CHAPTER-III WAVELENGTH ROUTING ALGORITHMS

CHAPTER-III WAVELENGTH ROUTING ALGORITHMS

Introduction A wavelength routing (WR) algorithm selects a good route and a wavelength to satisfy a connection request so as to improve the network performance. It is also referred to as a routing and wavelength assignment (RWA) algorithm. In a large network, RWA algorithms based on centralized control are not desirable. Distributed control is a viable alternative which can overcome the shortcomings of the centralized algorithms. Several distributed control protocols for wavelength routing are presented in this chapter. In general, longer-hop connections are subject to more blocking than shorter-hop connections. The fairness among the individual streams using connections with different hop lengths is an important problem in WDM networks. 3.1. CLASSIFICATION OF ROUTING & WAVELENGTH ASSIGNMENT TECHNIQUES ALGORITHMS Wavelength-routed WDM networks which are circuit-switched in nature are primarily targeted to wide area networks. A connection request or demand requires that a connection be established from a node, called the source node, to another node, called the destination node. A connection is released when it is no longer required. In the wavelength-routed WDM networks under study, a connection is realized by a lightpath. A lightpath is uniquely identified by a physical route (path) and a wavelength. The wavelength continuity constraint imposed by these networks requires that the same wavelength must be allocated on all the links of the chosen route from source to destination. This constraint is unique to WDM networks. 67

The wavelength continuity constraint degrades the overall network performance. It increases the probability of blocking connections. The connection blocking probability is defined as the percentage of connections rejected. A connection can use only a wavelength-continuous route. In a dynamic traffic environment, wherein connection requests arrive to and depart from the network dynamically in a random manner, the following situation may arise: A connection request for the node pair <.9, d> finds that a route is available, but is blocked as the route is not wavelength-continuous. This situation is depicted in Fig.3.1. Figure 3.1: Effect of the wavelength continuity constraint on pocket blocking The figure shows two lightpaths pi and p? on wavelengths w0 and wt respectively. Assume that there are only two wavelengths per fiber. Suppose that a request arrives at node 0 for a connection to node 2. There exists a route from node 0 to node 2. But, for this route, on the first link (0 -> 1) wavelength w/ is free, and on the second link (1 -> 2) w0 is free. Therefore, this route is not wavelength-continuous and consequently the request is blocked. If node 1 is equipped with wavelength conversion capability, for the given scenario, the 68

request can be accommodated. If every node in the network has full wavelength conversion capability, then it will yield the same performance as that of a conventional circuit-switched network. When a connection request arrives, a wavelength routing (WR) algorithm is used to choose a lightpath to satisfy the request. A WR algorithm has two components, route selection and wavelength selection. A WR algorithm is also known as a routing and wavelength assignment (RWA) algorithm. The route is chosen based on some cost criterion such as the hop length, and the wavelength is chosen based on some criterion such as wavelength usage factor in the entire network. WR algorithms are classified based on their route and wavelength selection methods. These two methods can be used in any order, one after the other or jointly. However, the order of selection has an effect on performance (5). A WDM network with N nodes and W wavelengths per fiber can be represented as a layered graph G (V, E). Here, V is the set of vertices and E is the set of edges. The graph G has W subgraphs (layers), G < 0 < W, each corresponding to one wavelength. A vertex in a subgraph G, corresponds to a node in the network and an edge corresponds to a wavelength i on the fiber connecting the end nodes of the edge. A route from one node to another node on wavelength i can be found from the subgraph G as and when required. 69

3.1.1. Route Selection Schemes Route selection algorithms can be broadly classified into three types: (i) fixed routing (FR), (ii) alternate routing (AR), and (iii) exhaust routing (ER). (i) In the FR algorithm, for every node pair p, only one candidate route Rp is provided. A candidate route for a node pair is fixed and does not change with changing network traffic conditions. (ii) In the AR algorithm, for every node pair p, a set of K candidate routes (more than one) is provided. The candidate routes are denoted by Rp0. Rpj,... RPK -1. When a connection request arrives for a pair p, one of the candidate routes in Rp will can be selected. (iii) In an ER algorithm, there is no restriction on selecting a route. For a given node pair p, a route among all possible routes for p is chosen. The cost of a route is usually computed based on its hop count, delay or congestion. If there exists no wavelength which is free on all the links of a route, then the cost of the route is infinity. Otherwise, its cost is finite. The cost of a route can be measured by its congestion. The congestion of a route depends on the number of wavelengths available on the entire route. The greater the number of free wavelengths, the lesser the congestion. 70

3.1.2. Wavelength Selection Schemes The wavelength selection schemes can be broadly classified into (i) most-used (MU), (ii) least-used (LU), (iii) fixed-order (FX), and (iv) randomorder (RN), depending upon the order in which the wavelengths are searched (14). i. The MU scheme gives preference to the wavelength which is used on the greatest number of links in the network. The wavelength are searched in descending order of use. The MU algorithm attempts to pack the lightpaths tightly into wavelengths so that many wavelengthcontinuous routes will be available for the connection requests which will arrive later. It is more suitable for centralized implementation and is not easily amenable to distributed implementation. ii. The LU scheme prefers the wavelength which is used on the least number of links in the network. It attempts to distribute the load over the wavelengths uniformly. The wavelengths are searched in ascending order of use. The intuitive idea behind this algorithm is that a shorter route can be found on a least-used wavelength when compared to the most-used wavelength. This leaves many links free for use by requests arriving later. This algorithm is also more suitable for centralized implementation and is not easily amenable to distributed implementation. iii. The FX scheme searches the wavelength in a fixed order. All the wavelengths are indexed, and they are searched in the order of their 71

index numbers. The first free wavelength found while searching in this order is preferred. By choosing the first free wavelength, the FX algorithm attempts ;to achieve performance closer to that of the MU algorithm. iv. The RN scheme searches the wavelengths in a random order. All the wavelengths are indexed. Every permutation of these indices is equally probable when generating the order randomly. The idea here is to spread the load uniformly on all the wavelengths. Consider a network which uses four wavelengths w0, wt, w2 and w3 on a fiber. Suppose that at some instant of time the wavelengths w0, wt, w2 and w3 are used on 2, 5, 1, and 4 number of links, respectively, and a new connection request arrives for a pair <s,d>. Assume that a route R is chosen for this pair and on this route R, the wavelengths w0, w2, and w3 are free. For this scenario, let us look at the order in which each of the wavelength selection algorithms will search before choosing a wavelength. The MU scheme attempts to search in the order w!? w3, w0, and w2 and selects the wavelength w3, as it is the most-used wavelength. The LU scheme attempts to search in the order w2, w0, w3, and W and selects the wavelength w2. as it is the least-used wavelength. The FX scheme attempts to search in the order w0, w!? w2, and w3 and selects the wavelength w0, as it is the first free wavelength. 72

The RN scheme attempts to search in an order, say, for example, wb w2, w3, and w0 and selects the wavelengths w2, as it is the first free wavelength. 3.2. RWA ALGORITHMS Having discussed various schemes for route selection and wavelength selection, we present the wavelength routing algorithms available in the {* literature listed below. These algorithms select the routes using some cost measure and then select one wavelength on the selected route from among the available wavelengths using a wavelength selection algorithm. In this case, the cost value of a route depends on the wavelength being considered (1). 1. Fixed Routing (FR) 2. Fixed Alternate Routing (FAR) 3. Exhaust Routing (ER) 3.2.1. Fixed Routing Fixed Routing is the simplest of all the algorithms. For every node pair p in the network, a fixed route Rp is computed offline. When a new fixed request arrives for a connection between node pair p, the algorithm checks whether some wavelength is free on all the links of Rp. If no wavelength is free on this fixed route, then the request is blocked. If more than one wavelength is free, a wavelength selection algorithm can be used to choose the best wavelength. The key advantage of this algorithm is that it is faster and hence the connection setup time is shorter. If H is the length of the longest fixed route for any node pair, then this algorithm runs in O(HW) time 73

units. The main drawback of this algorithm is that it results in poor network performance. This is because it searches only one route for a given route p, even though many routes may exist for this pair. A situation may arise wherein no wavelength is free on the route Rp but some wavelengths are free on some other route connecting the same pair of nodes. In this case the request will be blocked. Under light load conditions this algorithm performs slightly better. As the offered load in the network increases, the algorithm s performance starts degrading. The topology and connectivity of the network greatly influence the network performance. In a densely connected network, where there are many routes available for a pair of nodes, this algorithm performs poorly (7). Consider a network with 5 nodes, 6 links, and 4 wavelengths per link as shown in Fig. 3.2. Assume that a new request arrives at node 0 for a connection to node 4. Let p denote node pair <0,4>. The set of links on which each of the wavelength is available is given by wo : lo, fn I3 w, : 10, L, L w2 : 13 w3 : I0J3 Let the fixed route Rp used for p by this algorithm be Rp : lo»13 74

This route comprises two links 10 and 13. The set of available wavelengths on each of the link is 10 : w0, wbw3 13 : w0, w2, w3 Two wavelengths w0 and w3 are available on route Rp. Of these, w0 is used on 3 links and w3 is used on 4 links. To select one wavelength among these two, we can use an appropriate wavelength selection algorithm. The algorithm MU will choose w3, LU will choose w0, FX will choose w0, and RN will randomly choose one of the wavelengths. Figure 3.2: An Example network to illustrate RWA algorithms. 3.2.2. Fixed Alternate Routing Fixed alternate routing algorithm is an extension of the FR algorithm. It basically used the AR routing algorithm. For every node pair p, a set of K candidate routes (more than one) is provided. The candidate routes are denoted by Rpo, Rpi.... Rpk - 1- These routes are computed offline. The set 75

of candidate routes provided for a node pair is a subset of all the possible routes for the node pair, When a connection request arrives for the pair p, its candidate routes are searched in a fixed order and the first candidate route with a finite cost is selected. The hop count and delay are normally used as cost metric. If no route can be found with a finite cost, that is, no wavelength is free on any of the candidate routes, then the request is blocked. If more than one wavelength is free on the chose route, a wavelength selection algorithm can be used to choose one of them. Although this algorithm is slightly more complex than the FR algorithm, it also has the advantage of simplicity and shorter connection setup time. If H is the length of the longest candidate route for any node pair, then this algorithm runs in O(KHW) time units. It has better performance than the FR algorithm, as it has a choice among more than one candidate route for any pair of nodes. However, the candidate routes provided for a node pair may not include all the possible routes. As a result, the performance of this algorithm is not the best achievable (2). Consider the network in Fig. 3.2 and node pair p:<0,4>. Assume that the following two candidate routes are provided for this node pair: Rp0 : l(r~^3 Rpi: lj >1$ >13 The set of links on which each of the wavelengths is available is given by W0 : l(b In b W : W2 : 1 j ^2? I3? ^4? 1 w3 : lb fb 15 76

From the above, the availability of wavelengths on different links can be determined: lo : w0 h : w0, W], w2. w3 12 : w0, w,, w2, w3 13 : wt, w2, w3 14 : w2 15 : w2, w3 The algorithm finds that on the first candidate route Rp0, no wavelength (that is, no single wavelength on all the links of the route) is free; and on the second candidate route Rp]5 two wavelengths, w2 and w3 are free. To select one wavelength from among these two, any of the wavelength selection algorithms can be used. The wavelength selection algorithms MU, LU and FX will choose the wavelengths w3, w2 and w2, respectively. 3.2.3. Exhaust Routing Exhaust routing algorithm is expected to yield performance than the FR and FAR algorithms. Exhaust routing does not predetermine the candidate routes for any node-pair. Instead, it keeps the network state information in the form of a graph. This state information is dynamic, and will keep changing depending upon the dynamically changing traffic. When a new connection request arrives for a pair p, it chooses the best route (based on some cost criterion) among all the possible routes. Thus, by exploring all the possible routes, it attempts to increase the acceptance rate of connections. As explained earlier, the network can be modeled as a graph with W subgraphs, each 77

corresponding to one wavelength. A conventional shortest-path-finding algorithm can be used to find the least-cost route on each of these subgraphs so the best one can be chosen. The chosen route and the corresponding wavelength can be used to honor the request. If the cost of a route is measured by its hop length, the breadth-first search algorithm can be used to find the shortest path. Since the ER method considers all possible routes, it results in better performance of the network (6). In spite of this merit, this algorithm has some shortcomings. The worst-case time complexity of the algorithm is 0(N W), and hence it is slower. Moreover, this algorithm is more suitable for centralized implementation and less amenable to distributed implementation. Consider again the network in Fig. 3.2 and node pair p:<0,4>. The set of links on which each of the wavelengths is available is given by w0 : 10, U wi : b, I2, U, I5 w2 : h, b W3 : h,u From the above, the availability of wavelengths on different links can be determined: 10 : w0 11 : wh w2 12 : wb w3 13 : w2 C : w0, wb w3 Is : w, 78

There is only one route which has a free wavelength Wi. This route, R, f > Is > I2 > I4, will be found by this algorithm. Note that none of the candidate routes used by the FR and FAR algorithms has a free wavelength. Therefore, for this scenario, these algorithms will block the connection request, whereas the ER algorithm will satisfy the request by allocating it is lightpath with route R and wavelength W. 3.2.3.I. Dijkstra s Algorithm: The algorithm proposed by Dijkstra to find a shortest path from a node v to another node d on a directed graph is explained. The edges are assumed to have non-negative weights. The nodes are numbered from 0 to N-l. We describe the algorithm to find the corresponding shortest path. The algorithm has a maximum of N - / iterations. At every iteration, the shortest distance to a new node is found. Let wt(y,x) denotes the weight of the edge from y to x, if it exists. At any iteration, the value of dist(x) denotes the length of the best-known shortest path from s to x, traversing through only the nodes whose shortest distance has been found thus far. A node is said to be permanently labeled if its shortest distance has been found. Otherwise, it is said to be tentatively labeled. Initially, node s is permanently labeled and all other nodes are tentatively labeled. Also, for a node x, the value of dist(x) is infinity if there is no edge from s to x; otherwise its value is set to wt(s, x). The node with the least dist ( ) value among all the tentatively labeled nodes is chosen and 79

labeled permanently. Let this node by y. Now the dist( ) value of every tentatively labeled node x is updated as dist(x) = min(dist(x), dishy) + wt(y,x)) The above procedure is repeated until node d is labeled permanently. There can be at most N - 1 iterations and in every iteration O(N) number of operations are performed. Therefore, the worst-case time complexity of this algorithm becomes Q(N~ j. The above algorithm can be extended to find the shortest path to every node from a given source node (15). Whenever a node (say, x) receives a new dist () value from another node (say, y), node y is declared the parent of node x. When node x is permanently labeled, its shortest path to the source can be found by traversing the parent node of every node starting from x until the start node is reached. algorithm. We consider below an example to illustrate the working of the Consider the graph shown in Fig. 3.3. The weight of the every edge is printed adjacent to it. We trace the algorithm to find the cost of a shortest path from node 0 to node 5. Initially node 0 is permanently labeled and all other nodes are tentatively labeled. The dist ( ) value of each of the tentatively labeled nodes is computed as dist (1) = 5; dist (2) = oc; dist(3) = 2; dist(4) = c; dist(5)=oc. 80

Among the nodes that are tentatively labeled, node 3 is chosen and is permanently labeled, as it has the minimum dist () value. The shortest path to node 3 is found to be 0 >3 whose dist () value is 2. Now, the dist () value of each of the other nodes is updated, if required. Since node 1 and node 5 have shorter routes through node 3, their dist ( ) values are changed. The new values are dist (1) =3; dist(2)=oc; dist(4)oc; dist(5)=8 Figure 3.3: An Example graph to illustrate shortest-path-finding algorithms Next, node 1 is chosen and is permanently labeled, as it has the minimum dist () value. The shortest path to node 1 is found to be 0 >3 >1, whose dist () value is 3. Now, the dist () value of each of the other nodes is updated, if required. Since node 2 and node 4 have shorter routes through node 1, their dist () values are changed. The new values are dist(2)=4; dist(4)=7; dist(5)=8 81

Next, node 2 is chosen and is permanently labeled, as it has the minimum dist ( ) value. The shortest path to node 2 is found to be 0~>3 >1 >2, whose dist ( ) value is 4. Now, the dist () value of each of the other nodes is updated, if required. Since node 4 has a shorter route through node 2, its dist () value is changed. The new values are dist(4)=6; dist(5)=8 Among the remaining nodes, node 4 is chosen and is permanently labeled, as it has the minimum dist ( ) value. The shortest path to node 4 is found to be 0 >3 > 1 >2 >4, whose dist ( ) value is 6. Since node 5 has a shorter route through node 4, its dist () value is updated as dist(5)=7. Now, only node 5 is tentatively labeled. It has the minimum dist ( ) value and is permanently labeled. The shortest path to node 5 is found to be 0->3-» 1 >2 >45, whose dist ( ) value is 7. The procedure then terminates as node 5 is the destination node. 3.2.3.2. Breadth-First Search: In WDM networks it is not unreasonable to state that using the hop length as the cost of a route does improve the network s performance in terms of the blocking probability of connections. This is because, when fewer hops are used, more hops will be available for requests arriving later. We can use a breadth-first search algorithm to find the path with the minimum number of hops. The time complexity of this algorithm is 0( E ), where E is the number of edges in the graph. In the worst 82

case, E is 0(N2), but for mo.st of the practical networks the number of edges is far less than the square of the number of nodes. We describe below the algorithm to find a hop length of the shortest path from a node 5 to node d. It can be easily modified to find the shortest path. We use a queue denoted by Q to keep certain nodes at various stages of the algorithm. Initially Q contains only the source node s, whose dist ( ) value is initialized to zero. Initially, every node is unmarked. The following procedure is repeated until node d appears at the front of Q (20). Remove the node from the front end of the queue Q. Let this node bey. Mark y is signify that the cost of the shortest path to it has been found. For every unmarked node x for which there exists an edge from node y, update the dist ( ) value as given below and add it to the rear end of Q. dist(x) = dist(y) + 1 The above algorithm can be extended to find the shortest path to every node from a given source node. When a node (say, x) receives a new dist () value from another node (say, y), node y is declared the parent of node x. When node x is marked, its shortest path to the source can be found by traversing the parent node of every node starting from x until the start node is reached. Consider again the graph shown in Fig. 3.3. The weight of the all edges is assumed to be 1 as the hop length is used as the cost metric. Let the source 83

be node 0 and the destination be node 5. The contents of Q at various stages are Q: 0 dist(l)=l: dist{3) = 1 Q: 1 3 dist(2)=2; dist(4) = 2 Q: 3 2 4 dist(5) = 2; Q: 2 4 5 Q: 4 5 Q: 5 Initially, Q has only node 0. It is removed from Q and is marked. It has two adjacent unmarked nodes 1 and 3. These nodes are added to the queue at the rear end with dist () value 1. The value 1 is assigned because dist (0) is 0. Now, node 1 appears at the front of Q. It is removed from Q and is marked. The shortest path to node 1 is found to be 0-»l, whose length is 1. Node 1 has two adjacent unmarked nodes 2 and 4. These nodes are added to the queue at the rear end with dist () value 2. The value 2 is assigned because dist(l) is 1. Now, node 3 appears at the front of Q. It is removed from Q and is marked. The shortest path to node 3 is found to be 0-»3, whose length is 1. Node 3 has one adjacent unmarked node 5. Node 5 is added to the queue at the rear end with dist () value 2. The value 2 is assigned because dist (3) is 1. Now, node 2 appears at the front of Q. It is removed from Q and is marked. The shortest path to node 2 is found to be 0 > 1 >2, whose length is 84

2. Node 2 has no adjacent unmarked node and therefore no new node is added toq. Now, node 4 appears-at the front of Q. It is removed from Q and is marked. The shortest path to node 4 is found to be 0-»l >4, whose length is 2. Node 4 has no adjacent unmarked node and therefore no new node is added toq. Now, node 5 appears at the front of Q. It is removed from Q and is marked. The shortest path to node 5 is found to be 0-*3->5, whose length is 2. Since node 5 is the destination node, the task is accomplished and the procedure ends. 3.3. FAIRNESS AND ADMISSION CONTROL An important issue in WDM networks is the wide gap in blocking probability of connections with different hop counts. Usually an RWA algorithm favors connections with shorter-hop counts than those with iongerhop counts. In other words, it blocks more longer-hop connections than shorter-hop connections. This leads to the fairness problem. In order to improve fairness among connections with different hop counts, an appropriate control mechanism is required to regulate admission of connection requests. There will be a blocking probability associated with each source-destination pair and the corresponding arrival stream. In addition, there will be a global performance index, the average of all stream blocking probabilities weighted by the intensities of the traffic streams. The global measure, the network 85

average blocking probability, reflects the performance of the network as a whole, while the individual steam blocking capabilities reflect the grade of service for an individual customer. Therefore, both the global measure and individual measures are to be considered in evaluating an RWA algorithm. An algorithm which results in a large variance in individual blocking probabilities is said to be unfair. The fairness among individual streams can be improved at the cost of a loss in global performance. Any fairness improvement algorithm should ensure that the global performance loss is kept to a minimum (17). The wavelength continuity constraint increases the blocking probability of connections and thus degrades network performance. An RWA algorithm generally favors shorter-hop connections, if no appropriate measures are taken to improve fairness. In distributed routing, the reservation conflict (contention for resources such as wavelength channels) among different requests further widens the gap in the individual performance of connections. This reservation conflict occurs while searching a route for the availability of a free wavelength. Wavelength converters can be employed at strategic nodes to reduce the blocking of longer-hop connections. Although converters can improve the performance of longer-hop connections, they cannot solve the fairness problem altogether, as the shorter-hop connections also benefit from the presence of converters and also due to the nonoptimal placement of converters. In addition, converters add substantially to both the cost and 86

complexity of the network. Wavelength rerouting (dealt with in detail in Chapter 4) is another possible mechanism that can improve the performance of longer-hop connections. Wavelength rerouting moves a few existing lightpaths to new wavelengths to create a wavelength continuous route for a new connection request. Like wavelength converters, wavelength rerouting solves the fairness problem only partially. It is required that a fairness improvement algorithm have the following properties, in addition to improving fairness. 1. The loss in global performance must be within an acceptable limit. 2. Wavelength channel utilization must be high. 3. The algorithm must be flexible enough to choose a desired trade-off between fairness level and global performance loss. 4. The penalty incurred by shorter-hop connections must not be so high that their blocking probability becomes more than that of longer-hop connections. In other words, shorter-hop connections must not be overpenalized. 5. The algorithm must be suitable for networks with different degrees of connectivity. In particular, it must be useful for sparsely connected networks, where the fairness problem is more relevant. 87