocking rates for FR, FAR and Backtrack algorithms in a light-load situation.
Fig. 14. The blocking rates for FR, FAR and Backtrack algorithms in a medium-load situation.
length within one hop. Similarly, the time taken by the FAR is 2*兩Ef兩*t1. As for the backtrack algorithm, the best-case complexity is equivalent to that of the FR. However, the worst case happens when all the links in the routing tree are visited. The complexity will be 兩En兩*t1, in which 兩En兩 is the number of nodes in the routing tree. Note that the routing tree is built on-the-fly. The storage requirement in each routing table is illustrated in Fig. 3(a). It is not necessary to keep the routing trees for all destinations.
Fig. 15. The blocking rates for FR, FAR and Backtrack algorithms in a heavy-load situation.
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Fig. 16. The relationship between the load, the number of wavelengths and the blocking probability.
It can be seen that in a lightly-loaded situation a path can be easily found. The complexity for the backtrack routing at that case will be approximately equal to that of the FR. On the other hand, in a heavily-loaded situation, the FR and FAR are vulnerable to find a path within one or two trials. However, it is still feasible to find a path for the backtrack routing. In a given situation, the order of traversing the routing tree determines the complexity of the proposed algorithm. The searching of a feasible lightpath could be speeded up if information of the wavelength usage of the subtree is kept in the intermediate nodes. When the search backtracks to an upstream intermediate node, it could be more beneficial to try a downstream link with less traffic. Our future work is to investigate how to maintain the useful information.
5. Conclusion In this paper, we consider the wavelength assignment and the routing problems in the WDM networks. The connection requests to the WDM networks are prioritized according to their QoS requirements. We propose two strategies that use the priorities of the requests to perform the wavelength assignment. They are the static and the dynamic strategies. The static assignment preallocates a set of wavelengths for each priority class of requests and chooses one wavelength for a given request based on its priority and the available wavelengths for the given priority. The dynamic wavelength assignment selects a wavelength dynamically among all available wavelengths, but it controls the number of assigned wavelengths for a given priority class of requests by a pre-defined quota. Simulation results show that the dynamic strategy obtains a lower blocking rate than the static one does. The proposed solution to the routing problem is the backtrack routing. The backtrack routing algorithm along is integrated with the wavelength assignment to reduce the overall blocking rates in the system. The backtrack routing method builds a route tree for a given connection request. During the setup of a route, backtrack is allowed when some
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wavelength can not be assigned in a link. In the simulations, the proposed solution is compared to the fixed routing and the fixed alternate routing algorithms. The results show that our algorithm performs better in the light, medium and heavy-load situations. Experiments are also conducted to study the relationship among the number of wavelengths in a link, the load traffic in the system and the averaged blocking rates, based on the proposed solutions.
[5] [6]
[7]
[8]
References [9] [1] G. Sudhakar, N. Georganas, M. Kavehrad, Slotted aloha and reservation aloha protocols for very high-peed optical fiber local area networks using passive star topology, Journal of Lightwave Technology 9 (1991) 1411–1422. [2] B. Mukherjee, WDM-based local lightwave networks, part 1: singlehop systems, Network, May (1992) 12–27. [3] G.I. Papadimitriou, D.G. Maritsas, HARP: A hybrid random access and reservation protocol for WDM passive star networks, in: Proceedings of IEEE GLOBECOM 1994, pp. 1521–1527. [4] S. Tridandapani, J.S. Meditch, A.K. Somani, The MaTPi protocol:
[10] [11]
[12]
masking tuning times through pipelining in WDM optical networks, in: Proceedings of IEEE INFOCOM 1994, pp. 2140–2150. A. Acampora, M. Karol, M. Hluchyu, Terabit lightwave networks: the multihop approach, AT & T Tech Journal 66 (6) (1987) 21–34. N. Huang, H. Liu, An isochronous and asynchronous traffic scheduling algorithm for dual-star WDM networks, Journal of Lightwave Technology 14 (3) (1996) 273–287. N. Huang, G. Liaw, C. Chiou, On the isochronous paths selection problem in an interconnected WDM network, Journal of Lightwave Technology 14 (3) (1996) 304–314. C. Chen, L.A. Wang, S. Kuo, A wavelength encoded multichannel optical bus for local area networks, Journal of Lightwave Technology 14 (3) (1996) 315–323. R. Ramaswami, G.H. Sasaki, Multiwavelength optical networks with limited wavelength conversion, in: Proceedings of INFOCOM 1997. A. Birman, Computing approximate blocking probabilities for a class of all-optical networks, in: Proceedings of INFOCOM 1995. A. Birman, A. Kershenbaum, Routing and wavelength assignment methods in single-hop all-optical networks with blocking, in: Proceedings of INFOCOM 1995. A. Girard, Routing and dimensioning in circuit switched networks, Addison-Wesley, Reading, MA, 1990.
Backtrack routing and priority-based wavelength assignment in WDM networks Sheng-Tzong Cheng* Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan, ROC Received 13 February 1998; received in revised form 29 June 1998; accepted 29 June 1998
Abstract In this paper, we consider two key problems in the WDM networks: the wavelengh assignment and routing problems. The objective of the problems is to minimize the request blocking rate. We propose two priority-based methods for the wavelength assignment problem: static and dynamic strategies. Based on the priority of an incoming request, the proposed methods allocate a wavelength among the available wavelengths for the given priority. Analytic models and simulations are presented for the proposed wavelength assignment methods so as to analyse the link blocking rate. The simulation results show that the link blocking rate by the dynamic strategy is less than that by the assignment strategy. We also develop a routing algorithm that works together with the proposed wavelength assignment methods to reduce the overall blocking rates. The proposed routing method maintains a routing tree for a given connection request. Based on the routing tree, the algorithm finds a route with one available wavelength for each link along the route. We compare the proposed routing method with the fixed routing and fixed alternate routing algorithms. The experiments show that the proposed routing algorithm performs better than the fixed routing and the alternate routing methods. 䉷 1999 Elsevier Science BV. All rights reserved. Keywords: Backtrack Routing; Priority-based; WDM Networks; Wavelength assignment; Performance evaluation
1. Introduction One of the main issues of using communication networks is the availability of network bandwidth. As the number of network connections increases, the available bandwidth becomes inadequate and the quality of information service degrades. It is no doubt that new network techniques that support high-bandwidth requirements are essential. To solve the problem of the bandwidth shortage, the optical networks were advocated to be the choice for the networks of the next generation. The virtues of the optical networks are high bandwidth, high speed and reliability. Optical networks are able to provide high bandwidth in the range of terabits per second. Bandwidth of an optical link is divided into wavelengths. New components for optical networks, such as optical amplifiers, optical switches, optical wavelength (de)multiplexers and wavelength converters, are developed to exploit the available wavelengths in a link, as reported in the literature. In the context, the Wavelength Division Multiplexing (WDM) technology is proposed to utilize multiple wavelengths to establish
* Corresponding author. Tel.: ⫹86 275 7575; fax: ⫹86 274 7076; e-mail: [email protected]
connections concurrently and independently on a single optical fibre link. In this paper, we propose two wavelength assignment strategies and a routing method for WDM networks. The main objectives are to satisfy requirements of different types of quality of service (QoS) and to reduce the blocking rates. The connection requests are prioritized to support connections with different QoS requirements. Priorities are the index of assigning a wavelength to a given request. The proposed static wavelength assignment method pre-allocates a set of wavelengths for each priority class of requests and chooses one-wavelength for a given request based on its priority and the available wavelengths for the given priority. The dynamic wavelength assignment method selects a wavelength dynamically among the available wavelengths, but it controls the number of assigned wavelengths for a given priority class of requests according to a predefined quota. The proposed routing algorithm maintains a routing tree which includes possible paths for a given connection request. Based on the routing tree, it finds a non-blocked route in a fashion of backtracking. This paper consists of five sections. Section 2 surveys the background. In Section 3, we present our methods on the wavelength assignment and routing problem and the analytic models. In Section 4, we present a simulation model to
0140-3664/99/$ - see front matter 䉷 1999 Elsevier Science BV. All rights reserved. PII: S0140-366 4(98)00209-6
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Fig. 1. An example of the Static Assignment Scheme.
evaluate the performance and discuss the simulation results. The conclusion is drawn in Section 5. 2. Background In the literature, researchers propose various architectures for WDM networks. Two main kinds of networks reported are the single-hop and the multi-hop WDM networks. Single-hop WDM networks restrict a light-path connection to use the same wavelength on all links of the path without buffering or optical-to-electronic conversion [1–4]. The blocking rate increases dramatically as the number of links in a lightpath increases or the network complexity grows. Multi-hop WDM networks allow wavelength conversion to ease the restriction of wavelength continuity. Such networks scale well and block less traffic [5]. Huang et al. propose an architecture for interconnecting WDM-based start networks [6,7]. The star-coupler bridge (SCB) is used to interconnect two broadcast-and-selective networks, transmitting and receiving data through a dual bus between the two interconnected networks. Transmission is carried out by the time division multiplexing (TDM) technique. Each node in the interconnected networks either recieves data or transmits data via one wavelength at a given time slot. They consider the path assignment problem for isochronous and asynchronous requests and develop solutions based on the proposed architecture. The wavelength encoded multi-channel optical bus (WEMCOB) is proposed in Ref. [8]. They study a backbone network based on WEMCOB and show that such a network can offer the transmission rate of the order of gigabits per second. Ramaswami and Sasaki study the WDM networks with limited wavelengh conversion [9] and show that the throughput can be improved significantly for such networks. The WDM networks with wavelengh conversion are equivalent to circuit-switched networks. Hence, several papers on evaluating routing algorithms are based on circuit switching [10,11]. Fixed routing and fixed alternate routing methods [12] are studied. These two methods block a request if any
link in the pre-defined path(s) has no available wavelengh. The time complexity of the routing algorithm is O(兩E兩), where 兩E兩 is the number of links in the possible paths for a given request to find a non-blocking route. As stated previously, a WDM network with wavelengh conversion achieves a higher connection acceptance rate than one without wavelengh conversion does. The problem of wavelengh conversion can be solved by the wavelengh assignment. The simplest way of wavelengh assignment is the first-come-first-served (FCFS) method. Whenever a traffic request arrives, an attempt is made to reserve a wavelength from available bandwidth for this traffic request. The incoming traffic requests can only be accepted if an available wavelength is found. However, not much work was reported on the wavelength assignment with the QoS requirements. In this paper, we consider the wavelength assignment problem in which the priorities for the connection requests are given. The priority value of a request is obtained from its QoS requirement. The objective of our wavelengh assignment strategies is to minimize the blocking rates for different classes of requests. 3. Our approach 3.1. The proposed wavelength assignment methods The basic idea of the proposed methods is that the connection requests are treated differently according to their QoS requirements. The connection requests with higher QoS requirements, such as real-time video or sound, should have higher priority and, hence, should incur lower blocking probability. Two wavelength assignment methods are proposed: the static and dynamic wavelength assignment methods. 3.1.1. Static assignment method Assume that the network bandwidth contains m wavelengths, li, i 1,…,m, and the system have n priority values, p1, p2,…pn, where p1 is the highest priority. The proposed method pre-defines a preferred wavelength set for each priority class. Let WPi be the preferred wavelength set for a priority class pi. The static method chooses an available wavelength for a request of a priority class pi from its preferred wavelength set, WPi and WPj for j i ⫹ 1,…,n, if the wavelengths in WPi were assigned. The constraints on the preferred wavelength sets are listed as follows. 1. WPi 傽 WPj ⭋, ᭙ i 苷 j. Each wavelength can only be included once in a preferred wavelength set. 2. 傼i WPi {li 兩i 1; …; m}. All wavelengths are used. 3. 兩WP1兩 ⱖ 兩WP2兩 ⱖ … ⱖ 兩WPn兩, where 兩WPi兩 is the number of wavelengths in the preferred wavelength set of priority class pi. The number of available wavelengths for a higher priority class is not less than that of a lower priority one.
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Fig. 2. An example of a WDM network with 6 nodes.
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For a request of priority pi, the proposed method starts with finding a wavelength from WPi. If no wavelength is available in WPi, then it checks from WPi⫹1 to WPn until an available wavelength is found. If no available wavelength is found in WPi through WPn, the request is considered to be blocked. Fig. 1 illustrates an example. The illustrated system has three priority classes of connection requests (n 3) and three wavelengths (m 3). Suppose that, l1, is preferred to be assigned to priority p1, that l2 is preferred to be assigned to priority p2, and that l3 is preferred to being assigned to priority p3. The dash lines shown in Fig. 1 indicate the possible assignment for the higher priorities. We observe that l3 can be assigned to a connection of priority-p3 as well as one of higher priorities as indicated by dash lines. 3.1.2. Dynamic assignment method Unlike the static assignment method, the dynamic assignment method does not specify the preferred wavelength sets. A wavelength can be assigned to a connection request of any priority. To control the number of wavelengths assigned to a priority class, the dynamic method pre-sets a wavelength quota for each priority class. Assume that the network bandwidth contains m wavelengths, li,i 1,…,m, and the system has n priority values, p1, p2,…,pn, where p1, is the highest priority. Let qi denote the wavelength quota for priority class of pi or lower. The constraints on the quotas are stated as follows. 1. m q1 ⱖ q2 ⱖ …qn ⱖ 1. 2. qi29 ⫺ q2 ⱖ q2 ⫺ q3 ⱖ q3 ⫺ q4 ⱖ …qn⫺1 ⫺ q n ⱖ qn. The value of qi ⫺ qi⫹1 indicates the number of wavelengths initially reserved for the requests of priority pi and the value of qi ⫺ q2 indicates the number of wavelengths exclusively allocated for the requests of priority pi .
Fig. 3. (a) The routing table of Node 5; and (b) the route tree for a connection from Node 1 to Node 4.
The dynamic method can assign at most qi wavelengths to the requests with the priority pi or lower. A quota is specified for the requests of a given priority. In Constraint 2, the proposed method gives higher priority requests more wavelengths such that they have less chance to be blocked. To examine the used quota for each priority class, the wavelength assignment method keeps track of a counter for each priority class which records the number of wavelengths currently assigned to the requests of the priority class. Let w(pi) be the counter for priority class pi. Upon the arrival of method a new connection request of priority pi, the proposed P assigns a wavelength to it if the condition nxi w px ⬍ qi holds. For example, assume that the system has three priority classes and that the bandwidth contains three wavelengths. Suppose the dynamic method sets the quotas as follows: q1 3, q2 2 and q3 1. It means that at least one wavelength and at most three wavelengths can be assigned to the p1class requests, since q1 ⫺ q2 1 and q1 3. The method assigns at most two wavelengths to p2-class requests and at
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most one to p3. Note that p2-class and p3-class requests may get no wavelengths. Unlike the static scheme where each wavelength is ‘hardwired’ to a preferred wavelength set, the dynamic scheme has the flexibility of choosing a wavelength among all the available wavelengths. A simple solution to it is to pick up the next available wavelength in the system. 3.2. The backtrack routing algorithm The proposed routing algorithm requires the routing nodes to maintain their routing tables. A routing table records the information about the preferred outgoing ports for each destination. A routing node determines the outgoing ports for a given destination under various link conditions. The routing tables must be carefully maintained to avoid cyclic paths. The process of initializing the routing tables for all nodes is called the vectorization of the routing tables. Based on the network shown in Figs. 2, 3(a) illustrates an example of the routing table for Node 5. The proposed routing algorithm finds a route based on the depth first search (DFS) traverse and backtracking of a routing tree. A routing tree for a pair of source and destination contains the possible routes, where the source is the root of the routing tree and all leaf nodes indicate the destination. The information of routing trees is partially stored in the routing nodes in the network. During the traverse of a routing tree for a given pair of source and destination, the routing algorithm assigns the currently traversed node a wavelength, if there is one available and then it proceeds in the DFS order until a leaf node is reached. However, if any link during the traverse to a leaf cannot be assigned to a wavelength, the algorithm backtracks to the up-stream link and continues the route finding process. The connection request will be blocked, if the routing algorithm cannot find a route after the corresponding routing tree is completely traversed. Note that any link in the network will be visited at most once during the search of a feasible path. Therefore, the time complexity of the proposed routing algorithm is O(兩E兩), where E is the set of links in the network. Fig. 3(b) shows an example of the route tree for a connection from Node 1 to Node 4. Suppose the links (1,2) and (2,3) are assigned to a wavelength. The algorithm proceeds to the down-stream link (3,4). If the assignment fails, link (2,5) is visited. If the assignment for this link fails again, the algorithm backtracks to link (1,2) and then link (1,6). The algorithm for the backtrack routing performed by each node is shown below. 3.2.1. Procedure ROUTING (node, src, dest, req id, priority) top: Wait for a message; if (message REQUEST) {
if (dest node) /* check the address*/ Call CONNECTION_SETUP. Commit all the reserved resource for the connection req_id. Return to the top. else{ Look up the routing table; While there exists some unvisited link for the request req_id do Call WAVELENGTH_ASSIGNMENT(req_id, priority, link) if (successful) Reserve the wavelength and add the link to the path for this connection. Send a REQUEST message to NEXT_NODE Return to the top. end if. End while. Send a REJECT message to the previous node to cancel the wavelength reservation. Reclaim all resources for this connection. Return to the top. }/* End of the else part*/ }/* End of message REQUEST handling*/ if (message REJECT) { Look up the routing table. While there exists some unvisited link for the request req_id do Call WAVELENGTH_ASSIGNMENT(req_id, priority, link). if (successful) Reserve the wavelength and add the link to the path for this connection. Send a REQUEST message to NEXT_NODE. Return to the top. end if. End while if (src node) Return CONNECTION_REQUEST_FAILURE. else { Send a REJECT message to the previous node to cancel the wavelength reservation. Reclaim all resources for this connection. } Return to the top. }/* End of message REJECT handling*/ end Procedure. 3.3. Analytic models for the wavelength assignment methods 3.3.1. One priority class In this section, we consider the analytic model for the wavelength assignment strategies in a system with one
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Fig. 4. The state transition diagram for a system with one priority class.
priority class of requests. The analytic model will be extended to two-priority cases in the next section. For a system with only one priority class, the analytic model for the static and dynamic methods is the same as the FCFS method. The system is modelled as a continuous-parameter homogeneous Markov chain. We assume that the request arrivals form a Poisson process with rate r1 and the holding time for a connection request has the exponential distribution with mean 1/u1. Let N be the total number of wavelengths in the system. The system can be modelled as a birth–death process with finite states. A system state is characterized by the number of occupied wavelengths. The state transition diagram of the Markov chain model is shown in Fig. 4, this shows computing of the blocking rate. 3.3.2. Two priority classes Consider the following case in which a system has two wavelengths and two priority classes of connection requests. We assume the connections have the Poisson arrival rates and the exponential holding times. For the static assignment method to work, we set WP1 {l1} and WP2 {l2}. For the dynamic method to work, we set q1 2 and q2 1. We assume that the arrival rates for the first and the second priority requests have the Poisson distributions of r1 and r2, respectively. The holding times for them are exponential with means of 1/u1 and 1/u2, respectively. The state transition diagrams for the static and dynamic methods are shown in Figs. 5 and 6, respectively.
In Fig. 5 the interpretation of a state (x,y) is that x 0, if l1 is available; and x 1, if l1 is assigned to a request of the first priority. As for the value of y, y 0, if l2 is available; y 1, if l2 is assigned to a request of the first priority; and y 2, if l2 is assigned to a request of the second priority. Let r1 r1/u1 and r2 r2/u2. The blocking probability of the first priority requests can be computed by:
P 1; 2 ⫹ P 1; 1
r1 r2 ⫹
r21 rr 2 ⫹ r1 ⫹ 1 2 × 2 2 1 ⫹ r1 D
and the blocking probability of the second priority request is P 0; 1 ⫹ P 1; 1 ⫹ P 0; 2 ⫹ P 1; 2
r2
r1 r1 r2 rr 2 ⫹ r1 × ⫹ r1 r2 ⫹ 1 ⫹ 1 2 × 2 1 ⫹ r1 2 2 1 ⫹ r1 D
In Fig. 6 the, interpretation, of a state (x, y) is identical to that in Fig. 6. The blocking probability of the first priority requests is P(2,1) ⫹ P(1,1) ⫹ P(1,2), while that of the second priority requests is P(2,1) ⫹ P(2,0) ⫹ P(0,2) ⫹ P(1,1) ⫹ P(1,2). As for the general cases of analysis of the static and the dynamic assignments and the routing mechanism we apply the simulation modets to evaluate the performance and the blocking rates of them, as shown in the next section.
Fig. 5. The state diagram for the static assignments.
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Fig. 6. The state diagram for the dynamic assignment.
4. Simulations and results 4.1. Wavelength assignment We evaluate the performance of the proposed wavelength assignment methods by simulation. The wavelength assignment methods are evaluated on a simplified network with only one link. The simulated network has five priority classes and the bandwidth contains 80 wavelengths, l1 to l80. The related simulation parameters for the proposed wavelength assignment methods are listed later. WP2 {li 兩i 17; …; 32}, 1. WP1 {li 兩i 1; …; 16}, WP3 {li 兩i 33; …; 48}, WP4 {li 兩i 49; …; 64}, and WP5 {li 兩i 65; …; 80}. 2. q1 80, q2 64, q3 48, q4 32 and q5 16. We generate two traffic patterns: Binomial and Poisson. In the first traffic pattern, at each time unit, a decision is made about whether a request shall be generated. The probability of generating a request at each time unit is 0.1. If a request is to be generated, it has equal opportunity of being one of the five priority classes. Namely, the probability for a request to be of the ith priority is 0.2, ᭙ i 1…,5. The wavelength holding time for a request has the exponential distribution of mean 100 time units (i.e. u 0.01). If a request is generated and there is no available wavelength for it, it is considered to be blocked and removed from the system. For the previous traffic pattern, 20 runs are
generated and simulated to compute the averaged blocking probability for each priority class. The time taken to simulate each run is the time to simulate 10 000 requests. The blocking probability of each priority class is obtained by dividing the number of blocked requests over the total number of issued requests. The averaged blocking probability for a priority class is the averaged value of the blocking probability of each priority class over 20 runs. We present the comparison between the two assignment algorithms in Fig. 7. In the second traffic pattern, the arrivals of the requests follow the Poisson process with the rate of 0.07 (i.e. r 0.07). Given an arrival, the opportunity for it to be one of the five priority classes is 0.2. The wavelength holding time also has the exponential distribution of mean 100 time units. Altogether 20 runs are simulated, in which each run has 10 000 requests. The computation of the averaged blocking probability for a priority class is the same as that described in the last paragraph. The simulation results are given in Fig. 8. Figs. 7 and 8 plot the blocking rates and the averaged blocking rates for the two traffic patterns. The averaged blocking rate is computed by summing the blocking probabilities for the five priority classes and dividing it by 5. These two figures illustrate the point that the dynamic strategy has more balanced blocking rates than the static one has, since the discrepancy between the averaged blocking rate and the blocking rate of a priority class is smaller in the
Fig. 7. The blocking rates for Binomial traffic pattern.
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Fig. 8. The blocking rates for Poisson traffic pattern.
dynamic strategy. The static strategy has smaller blocking rates for high priority classes, but the blocking rates increases sharply as the priority becomes lower. Both figures show that the dynamic strategy performs better on the averaged blocking rate. 4.2. The fixed routing vs backtrack routing algorithms 4.2.1. Simulation design In this section, we present the simulation results about the proposed backtrack routing algorithm with the dynamic wavelength assignment method. We study a mesh network as shown in Fig. 9. The 9 × 9 mesh network contains 81 nodes and 144 links. Each link has 16 wavelengths. The regularity of mesh networks makes the vectorization of the routing tables easy. A node in the simulated network is identified by its X and Y-dimension coordinates. The vectorization of the routing table for a node (xr, yr) is performed by checking the relative position between the destination node (xd, yd) and the node (xr, yr). If xd ⬎ xr then the ‘right’ port of node (xr, yr) is
Fig. 9. The network structure for simulating the routing algorithms.
Fig. 10. The related network status for the connection from node N11 to node N54.
included in the routing table. If xd ⬍ xr the ‘left’ port is included instead. Similarly, if yd ⬎ yr the ‘down’ port is included, while if yd ⬍ yr, the ‘up’ port is included. Therefore, given a destination, there may be at most two outgoing ports for it. The example in Fig. 10 demonstrates how the backtrack routing algorithm works. Upon the arrival of a connection request from N11, to N54, the network contains several blocked links for the request represented by the bold line segments in Fig. 10. Fig. 11 represents the traversed tree nodes during the route finding. Note that, in Fig. 12, when N43 is visited at the second time, the algorithm backtracks to N33 without trying the outgoing ports (links) of N43. The reason is that the links X43 and Y43 were checked when N43 was visited the first time. It can be seen that the worst-case complexity of the algorithm is the number of links in the system. We evaluate our routing algorithm by comparing it with two base routing algorithms: the fixed routing (FR) and fixed alternate routing (FAR) algorithms. The FR algorithm follows the X-dimension first and then the Y-dimension until the destination is reached. FR only provides one route for every source-destination pair. The FAR algorithm gives an alternate route, beside the route provided by FR. The alternate route follows the Y-dimension first and then the Xdimension until the destination meets. If any link in the primary path cannot be assigned to a wavelength, the FAR algorithm tries the alternate route. An illustration for the two algorithms is given in Fig. 12. 4.2.2. Simulation results The simulated network system has four priority classes. The dynamic wavelength assignment method defines the following quota values: qi 16, q2 12, q3 8 and q4 4. The connection requests at a node have the Poisson arrival rates CR and the connection holding time has the exponential distribution with mean u 100. A connection request has an equal opportunity of being one of the four
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Fig. 11. The traversed routing tree for the connection from N11 to N54.
priorities (i.e. 0.25 for each priority class). The destination of a request is randomly decided. We simulate three traffic load situations: fight, medium and heavy load. The light-load situation has CR 0.0015, i.e. r 0.15; the medium-load situation has CR 0.015, i.e. r 1.5; and the heavy-load situation has CR 0.15, i.e. r 15. The shown results are the averaged values over 10 runs under the identical load situation. Each run generates 6000 requests. In each run, the simulation records the blocking rate for each routing algorithm at the time when 1000, 2000, 3000, 4000, 5000 and 6000 requests are served. The results for the light, middle and heavy load situations are shown in Figs. 13–15, respectively. The figures illustrate that the backtrack algorithm outperforms the other two algorithms. 4.3. Cost effectiveness evaluation The previous simulation assumes that the network bandwidth has 16 wavelengths. It is intuitive to claim that as the number of wavelengths in a link increases, the probability of a request being blocked is smaller and smaller. However, in the current optoelectronic technology, the number of wavelengths carried by an optical routing node is in the range of tens to one hundred. To explore an optical routing node with N wavelengths, N router switches and O(N 2) edges are required to connect the multiplexers and de-multiplexers between them. Therefore, even the availability of wavelengths from an optical fiber is abundant, the utilization of the wavelengths is limited. To evaluate the cost effectiveness of the proposed backtrack routing and dynamic wavelength assignment method, simulations are conducted to study the relationship between the number of wavelengths and the averaged blocking rate in a system under various load conditions. In the simulation design, the number of wavelengths in a link, N, is a parameter that has the possible values of 16, 32
and 64. Given a value N, the simulation program equally divides N wavelengths into 4 parts, and sets q1 N, q2 3N/ 4, q3 N/2 and q4 N/4. The holding time for each connection request has the exponential distribution of mean 100 time units (u 0.01). The arrival rate of each priority class has the Poisson distribution r such that r r/u 0.5, 1.0, 1.5,…,25, are the controlled values. For each combination of (N, r), 10 runs are generated and simulated. In each run, the time taken to simulate is the time when 10 000 requests are generated. The blocking probability is computed as well. The detailed results are shown in Fig. 16. From Fig. 16 we can see the proposed algorithm and the designed simulations provide a way for the optoelectronic engineers to evaluate the cost effectiveness of the whole system. Given a tolerable value of blocking rate, the designers have the options to choose the optical routing nodes with the most economic number of wavelengths under various predicted load traffic. 4.3.1. Evaluation of connection latency The time taken to find a path by the FR is 兩Ef兩*t1, in which 兩Ef兩 is the number of hops along the path and t1 indicates the time taken by the wavelength assignment to allocate a wave-
Fig. 12. The base routing algorithms.
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Fig. 13. The blocking rates for FR, FAR and Backtrack algorithms in a light-load situation.
Fig. 14. The blocking rates for FR, FAR and Backtrack algorithms in a medium-load situation.
length within one hop. Similarly, the time taken by the FAR is 2*兩Ef兩*t1. As for the backtrack algorithm, the best-case complexity is equivalent to that of the FR. However, the worst case happens when all the links in the routing tree are visited. The complexity will be 兩En兩*t1, in which 兩En兩 is the number of nodes in the routing tree. Note that the routing tree is built on-the-fly. The storage requirement in each routing table is illustrated in Fig. 3(a). It is not necessary to keep the routing trees for all destinations.
Fig. 15. The blocking rates for FR, FAR and Backtrack algorithms in a heavy-load situation.
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Fig. 16. The relationship between the load, the number of wavelengths and the blocking probability.
It can be seen that in a lightly-loaded situation a path can be easily found. The complexity for the backtrack routing at that case will be approximately equal to that of the FR. On the other hand, in a heavily-loaded situation, the FR and FAR are vulnerable to find a path within one or two trials. However, it is still feasible to find a path for the backtrack routing. In a given situation, the order of traversing the routing tree determines the complexity of the proposed algorithm. The searching of a feasible lightpath could be speeded up if information of the wavelength usage of the subtree is kept in the intermediate nodes. When the search backtracks to an upstream intermediate node, it could be more beneficial to try a downstream link with less traffic. Our future work is to investigate how to maintain the useful information.
5. Conclusion In this paper, we consider the wavelength assignment and the routing problems in the WDM networks. The connection requests to the WDM networks are prioritized according to their QoS requirements. We propose two strategies that use the priorities of the requests to perform the wavelength assignment. They are the static and the dynamic strategies. The static assignment preallocates a set of wavelengths for each priority class of requests and chooses one wavelength for a given request based on its priority and the available wavelengths for the given priority. The dynamic wavelength assignment selects a wavelength dynamically among all available wavelengths, but it controls the number of assigned wavelengths for a given priority class of requests by a pre-defined quota. Simulation results show that the dynamic strategy obtains a lower blocking rate than the static one does. The proposed solution to the routing problem is the backtrack routing. The backtrack routing algorithm along is integrated with the wavelength assignment to reduce the overall blocking rates in the system. The backtrack routing method builds a route tree for a given connection request. During the setup of a route, backtrack is allowed when some
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wavelength can not be assigned in a link. In the simulations, the proposed solution is compared to the fixed routing and the fixed alternate routing algorithms. The results show that our algorithm performs better in the light, medium and heavy-load situations. Experiments are also conducted to study the relationship among the number of wavelengths in a link, the load traffic in the system and the averaged blocking rates, based on the proposed solutions.
[5] [6]
[7]
[8]
References [9] [1] G. Sudhakar, N. Georganas, M. Kavehrad, Slotted aloha and reservation aloha protocols for very high-peed optical fiber local area networks using passive star topology, Journal of Lightwave Technology 9 (1991) 1411–1422. [2] B. Mukherjee, WDM-based local lightwave networks, part 1: singlehop systems, Network, May (1992) 12–27. [3] G.I. Papadimitriou, D.G. Maritsas, HARP: A hybrid random access and reservation protocol for WDM passive star networks, in: Proceedings of IEEE GLOBECOM 1994, pp. 1521–1527. [4] S. Tridandapani, J.S. Meditch, A.K. Somani, The MaTPi protocol:
[10] [11]
[12]
masking tuning times through pipelining in WDM optical networks, in: Proceedings of IEEE INFOCOM 1994, pp. 2140–2150. A. Acampora, M. Karol, M. Hluchyu, Terabit lightwave networks: the multihop approach, AT & T Tech Journal 66 (6) (1987) 21–34. N. Huang, H. Liu, An isochronous and asynchronous traffic scheduling algorithm for dual-star WDM networks, Journal of Lightwave Technology 14 (3) (1996) 273–287. N. Huang, G. Liaw, C. Chiou, On the isochronous paths selection problem in an interconnected WDM network, Journal of Lightwave Technology 14 (3) (1996) 304–314. C. Chen, L.A. Wang, S. Kuo, A wavelength encoded multichannel optical bus for local area networks, Journal of Lightwave Technology 14 (3) (1996) 315–323. R. Ramaswami, G.H. Sasaki, Multiwavelength optical networks with limited wavelength conversion, in: Proceedings of INFOCOM 1997. A. Birman, Computing approximate blocking probabilities for a class of all-optical networks, in: Proceedings of INFOCOM 1995. A. Birman, A. Kershenbaum, Routing and wavelength assignment methods in single-hop all-optical networks with blocking, in: Proceedings of INFOCOM 1995. A. Girard, Routing and dimensioning in circuit switched networks, Addison-Wesley, Reading, MA, 1990.