REROUTING ALGORITHM FOR WAVE LENGTH DIVISION MULTIPLEXED NETWORKS by ISERP ISERP

S.REVATHI et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 1, Issue No. 2, 102 - 111

REROUTING ALGORITHM FOR WAVE LENGTH DIVISION MULTIPLEXED NETWORKS S.REVATHI, Asst . Prof (S.G) SENSE , V.I.T UNIVERSITY, vellore-14. Email.srevathi@vit.ac.in

A.JABEENA, Asst . Prof (S.G) SENSE , V.I.T UNIVERSITY, vellore-14.

In a wavelength routed WDM network, a lightpath needs to be wavelength continuous .The wavelength continuity constraint imposed by WDM networks results in inefficient utilization of wavelength channels. A request may have to be rejected even though a route is available because of non availability of the same wavelength on all the links of the route. Due to this inefficient utilization of wavelength channels, more connections are blocked.The wavelength continuity constraint can be relaxed at a node by placing optical wavelength converters at the node, but wavelength converters are very expensive. Wavelength rerouting moves a few existing lightpaths to new wavelengths to create a wavelength continuous route to satisfy a new connection request[14]. Wavelength rerouting is advantageous when compared to general rerouting, which is very expensive in terms of service disruption and control overhead because general rerouting can change the route as well as the wavelength of existing lightpaths in order to accommodate a new request. Wavelength rerouting finds application is networks with dynamic traffic demand. Further, it is useful in case of network component failures[6]. When a network component such as a node or link fails, all the lightpaths that are currently using the component fail. To restore service on these lightpaths, new lightpaths need to be established between end nodes of failed lightpaths. In such a scenario, wavelength rerouting of unaffected lightpaths helps to restore failed lightpaths. In response to a new request, an RWA algorithm is used to select a wavelength-continuous route to satisfy the request[4]. When no wavelength-continuous

Abstractâ&#x20AC;&#x201D; This paper analyses the wavelength rerouting in wavelength division multiplexed networks where the light path between a node are dynamically established. The constraint on wavelength continuity imposed by WDM networks results in poor blocking performance. The design and simulation of wavelength rerouting algorithm on ARPA-2 network and its performance analysis in comparison with conventional routing algorithm based on blocking performance have showed that the time required for processing connection requests is faster. Keywordsâ&#x20AC;&#x201D;wavelength division multiplexing (WDM), wavelength retuning, wavelength rerouting, wavelength routing.

Dr.P.ARULMOZHIVARMAN, Associate professor,SENSE VIT UNIVERSITY,Vellore-14

INTRODUCTION

Wavelength Division Multiplexing (WDM) means transmitting many light beams of different wavelengths simultaneously through an optical fiber and wavelength routing means a network switching (routing) node that routes signals based on their wavelengths meets the tremendous bandwidth demand[6].A WDM optical network consists of wavelength routing nodes interconnected by point to point optical fiber links in an arbitrary topology[7]. WDM optical network networks are receiving increasing attention from the telecommunications industry, network operators, and research communities all over the world.. WAVELENGTH REROUTING ALGORITHMS

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The controller sends control messages to the intermediate switches (routing nodes) on the path of the rerouted lightpath. These messages are used to set the state of the switch such that the new wavelength is switched from an inbound link to an appropriate outbound link. Then, the source node prepares to switch data transmission from the old wavelength to the new wavelength. The source node appends an end-of-transmission (EOT) control packet after the last packet ion the old wavelength and holds the first packet on the new wavelength for a guard time[14]. The EOT packet is used to inform the destination node that the data transmission via the old wavelength has ended and data will soon arrive via the new wavelength. The guard time prevents data from being lost during the transient period of lightpath migration. The source node tunes its transmitter to the new wavelength and, after the end of the guard time, starts transmitting data via the new wavelength. Upon detecting the EOT packet, the destination node tunes its receiver to the new wavelength and becomes ready for receiving data via the new wavelength. The guard time determines the disruption period of MTV-WR operation. The guard time is bounded by the sum of the switching times of tunable optical transmitter and receiver, the processing time of the EOT control packet at the destination node, and the differential propagation delay of sending messages through two wavelengths due to the wavelength dispersion of optical fibers or optical devices. Based on realistic assumptions and practical values, it has been shown that the guard time is only of the order of microseconds. This disruption time is much smaller when compared to that incurred by rerouting-after-shutdown (RAS), which is of the order of a hundred

While rerouting can be used to improve wavelength channel utilization, there will be low or even zero throughput during the rerouting process. Transmissions along the rerouted lightpaths must be temporarily shut down to prevent data from being lost or misrouted. The throughput loss is pronounced in all optical networks, as a wavelength channel is expected to carry gigabits of information flow[1]. Therefore, the shutdown period will cause significant data loss. Moreover, the period of disruption will be longer because of the longer propagation delay for transmitting signaling messages in a wide area network. Therefore, minimization of the incurred disruptions (for example, the number of rerouted lightpaths or the disruption period of the existing lightpaths) is imperative for rerouting in all-optical wide-area networks. Wavelength rerouting has two components, the rerouting operation (lightpath migration) and the rerouting algorithm. The rerouting operation deals with the migration of lightpaths. It is desirable that a rerouting operation have shorter disruption time and makes switching control at the routing nodes simpler. The rerouting algorithm determines the lightpaths that can be rerouted and selects a few among them to create a wavelength-continuous route to satisfy a connection request. The basic operations used for lightpath migration are wavelength retuning (WR) and move-to-vacant (MTV) [1].Wavelength retuning retunes the wavelength of a lightpath maintaining its path. First, it facilitates control because the path is not changed and the same switching nodes are used. Second, computationally simpler rerouting algorithms can be developed, as only changing the wavelength of an existing lightpath needs to be considered. Applying the WR operation only may be disadvantageous, as it does not bother if the path on the new wavelength is vacant. Move-to-vacant reroutes a lightpath to a vacant route with no other lightpaths. It has some advantages. First, it does not interrupt other lightpaths since there is no other lightpath on the

new route of the rerouted lightpath[5]. Second, it preserves transmission on the old route during setup of the new route, and therefore the disruption period is reduced. MTV operation requires a complex algorithm, as it does not necessarily maintain the path of the lightpath. Move-to-vacant wavelength retuning (MTV-WR) moves a lightpath to a vacant wavelength on the same path. It can greatly reduce the disruption period. MTV-WR operation has advantages of both MTV and WR operations while overcoming their drawbacks. The implementation of this operation is explained as follows[6]. A central controller is used for sending control messages to set up, migrate, and release lightpaths. The following steps are used for light path migration.

route is available, normally the request is blocked. However, a situation may arise wherein a route is available but no common wavelength is free on the links, leading to blocking of the request. In this case, a wavelength rerouting algorithm can be used to determine if it is possible to avoid blocking but creating a wavelength-continuous route by moving a few existing lightpaths to new wavelengths[5]. If it is successful, then the request is honored by allotting the newly chosen wavelengthcontinuous route .

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wherein moving lightpaths in parallel may not be beneficial. In this case, moving lightpaths in a certain sequential order may be useful. A scheme which moves lightpaths in sequence to vacant wavelengths, maintaining their path is called sequential MTV-WR. Here, lightpaths are moved in different passes. In the first pass, a certain number of lightpaths are moved. This will result in creation of vacant wavelengths for some other lightpaths. In the next pass, these lightpaths will be moved. This continues over several passes until a wavelength-continuous route is found for the new request or no more lightpaths can b e moved. The delay in executing sequential MTVWR is the sum of the delays in executing MTVWR in different passes. This results in longer delay[14].

microseconds. In RAS operation, the central controller first sends control messages to the source nodes of the rerouted lightpaths to stop transmission. In response to these messages, the source nodes send acknowledgements to he controller. The network controller, after receiving acknowledgements from all the source nodes, sends control signals to the source and destination nodes of rerouted lightpaths to restart transmission[14]. REROUTING SCHEMES A rerouting scheme makes use of the basic lightpath migration operations. When developing a rerouting algorithm, the kind of rerouting scheme employed must be taken into consideration. We discuss two rerouting schemes, parallel MTV-WR and sequential MTV-WR. These schemes use MTV-WR operation for migrating lightpaths. The parallel MTV-WR scheme moves each of the rerouted lightpaths to a vacant wavelength on the same path in parallel. The rerouted lightpaths should be on a disjoint set of links. Since all the lightpaths on a particular wavelength are link-disjoint, there is no need for any algorithm using this scheme to check link disjointness of MTV-WR. Since it uses MTVWR operation, it has all the advantages of MTVWR. Further, it has another advantage. The overall delay of executing parallel MTV-WR is the maximum of the delay in executing MTVWR for each of the migrated lightpaths. Therefore the delay is very small. Fig depicts a state of a network with three wavelengths w0, w1, and w2 per fiber link. It shows five lightpaths, p1, p2, p3, p4, and p5. Lightpath p1 uses path 1-3-4 on w0, p2 uses path 1-2 on w0, p3 uses path 2-4 on w0, p4 uses path 1-2-4 on w1, and p5 uses path 1-3-4-2 on w2. Here, MTV-WR operation is permissible for p1 and p2 only. This is because p1 can be migrated to a vacant wavelength w1 maintaining its path 0oand p2 can be migrated to a vacant wavelength w2 maintaining its path. Suppose that a new request arrives for a connection between node 2 and node 3. No free wavelength-continuous route is available to satisfy this request. By migrating p1 and p2 in parallel to wavelengths w1 and w2, respectively, the new request can be accommodated by assigning to it a lightpath p4 that uses path 2-1-3 on w0. Let d1 be the delay for migrating p1 and d2 be the delay for migrating p2. The delay for executing parallel MTV-WR is given by max(d1,d2). In spite of its simplicity and short delay, parallel MTV-WR has a shortcoming. It may not be always possible to use MTV-WR in the best possible way. There may arise a situation

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Figure 1(b)

Illustration of parallel MTV-WR. 1(a)Before using parallel MTV-WR 1(b) After using parallel MTV-WR

Figure1 (a)

the lightpaths and the order in which they should be moved to accommodate a new request. Such an algorithm is computationally intractable. The sequential MTV-WR is illustrated in Fig which depicts a state of a network with three wavelengths w0, w1, and w2 per fiber link. It shows five lightpaths p1, p2, p3, p4, and p5. Lightpath p1 uses path 1-2-3 on w0, p2 uses path 1-2 on w1, p3 uses path 3-4-5 on w1, p4 uses path 2-3-4-5 on w2, and p5 uses path 4-5 on w0. Here, only lightpath p2 can use MTV-WR. It can be moved to w2, maintaining its path. If a between node 1 and node 4, it cannot be honored as there does not exist a wavelength continuous route for it. However, lightpaths can be moved in two passes using sequential MTV-WR to accommodate this request. In pass 1, lightpath p2 can be moved to w1. This operation creates a vacant wavelength w1 for p1 on its path. In pass 2, lightpath p1 can be moved to w1. Now, the new request can be assigned p6, which uses path 1-2-3-4 on w0. Let d1 be the delay for migrating p1 and d2 be the delay for migrating p2. The delay for executing sequential MTV-WR is given by d1 + d2 ALGORITHM AG This algorithm is to create an auxiliary graph with crossover edges. Hence we call this algorithm AG [1].The objective of this algorithm is to minimize the weighted number of rerouted lightpaths in networks with the parallel MTVWR rerouting scheme. The weighted number of rerouted lightpaths for a chosen path is the weighted number of existing lightpaths intersected by the path. In other words, it is the sum of weights of the lightpaths whose edges are used by the chosen path. It is important to note that every intersecting lightpath is counted only once, independent of how many of its edges are used by the path considered. . The algorithm uses a layered graph representation of the underlying WDM network. The network with N nodes and W wavelengths per fiber link is represented as an undirected graph with W subgraphs, each with N nodes. Here, a subgraph corresponds to a wavelength. It is also referred to as a layer or a wavelength plane. The nodes in a subgraph on some wavelength plane correspond to routing nodes in the network and the edges correspond to the wavelength channel on the fiber links of the network. A weight proportional to the number of hops used is assigned to an edge used by a retunable lightpath. A lightpath is said to be retunable if there exists a wavelength (other than the one used by the lightpath) which is free on every link along the route used by the lightpath.

2(a)

Figure

Figure 2(b) Illustration of sequential MTV-WR 2(a)Before using sequential MTV-WR 2(b After using sequential MTV-WR Another major drawback of this scheme is that it requires a complex algorithm to decide ISSN: 2230-7818

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Let a and b be the end points of the first edge and c and d be the endpoints of the second edge. If H is the weight of an edge, the cost of using the above two edges is 2h. However, there exists a crossover edge between a and d with a lesser cost of h. Therefore, the shortest-path finding algorithm will choose this single edge instead of the above two edges. ILLUSTRATION Consider a graph representing a network with nine nodes on some wavelength plane as shown in Fig.3. It shows two lightpaths p1 (between nodes 1 and 4) and p2 (between nodes 6 and 9).The unlabeled edges indicate that the wavelength channels on the corresponding fiber links are free. The numerical values shown over the edges in the graph represent the edge weights. Note that the weight of an edge of a lightpath is its hop length. Further note that the weight of a free edge is such that the cost of the longest path with only free edges is less than the weight of any labeled edge.

A tiny value is assigned to a free edge as its weight. It is chosen such that the weight of any edge that is currently being used by a retunable lightpath is greater than the cost of the longest path with only free edges. The AG algorithm finds a minimumcost path between a source node and a destination node[5]. The objective is to choose a path that intersects a minimum (weighted) number of existing retunable lightpaths. The cost of a path is defined as the sum of the weights associated with the distinct lightpaths whose edges appear on the path plus the number of free edges times a tiny value ℮. The algorithm works in two phases. Phase 1 selects a route that does not require rerouting of any existing lightpath. Phase 2 is invoked when phase 1 fails. Phase 2 selects a route that requires minimum number of existing lightpaths to be rerouted. In phase 1, a conventional shortestpath-finding algorithm (such as Dijkstra’s algorithm) is used to select shortest paths on each of the W subgraphs. The path with the least cost among all the above W shortest paths is chosen. While finding a shortest path, only free edges are considered, and they have equal weight. The chosen minimum-cost path is the one with a minimum number of physical hops. Phase 2 proceeds in three stages. In stage 1, all the retunable lightpaths are identified. In stage 2, an auxiliary graph is constructed by creating crossover edges for every retunable lightpath. A crossover edge between node x and node y for a retunable lightpath p is created whenever there exists a path of length 2 or more between x and y comprising only the edges of p. In stage 3, shortest paths are found using a conventional shortest-path-finding algorithm on each of the W subgraphs, and one with the least cost is chosen. The chosen path requires that a minimum weighted number of lightpath be rerouted. If no path with finite cost can be found, the connection request is rejected. The edges are assigned weights as follows. The edges used by a retunable lightpath and all the associated crossover edges are assigned a weight equal to the hop count of the lightpath. Every free edge is assigned a tiny value ℮. This value is chosen such that the cost of the longest path with only free edges is less than the weight of any edge used by a retunable lightpath. A value 1/N or less ℮ will serve this purpose. The shortest path found will traverse at most one edge (or crossover edge) of any retunable lightpath. This is because all the edges that corresponds to a retunable lightpath are assigned same weight. Suppose that a path traverses two edges of a retunable lightpath[6].

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Figure 3, A graph G on some wavelength plane Now assume that a request for connection between nodes 2 and 9 arrives and no free route is available to satisfy the request. Also, assume that the two lightpaths p1 and p2 are retunable. There does not exist any finite-cost path between nodes 2 and 9 traversing only the free edges on the given wavelength. Assume that there does not exist any finite cost-path between nodes 2 and 9 on other wavelengths. The algorithm fails to find a route in phase 1 and invokes phase 2. The stage 1 of phase 2 finds that both the lightpaths p1 and p2 are retunable. Then an auxiliary graph Gaux is constructed by stage 2 of phase 2 by creating additional edges

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and stage 1 of phase 2 finds that all the three lightpaths are retunable. Then, stage 2 builds an auxiliary graph by creating crossover edges as shown in Fig. 5(b). The path 8→4→5 with cost 4 will be reported by stage 3 of phase 2 as the resulting path with minimum weighted number of existing lightpaths to be rerouted. The result is not correct as there exists a path with a lesser cost of 3.3. The reason this algorithm fails to find the minimum cost path for the above example is now explained. The path 8→6→9→7→3→5 traverses two edges of p1 on the auxiliary graph. However, these two edges are not contiguous, as they are separated by a free edge. The algorithm does not have any knowledge that these two edges belong to the same lightpath and therefore it counts their weight twice instead of once. Consequently, this algorithm finds that the cost of the above path is 6.3 (which is not correct). If a crossover edge exists from node 6 to node 3, this problem will not arise. However, the algorithm will not create such a crossover edge, as node 3 appears before node 6 on the path of p1 and node 3 cannot be reached from node 6 by traversing only the edges of p1

for the retunable lightpaths p1 and p2 as shown in Fig. 4. It can be seen that the number of edges in Gaux is more than that in G. Now a shortest path finding algorithm is used by stage 3 and the path 2-3-7-9 (equivalent to 2-3-7-8-9) is chosen on this wavelength. The cost of using path 2→3→7→9 on Gaux is 6.1, as it traverses a free edge (with weight 0.1), an edge (with weight 3) of p1, and an edge (with weight 3) of p2. The new request can use the path 2→3→7→8→9 on G after migrating p1 and p2

Figure 4, The auxiliary graph Gaux of G

The algorithm selects minimum weighted number of lightpaths to be rerouted when the lightpaths, links, and channels are all bidirectional. It fails to choose the minimum for the unidirectional case. The following example illustrates the failure of the algorithm to select minimum weighted number of lightpaths when the lightpaths, links, and channels are all unidirectional. The graph shown in Fig. 5(a) describes the state of a network on some wavelength plane at some instant of time. It shows three lightpaths p1, p2, and p3 with the unidirectional paths 7→3→6→9, 8→4→1, and 2→4→5, respectively. Assume that all these lightpaths are retunable. The weight of a free edge is 0.1 and that of edges labeled p1, p2, and p3 are 3, 2, and 2 (equal to the hops used), respectively. Assume that there is a request for a session from node 8 to node 5 and no route is available to satisfy it. In such a scenario, the phase 1 of the algorithm fails

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Figure 5(a) A graph with unidirectional path 5(b) The corresponding auxiliary graph ARPA TOPOLOGY For the analysis of this rerouting algorithm we use ARPA(Advanced Research Projects Agency) topology.

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RESULTS AND ANALYSIS The network topology of ARPA2 network is simulated in MATLAB.

1 1 1 1 1 1 1 1

2 6 3 8 2 6 2 6 2 6 2 6 3 8 2

10 11 9 12 9 12 13 10 15 14 10 15 11 16 6 9 12 13

1 3 8 11 16 18 1 2 6 9 12 13 1

Figure 6, ARPANET topology

path bet 1 and 10 = path bet 1 and 11 = path bet 1 and 12 = path bet 1 and 13 = path bet 1 and 14 = path bet 1 and 15 = path bet 1 and 16 = path bet 1 and 17 = 17 path bet 1 and 18 = path bet 1 and 19 = 17 19 path bet 1 and 20 = 20 path bet 1 and 21 = 20 21

SIMULATION OF BLOCKING PROBABILITY USING A CONVENTIONAL ROUTING ALGORITHM

The blocking percentage for the WDM ARPA2 network is simulated.We find that the blocking probability is very high. We need to reduce the blocking probability after applying our algorithm 100 95

Figure 7, Simulated ARPA topology Dijkstraâ&#x20AC;&#x2122;s shortest path finding algorithm is applied to find the various shortest path between source and destination nodes on ARPA2 network. The ARPA2 network has 21 nodes 25 bidirectional links. The various shortest paths are found assuming unity wages:

path bet 1 and 2 = path bet 1 and 3 = path bet 1 and 4 = path bet 1 and 5 = path bet 1 and 6 = path bet 1 and 7 = path bet 1 and 8 = path bet 1 and 9 = ISSN: 2230-7818

1 1 1 1 1 1 1 1

2 3 2 2 2 2 3 2

4 4 6 6 8 6

5 7 9

The blocking percentage

90 85 80 75 70 65 60 55

15 No. of Links

Figure 8, Simulation of blocking probability using a conventional routing algorithm Thus the blocking probability of ARPA2 network is plotted prior to the application of rerouting algorithm. APPLICATION OF ROUTING ALGORITM ON ARPA-2 TOPOLOGY Here a connection request is tried to be satisfied by applying a routing algorithm and checking for free wavelength along the path and assigning the same. No of connection required: 4 No of nodes in the network: 21 No of wavelengths: 3 No of links in the network: 25

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Source node: 1 Destination node: 4 Path= 1 2 4 Nodes are assigned with wavelength: 2

Source node: 1 Destination node: 4 path= 1 2 4 Nodes are assigned with: 2

Source node: 2 Destination node: 5 Path= 2 4 5 Nodes are assigned with wavelength: 3

Source node: 2 Destination node: 5 path= 2 4 5 Nodes are assigned with: 3

Source node: 2 Destination node: 4 Path= 2 4 Connection request may be blocked

Source node: 2 Destination node: 4 path= 2 4 connection request is blocked

Enter the no. of lightpaths to be retuned: 2 Enter the lightpath to be retuned Enter the source node: 1 Enter the destination node: 4 Alternate path ap = 1 3 8 5 4 Nodes are assigned with wavelength: 2

Source node: 1 Destination node: 5 path= 1 2 4 5 Nodes are assigned with: 1

Enter the lightpath to be retuned Enter the source node: 2 Enter the destination node: 5 Alternate path ap=2 1 3 8 5 Nodes are assigned with wavelength: 3 Path= 2 4 Nodes are assigned with: 2

Figure 9, Simulation of blocking probability using routing algorithm on ARPA network Here itâ&#x20AC;&#x2122;s found that the fourth connection request is blocked and hence blocking probability is high. APPLICATION OF REROUTING ALGORITHM ON ARPA-2 TOPOLOGY A rerouting algorithm, which tries to satisfy the connection request that is blocked by routing algorithm is applied by migrating existing lightpaths to new or alternate routes and hence assigning wavelengths. Source node: 1 Destination node: 5 Path= 1 2 4 5 Nodes are assigned with wavelength: 1

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Figure10, Simulation of blocking probability using rerouting algorithm on ARPA network Hence in addition to satisfying connection requests a rerouting algorithm also reduces the blocking probability.

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BLOCKING PROBABILITY DIFFERENT WAVELENGTHS

FOR

LOAD: 20E CASE 1: 5 CASE 2: 10 CASE3:15

It is inferred that for a constant wavelength channel increasing the load of the network increases the blocking probability.

CONCLUSION The rerouting algorithm was implemented on ARPA network and found out that it reduces the blocking probability effectively than a routing algorithm. The performance of the algorithm has been evaluated through extensive simulation. It has been observed that the rerouting algorithm improves the blocking performance considerably reducing the blocking probability on the average by 25% and only very few lightpaths are required to be rerouted per rerouting. Also the time required for the execution of rerouting algorithm is very less. Also the performance of this algorithm under various load conditions and wavelength channels are analyzed. REFERENCES

It is found out that that for a constant load increasing the number of wavelength channels and applying a rerouting algorithm decreases the blocking probability.

[1] K. C. Lee and V. O. K. Li, “A wavelength rerouting algorithm in wide-area all-optical networks,” J. Lightwave Technol., vol. 14, pp. 1218–1229, June 1996.

Figure 11,Simulation of blocking probability for different wavelengths

BLOCKING PROBABILITY DIFFERENT LOADS

Load3 : 30E

Channel=15 Load1 : 10E Load2 : 20E

FOR

Figure 12, Simulation of blocking probability for different loads. ISSN: 2230-7818

[2] R. Ramaswami, “Multiwavelength lightwave networks for computer communication,” IEEE Commun. Mag., vol. 31, pp. 78–88, Feb. 1993. [3] I. Chlamtac, A. Ganz, and G. Karmi, “Lightpath communications: An approach to high bandwidth optical WAN’s,” IEEE Trans. Commun., vol. 40, pp. 1171–1182, July 1992. [4] R. Ramaswami and K. N. Sivarajan, “Routing and wavelength assignment in alloptical networks,” IEEE/ACM Trans. Networking, vol. 3. pp. 489–500, Oct. 1995. [5] D. Banerjee and B. Mukherjee, “A practical approach for routing and wavelength assignment in large wavelength routed optical networks,” IEEE J. Select. Areas Commun., vol. 14, pp. 903–908, June 1996. [6] A. Birman and A. Kershenbaum, “Routing and wavelength assignment methods in singlehop all-optical networks with blocking,” in Proc. INFOCOM’95, 1995, pp. 431–438.

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[7] S. Baroni and P. Bayvel, “Wavelength requirements in arbitrarily connected wavelength-routed optical networks,” J. Lightwave Technol., vol. 15, pp. 242–251, Feb. 1997.

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