Multihop Routing and Wavelength Assignment Algorithm for Optical WDM Networks

We propose a new routing and wavelength assignment scheme that improves the blocking probability of WDM networks and offers a very good utilization of the networks resources. This heuristic results in high quality of service, prioritization of the LAN networks and lower installation costs compared with the traditional RWA algorithms applied in WDM networks. It is based on the distributed Dijkstra sparse placement routing algorithm, first-fit wavelength reservation and traffic multiplexing. We apply load balancing and a sparse electronic switch placement algorithm during the process of finding the optimal lightpath in order to reduce the number of dropped lightpath sessions to zero, minimize the number of opaque nodes and maximize the utilization of the network.


Introduction
New customer-oriented applications and triple p lay services are rapidly pushing the development of telecommun ications. As a result, there is an increasing demand fo r network bandwidth and quality of service [1]. An optical network based on the WDM (Wavelength Div ision Multiplexing) technique is considered as a very promising approach for developing future large bandwidth networks. A WDM optical network consists of nodes interconnected by optical fibers, wh ich transfer optical signals at different wavelengths, the so-called lightpaths. These networks are deployed main ly as backbone networks for nationwide or g lobal coverage. The nodes in these networks actually represent the access stations for different LAN networks. The future of optical W DM networks are all-optical networks, where the lightpath is routed from the source node to the destination node without undergoing optical-electrical-optical (O/ E/O) conversion at any intermediate node, which means that the signal remains in the optical domain.
However, in the current phase, these networks are facing many technical difficulties [2][3][4][5][6]. One o f them is the problem of overcoming the physical impairments introduced by long-haul fibers and cascading optical co mponents such as erbiu m-doped fiber amplifiers (EDFA) and optical crossconnects (OXC). Cont ributing facto rs include opt ical The second problem of W DM networks concerns the routing and wavelength assignment (RWA) process, which consists of two different underlying problems: routing and wavelength assignment. In wavelength-routed networks data are transferred along lightpaths established between the source node and the destination node. A lightpath in a WDM network is created if and only if there is an availab le route and available wavelength. Both steps must succeed for a lightpath to be established. This involves routing and signaling to reserve a wavelength on each link along the selected path [8]. A lightpath connection request may be blocked on the path because there is no wavelength available on any of the links along the selected path. In order to get really optimal solutions, it is necessary to solve both problems. That is why an efficient and swift RWA algorith m must be imp lemented bearing in mind the objective that all network resources are optimally utilized. The selection of the route must be such that all the traffic is evenly balanced between all network resources.
The third problem is related to the blocking probability. When the traffic load is excessive, the blocking probability is very high. To prevent these situations when some link is fully utilized and there are no resources to provide service over that lin k, the alternative path wh ich will avoid that link must be found. But, if the alternative route does not provide the solution this could be handled by dividing the nodes of the WDM network into several groups according to the priority. The LA N network connected to the node that has a higher priority will be given advantage during the process of reserving network resources over the LA N network that has a lower priority. All traffic for which the resources have not been found during routing and wavelength assignment can be mu ltiplexed over the same wavelength using some of the next generation SONET/SDH technologies [9]. In this way, the probability of b locking will be much lower. The drawback of this solution is that a lower bit stream will be offered to some of the low priority nodes. In other words, some of the sessions will not be blocked, but they will have a lower bandwidth.
This paper deals with all the above mentioned problems that WDM networks are facing today. We propose an efficient routing and wavelength assignment heuristic, which at the same time, min imizes the blocking probability of lightpaths in the WDM network and selects the route for a given physical topology in such a manner that all t raffic is evenly balanced between all network resources. For all traffic that has a lower priority and for which the RWA algorith m d id not find the path, we propose traffic mu ltip lexing wh ich will p revent blocking of lightpaths. To our best knowledge, this is the first research work in investigating routing and wavelength assignment for optical WDM networks together, which optimizes quality of service and capital expenditure of networks based on the distributed Dijkstra sparse placement routing algorith m, first-fit wavelength reservation and traffic mu ltip lexing.
In [10] the multihop routing and wavelength assignment algorith m is applied, but signal degradation in the system and traffic mu ltiplexing is not considered. Reference [11] proposes a graph transformation method for performing RWA in networks with sharable wavelength conversion. Given a network with N nodes and W wavelengths, they formed an au xiliary graph with 2NW vertices in which each vertex represented entering or exiting the node on a given wavelength channel. The RWA was performed by use of Dijkstra's algorithm to find the shortest path through the auxiliary graph. In [12] it is proposed that RWA could be divided in three separate steps: routing, selection of regeneration sites and wavelength assignment. The RWA problem is also analyzed in [7], but only for transparent optical networks. The wavelength assignment scheme that improves the blocking probability of WDM networks that use limited-range wavelength converters is analyzed in [13]. The sparse electronic placement algorithm is discussed in [2,5] in which a number of opaque nodes used for regeneration are sparsely placed in the network. Reference [3] gives an excessive overview of recent studies regarding translucent optical networks.
The rest of this paper is organized as follows: in Section 2, we describe the network and switch architecture of translucent optical networks; in Sect ion 3, a description of the routing and wavelength assignment algorith m is made. We address the statement of the problem in Section 4, present the numerical results of the simu lation in Section 5 and give conclusions in the last section.

Network and Switch Architecture
Optical networks, in which each node routes some lightpaths transparently, while others go through optical-electrical-optical 3R-regeneration, are known as translucent. The sparse placement algorith m defines at which node in the network to place an electronic core capable of 3R-regeneration. The placement should provide fo r all physical impairments in the lightpath to be compensated and for all traffic in the network to be balanced. A translucent WDM optical network consists of a number of nodes interconnected by fiber links. Each of the links is capable of carrying W wavelengths. Long fiber lin ks may be interspersed with inline optical amp lifiers (e.g. EDFA ). We assume that two ad jacent nodes are connected with one pair of unidirect ional fibers to provide the bi-direct ional connectivity.
A lightpath starts fro m the source node transmitter and terminates at the destination node receiver. The sparse regeneration node model allows all-optical switching in all nodes, while some of the nodes in the network are 3R-regeneration capable. When a lightpath is routed through intermediate regenerators at these regeneration capable nodes, it is divided into several frag ments by the O/E/O regeneration. This process is planned in such a manner that the node receives the optical signal having the power sufficient for accurate decision.
The RWA algorith ms and simulation processes are applied in this paper on the following two broadly used topologies of the optical networks [4,5,16]: 15-node/21-link Pacific Bell network topology and 24-node/43-link USANET network topology.
Translucent networks with sparsely placed opaque nodes contain two types of nodes, opaque and transparent. Opaque nodes can regenerate optical signals and convert wavelengths electronically, while transparent ones have the optical switching function only. At the opaque node, all arriving signals are detected and processed in the electronic domain. This node can also perform wavelength conversion, because it applies the switched outgoing signal to a new laser source. On the contrary, the all-optical t ransparent node provides a purely optical switching function for incoming optical signals, but cannot perform signal 3R-regeneration. Sparse regeneration uses the O/E/O regeneration resources sparsely distributed in the network.
Each network node consists of an optical core (optical crossconnect -OXC) and an access station. An OXC consists of mult iplexers, optical switches, input/output amp lifiers, taps and demultip lexers. Optical trans mitters and receivers are in an access station. Opaque nodes are assigned a number of optional electronic processing modules (electronic core). At each node, the wavelengths of the inco ming fiber links are demult iplexed and switched in the OXC, and then mu ltip lexed onto the outgoing fiber links [3,4]. In case of a regeneration capable node, the signal is sent to the electronic core where all input optical signals are converted to the electronic form, then processed at the 3R-regeneration unit (retiming, reshaping, reamp lificat ion), and finally converted back to optical signals, which is the end of the regeneration process.
The electronic switch is also capable of mult iplexing the traffic fro m d ifferent nodes. The traffic is buffered, segmented and packed into payloads. The payloads from different clients may be mu ltiplexed using either a sequential round-robin method or a queuing schedule [9]. The mu ltip lexing method choice depends on the size of client frames and on the frequency of arrival. Round-robin is typically used when client frames to be mu ltiplexed are almost synchronous and preferably of the same length. A queuing schedule is used when client frames are asynchronous, there is substantial variability in frame length, and there is a random arrival of packets. In such cases, the incoming client frames need to be buffered, retimed to reduce jitter, and then mult iplexed. One of the benefits, but also weaknesses of the queuing schedule is that it requires a buffer length with marg in and an intelligent scheduler algorith m.

Routing and Wavelength Assignment
Formally, the RWA problem can be stated as follows: given a set of lightpaths that need to be established within the network, and given a constraint on the nu mber of wavelengths (fiber capacity constraint), determine the routes over which these lightpaths should be set up and also determine the wavelengths which should be assigned to these lightpaths so that the maximu m number of lightpaths is established [14]. While the shortest path routes (according to distance, available resources, or by some other criteria) may often be preferab le, this choice may somet imes have to be sacrificed in order to allow more lightpaths to be set up. In general, good RWA algorithms allow several alternate routes for each lightpath that needs to be established. Lightpath sessions that cannot be set up due to constraints on routes and wavelengths are said to be blocked. That is why it is very important to imp lement the routing algorith m which will find the shortest path route according to several criteria, but also several alternate routes in case that resources on the shortest path are already reserved.
RWA of lightpaths in optical networks is usually done in two steps. The first step tries to find a route between the node pair, and the second assigns wavelengths for links of the route. The literature suggests different solutions, with separate or simu ltaneous handling of these steps.. One approach is to route all connections first, and then assign wavelengths to them as a separate step. With this strategy, it is possible to have no availab le wavelengths for the found route. Another approach is to comb ine the steps so that routing is tied to a particular wavelength. This latter approach is typically acco mplished by starting with a particular wavelength and reducing the network topology to only those links on which this wavelength is available. The routing algorith m is then run on this pruned topology. If a suitable route cannot be found, another wavelength is chosen and the process is run through again for the matching topology. With this combined approach, a free wavelength is guaranteed for any found route [12]. In this paper, we have applied the combination of the first and second approach: we start with separate steps first, but if we find insufficient network recourses we tie the routing algorithm to the wavelength assignment in order to find an alternate solution.

Routing Algorithm
The purpose of the routing algorith m is to select an appropriate route from source to destination among all existing routes in the network. If there is more than one choice in selecting the route, the controller can select the route according to some heuristics, such as the shortest path routing, load balancing routing, etc. We used both criteria in the routing algorithm.
Given that a lightpath is to be set up between a source node and a destination node, we consider the distributed Dijkstra's shortest cost (weight) path algorithm to be capable of determin ing the best route with a carefully chosen way to assign a cost to each link [15]. For the problem under consideration, the overall objective is to optimize the balance between the lightpath lengths and the efficient usage of the network traffic capacities.
For each lightpath demand, we assign a weight ij c to each network lin k (i, j), wh ich is defined as: where ij a and W denote the number of currently available and the number of total wavelengths on the link (i, j), respectively, and ij l is the physical link length in kilo meters [4].
As we have previously emphasized, the longer an optical signal travels over a transparent path (path without opaque nodes) and the more switching nodes the signal passes through, the higher the signal quality degradation is. Therefore, in the paper [6,16] it is proposed to use two parameters described as follows: Lhop is the acceptable maximu m t ransparent path length (there are no opaque or regeneration nodes on the route) measured in hops (the number of intermed iate nodes passed through) and Llen is the acceptable maximu m geographical transparent length of the optical signal in kilo meters. If the length of the route is larger than the length Llen or the service signal travels mo re hops than Lhop, the end receiver will not detect the service signal. Then, the lightpath should be regenerated at intermediate nodes.
On the other hand, if we use only this criterion, some of the links in the network will suffer fro m excessive traffic, and some other lin ks will occupy only a small p roportion of the bandwidth. In order to utilize the network efficiently, we take the nu mber o f currently occupied paths as the current cost (weight) of the lin k, and for any additional path transported by that link the weight is increased by the factor . The route for a new lightpath is the least weight route between the source-destination node pair. In other words, this algorithm attempts to even out the utilizat ion of lin ks in the network and the lightpath distance. The selection of nodes which will be capable of performing O/E/ O conversion is made based on the following two criteria: destination signal quality and uniform traffic distribution across the network. The obtained result is a translucent optical network [16].

Wavelength Assignment
The simp lest wavelength-routed networks assign one wavelength to all links of the connection between the source node and the destination node. This requirement is known as the wavelength continuity constraint. This constraint can be avoided by use of wavelength converters at intermediate nodes. A wavelength converter is a device that converts the input wavelength λi into a d ifferent output wavelength, λo. In wavelength-routed networks with wavelength converters, a lightpath can be established even if there is no common wavelength on all links along the path. This approach can improve the blocking probability and the efficient utilization of wavelengths [13]. That is why we have used the wavelength converters in the opaque nodes of the optical network fo r improving the blocking probability.
There are several wavelength assignment heuristics that have been proposed in the literature: Random, First-Fit, Least-Used, Most-Used, Min-Product, Least Loaded, Wavelength Reservation, etc [14]. These heuristics can be implemented and combined with different routing schemes.
There are schemes which attempt to reduce the overall blocking probability for new connections and there are some which aim to reduce the blocking probability for connections that traverse more than one link. In this paper we use a combination o f First-Fit and Wavelength Reservation assignment heuristics.
In the First-Fit wavelength assignment heuristic all wavelengths are numbered. When searching for available wavelengths, a lo wer numbered wavelength is considered before a h igher nu mbered wavelength. The first availab le wavelength is then selected. The computation cost of this scheme is low because there is no need to search the entire wavelength space for each route [17]. In the Wavelength Reservation heuristic a given wavelength on a specified link is reserved for the traffic stream, usually a mult ihop stream. For examp le, in Fig. 2, the wavelength λ1 on the lin k (8,9) may be reserved only for the connection from node 6 to node 10 (it has priority over the connection between nodes 8 and 9); thus, a connection request from node 8 to node 9 cannot be set up on λ1 on link (8,9). In th is case the alternate route must be found for connection between nodes 6 and 10. This scheme reduces the blocking for mu ltihop traffic.
In this paper we have co mb ined the two schemes. We have taken the following algorithm: λi (1≤i≤W) is assigned to the lightpath if the fo llo wing conditions are fulfilled: λi is available along the selected route, total transparent path length is shorter than the transparent length Llen, nu mber of transparent nodes on the lightpath is less than Lhop and the route is not reserved for a higher priority connection. If some of the conditions are not satisfied, another route is searched for.

Problem Statement
The optical network is represented by an oriented mu ltigraph G(V,E) with a node set V = {n1 ,n 2,…,nN} and an arc-edge set E = {l1 ,l2 ,…,lL} labeled with the geographical fiber lin k distance, where each edge is associated with a two directional fiber. Throughout the paper, we assume that all fiber lin ks have the same capacity, i.e. the number W of availab le wavelengths. The multihop routing and wavelength assignment algorithm with minimu m blocking rate (mul_ RWA_min_BP) which we propose in this paper works as follo ws.
For each connection request from source to destination, we attempt to establish a lightpath, i.e. a sequence of wavelength subpaths. In each subpath we can assign the same wavelength and the set of subpaths define a path fro m source to destination, subject to the following set of constraints [10]: (i) collision-avoidance constraints, i.e. two different lightpaths using the same fiber must have distinct wavelengths; (ii) fiber capacity constraints, i.e. the number of lightpaths using the same fiber should not exceed the capacity of the fiber defined by the maximu m nu mber of wavelengths per fiber; (iii) hop constraints, i.e. no more than Lhop transparent nodes should be on the path; (iv) length constraints, i.e. the transparent path should not be longer than Llen in kilo meters.
Distributed Dijkstra algorith m provides an optical network with the necessary number of nodes capable of performing O/ E/ O conversion, with routes between any two nodes [16]. For the first pair in the sequence of priority nodes, the chosen route is observed and every link of the chosen route is searched for the same available wavelength. The algorith m proceeds by checking the wavelength number 1, followed by nu mber 2 and, finally W. If the wavelength is available, the algorith m reserves it. Otherwise, the algorithm returns and finds the last opaque node in the route, and reserves the first available wavelength between that node and the destination. But, if it is still unable to find an availab le wavelength, it goes further back to the next opaque node and reserves an available wavelength between these two opaque nodes, repeating the procedure until it reaches the source. If, at any point of the route, it is unable to find an availab le wavelength which would enable the task fulfillment, the algorith m is interrupted. Once the algorithm is interrupted, the link for wh ich no availab le resources have been found in order to perfo rm the connection is removed fro m the network (by setting the link price to infinity) and Dijkstra algorith m is set off once again to determine a new route. Once the route is determined, the whole procedure starts all over again, i.e. the same available wavelength is looked for throughout the route, and so forth. If enough available resources cannot be found in this route either, another link is removed fro m the network and the Dijkstra algorith m called for once again. Such procedure is repeated until a route with sufficient resources is found or until the Dijkstra algorith m reports that there are no available routes between the two nodes.
If there are no available routes between the two nodes, we return to the initial route and observe whether the source and destination are opaque nodes. If so, the signal is mu ltiplexed and packed together with other signals over the same wavelength. If not, the opaque nodes closest to the source and destination are searched for and, if there is an available wavelength to connect the source and destination with these two nodes, mult iplexing is performed between the two nodes. If this is not possible, then the source and/or destination are identified as opaque nodes. The procedure is also repeated for other nodes in the network. This way it is possible to have a higher number of nodes with O/ E/O conversion than in the translucent network, but still lower than in the opaque network. Multip lexing is performed only for lo wer p riority traffic. In this way, the quality of service is increased since there is no blocking, but the available flo w decreases for each mu ltiplexed session.
A dedicated program was developed in order to realize the mu l_RWA_ min_ BP algorithm. It consists of the procedures and functions described as follows: INPUT parameters: the network G(V,E); the number of wavelengths W; the maximu m length in hops Lhop; the ma ximu m length in kilo meters Llen; the matrix T=(Tsd) where Tsd is the number of connections from ns (source) to nd (destination); the list of nodes whose ingoing and outgoing traffic has priority towards the rest of the nodes.
The set S defines the overall set of connection requests induced by the T matrix. Let N be the number of nodes and L be the number of links in the network. We also use the following notation: p is a cursor on the current node, where s is a source node, d is a destination node and e designates the node with the O/ E/O capabilit ies, (i,j) defines the link between the nodes i and j and The LIGHT_SELECT procedure checks whether the path obtained by the D.D.S.P.R_ALGORITHM has availab le lightpaths with minimal conversions at intermediate nodes. It starts with the first lambda and then follows the path fro m source node to the destination node reserving this first lambda. If the first lambda in some link on lightpath have previously been reserved by some other lightpath, the procedure continues with the second lambda. A lambda that is available on the whole path is reserved and the procedure is terminated, otherwise zero is returned to indicate that this procedure has failed.
If the procedure returns zero, the cursor is placed on the first opaque node on the path and the same procedure is run again but now just on the rest of the path from th is opaque node until destination node. If this procedure returns zero again these steps are repeated if there are additional O/ E/O converters on the path.
In case the final result of the LIGHT_SELECT procedure is zero, the REMOVE_ LINK function is run. For the link (i,j) on the path where all wavelengths are reserved we put ij c = ∞ .
The PATH_λs_EXIST procedure checks whether the function D.D.S.P.R_ALGORITHM has found the path for the session λs.
The OPAQUE_ NODE_SELECTION function is run if there is no path for the session λs and the source and destination have no conversion capabilit ies. If there is no nodes on the path having O/E/O converters the source and destination node are selected to have 3R regenerators. Otherwise one additional node has to be selected so that path has available lightpaths with minimal conversions. This is done through several iterations. If the source node has O/E/O converters the other node is selected on the path between the node closest to the source node which also has O/E/O converters and the destination node. If the destination node has O/E/O converters the other node is selected on the path between the node closest to the destination node which also has O/E/O converters and the source node. If both source and destination node has no O/E/O converters and there are such nodes on the path the traffic is mult iplexed between two selected nodes which assures that there will be minimal conversions.
The RESERVA TION function reserves all lambdas on the path, as the result of the LIGHT_ SELECT procedure which finds available lambdas on the path.
The MUX function multip lexes the traffic between two chosen nodes with O/ E/ O capabilities on the path and packs them with all other multip lexed traffic between the node pairs fro m other sessions.
The OUTPUT parameters are: blocking probability for the sessions in the matrix T, nu mber and arrangement of opaque nodes in the network, network utilization (percentage of used wavelengths in the lin ks), percentage of the sessions that have been multip lexed.
The complete algorith m is summarized in Figure 1. The upper bound of the standard Dijkstra algorith m computation complexity is O(N2) at worst [11] and the D.D.S.P_A LGORITHM co mputation comp lexity can be improved to O(L+NlogN). Since this algorith m can be run several times during the mul_RWA_ min_BP heuristic, the computational comp lexity and running times are of the order of O (L2+N·L·logN), which can be very time consuming for large nu mbers of N and L.

Numeric Results
No heuristic can be validated until it is supported by practical results. In order to demonstrate the proposed algorith m performance, we made a simulat ion. Not being able to find a suitable simulator that could support our routing problem, we designed and developed a simulator to implement routing and wavelength assignment in optical transport networks. The simulator was developed in Java language. All experiments were conducted on a 3 GHz PC with 4G RAM. The simu lator accepts input parameters such as the number of nodes in the network, lin k in formation with associated weight, number of wavelengths per fiber, maximu m t ransparent length measured in hops, maximu m transparent geographical length in kilo meters and traffic matrix with a nu mber of sessions between every pair of nodes. The outputs of the simu lator are the nu mber and placement of opaque nodes, the utilization, the number of successfully connected sessions and the number of sessions that have to be mult iplexed with other traffic.
All these input parameters can be init ialized before running simu lations to obtain results for a g iven selection of parameters. Permutation routing was used in order to find out the sample source-destination pairs in wh ich every node in the network acts as the source for every other node in the network. The total nu mber of source-destination pairs in permutation routing depends on the number of nodes. Extensive simulations are then carried out for each combination o f parameters of interest and the obtained results are presented.
In this section, we conduct four cases of simulat ion experiments in order to measure the network performance under different input settings. We study the follo wing four cases: transparent optical network, translucent optical network, translucent optical non-blocking network, opaque optical network. The translucent optical network is obtained as a result of the D.D.S.P_ALGORITHM and the translucent optical non-blocking network as a result of the mu l_RWA_ min_ BP heuristic. In order to compare these 4 cases we apply two network topologies: Pacific Bell network topology and USANET network topology. We use the following data range for the parameters: Lhop: 3 ÷ 4 hops; W: 1 ÷ 256 wavelengths; Llen: 2,000 ÷ 5,000 km; traffic matrix: 50 ÷ 400 sessions per iteration.
The simulator outputs are compared in order to evaluate the proposed algorithms. To investigate the effectiveness of the proposed wavelength-assignment algorith m, we created a network simulat ion in which the lightpath requests arrive with a previously defined number of requested sessions between two nodes. The number of requested sessions are placed in the mat rix T. New matrix is created for every iteration following the rule with probability of session appearances. Let the Pij(n) represents the probability that between nodes i and j there are n requested sessions in matrix T. We use the following values: Pij(0)=0.6, Pij(1)=0.35, Pij(2)=0.04, Pij(3)=0.007 Pij(n>3)=0.003, for every pair (i,j).
All these probabilities had discrepancies of ±10% during the process, and 10,000 iterat ions were perfo rmed fo r each input parameter instance. As discussed earlier, the goal is to have a less expensive network, evenly balanced network traffic, low blocking probability and prioritized traffic regarding the source-destination pair. The general results for all cases are as follows.  Figure 2 shows the session blocking p robability for all four network configuration types depending on the number of wavelengths, for the Pacific bell network. It is obvious that the non-blocking translucent network shows the best performance, having no blocked sessions, while other network types have the negligibly small b locking probability only when W reaches 16. Th is results from the search for alternate paths, and if there are no free resources in that case, the sessions are mult iplexed. The proposed algorith m has much greater results in regard with the quality of service compared with the algorith m in [16] because none of the requested sessions are not blocked. But on the other side some of the sessions must have reduced bit rate due to the mu ltip lexed traffic. Figure 3 shows the dependence of the session blocking probability on the number of requested sessions expressed through the matrix T, for the case of the Pacific bell network. The number of requested sessions is shown in decimal notation since it represents the average value for 10,000 iterations. Simu lation results show that, unlike other network types, the non-blocking translucent networks has no blocked sessions regardless of the network traffic increase. The proposed heuristic proved to be immune to the quantity of traffic generated with in the Pacific bell network.   Figure 4 shows the percentage of sessions which were mu ltip lexed in case of using the non-blocking translucent heuristics for the Pacific bell network. Simu lation was performed depending on the number of sessions from matrix T, for three wavelength number values. The results show that if W = 4 less than 40% of the sessions must be mu ltip lexed in order to have the zero blocking p robability, while this percentage is much lo wer for a larger nu mber of wavelengths, which is log ical due to the decreased number of potential session paths. However, this percentage still enables all priority users to have the guaranteed quality of service. Figure 5 shows the resource utilization achieved in the case of the Pacific bell network. It is shown how the utilizat ion of network resources necessary for serving all sessions (number of occupied wavelengths per link) changes depending on the number of sessions. The non-blocking translucent heuristics has the highest utilizat ion (up to 90%), meaning that almost all network resources are emp loyed for realizing the requested flow. Some wavelengths transmit a h igher number of sessions, thus decreasing the individual session flow, but on the other hand, they disable blocking.  Table 2 gives the number of opaque nodes for the USANET network fo r all four optical network configuration types. For higher values of the parameter W there is a certain saving in equipping the network with additional electronic devices for signal conversion and processing. If W = 64, as many as 70% nodes can be completely transparent for signals in the optical do main.  Figure 6 shows the session blocking p robability for all four network configuration types depending on the number of wavelengths. It is obvious that the non-blocking translucent network again shows the best performance, having no blocked sessions, while other network types have the negligibly s mall blocking probability only when W reaches 24. Figure 7 shows the dependence of the session blocking probability on the number of requested sessions expressed through the mat rix T, for the case of the USANET network. The number of requested sessions is expressed through average value of 10,000 iterat ions. The simulat ion results show that the non-blocking translucent heuristic has no blocked sessions regardless of the increase in network traffic. The proposed heuristic proved to be immune to the quantity of traffic generated within the USANET network as well.  Figure 8 shows the utilizat ion achieved in the case of the USANET network. It is shown how the utilizat ion of network resources necessary for serving all sessions changes depending on the number of sessions. The non-blocking translucent heuristics has the highest utilizat ion (over 90%), meaning that almost all network resources are emp loyed for realizing the requested flow. Regardless of the exceptional network load and of the fact that all resources are engaged, the quality of service provided by the proposed heuristic is still constant.

Conclusions
In this paper, we study a non-blocking translucent wavelength routed optical network architecture that effectively overco mes the signal quality degradation in a fully transparent network, while using much less wavelength-convertible 3R O/ E/O regenerators than a fully opaque network, while improving blocking probability compared to a tradit ional t ranslucent network. We study the problem of finding the shortest and alternative paths in the RWA algorith m and mult iplexing the sessions in W DM optical networks. These nodes are selected and the routing assignment is done by applying the distributed Dijkstra algorith m. The novelty lies in optimizing the process of analyzing the signal quality degradation, network load balancing, number of opaque nodes and quality of service.
The comparison of the proposed RWA heuristic with other commonly used strategies in terms of blocking probability and network utilization is presented. The simu lation results show that the proposed heuristic has no blocking sessions compared with other best algorith ms. Our nu merical simu lation demonstrates that, for larger nu mber of wavelengths, it is sufficient to equip no more than 30% of nodes with electronic 3R-regeneration capability. Our results further show that network performances can be improved by increasing the number of wavelengths. Accordingly, we show through simulat ion that the proposed algorithm g ives very good results for small and mediu m sized networks. Since the comp lexity of the problem is relatively high for large networks (mo re than 30 nodes), we need to apply additional relaxat ions.