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Procedía Computer Science 34 (2014) 71 - 78

The 9th International Conference on Future Networks and Communications (FNC-2014)

Analysis of Routing and Wavelength Assignment in Large WDM Networks

Ravi Teja Kogantia, Deepinder Sidhua*

aDepartment of Computer Science and Electrical Engineering, University of Maryland,Baltimore County, Baltimore,21250, USA

Abstract

In Wavelength Division Multiplexing (WDM) network, for a given connection request, a route has to be found, and a dedicated wavelength has to be assigned along that route. This problem of assigning route and wavelength to the connection request, using minimum network resources, is called Routing and Wavelength Assignment (RWA) Problem. This paper focuses on the analysis of proposed RWA algorithms in large WDM networks. We use simulations and analysis of randomly generated large networks under dynamic traffic and static traffic, with and without protection of the connection request. The protection of the primary route between source and destination is considered by setting up a dedicated backup path in case of failures. The wavelength requirements are analyzed using different wavelength assignment heuristics under different routing techniques for a set of connection requests. We find that, the fixed alternate routing packs connection requests into less number of wavelengths than the fixed routing and that most-used wavelength assignment heuristic performs slightly better than the first-fit wavelength assignment heuristic.

© 2014 Published byElsevierB.V. Thisis anopen access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of Conference Program Chairs

Keywords: Wavelength Division Multiplexing (WDM); Routing and Wavelength Assignment (RWA); Lightpath; Backup Path; Alternate Path; Routing Heuristics; Static Traffic Model; Dynamic Traffic Model; Wavelengths Requirements; Simulations

1. Introduction

The Wavelength Division Multiplexing is of high importance these days because of its capability of handling the high bandwidth requirements using multiple wavelengths [2][12]. These wavelengths are combined and transmitted

* Corresponding author. Tel.: +1-(410)-772-3275. E-mail address: dsidhu@telenix.com

1877-0509 © 2014 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of Conference Program Chairs doi: 10.1016/j.procs.2014.07.047

over the same link (fibre). A channel using fixed wavelength through which end users communicate in WDM network is called lightpath [2]. For a given lightpath request, setting up the route and the wavelength in the network is known as Routing and Wavelength Assignment (RWA) problem [2][15][12]. The route chosen between source 's' and destination 'd', has to be allocated the same wavelength. This property of the lightpath is called 'wavelength continuity constraint' [15][3][16]. Also, the two lightpaths that share the same link cannot be assigned the same wavelength. This property is known as 'wavelength clash constraint' [15]. The RWA problem is NP complete. Because of this, heuristics are necessary to solve the RWA problem [12]. The RWA problem has been always divided into two sub problems: Wavelength assignment problem and Route assignment problem.

The traffic models for a network fall into two categories: static and dynamic traffic. In static traffic model, the lightpaths that are to be scheduled over a WDM network are known in advance and once they are set up they remain unchanged. In a dynamic traffic model, each lightpath request comes one after another randomly, remains in the network for some time, and later disappears. In WDM network, each lightpath carries a large amount of data at the rate of several gigabytes per second. In such a case, failure in any component of network may result in huge data loss. To prevent such a situation, WDM network should be able to handle the failures. This survivability to the network can be provided using several path/link protection/restoration schemes.

There has been a great deal of work done on the design of algorithms to solve RWA problem for small WDM Networks but there has not been much work done on the analysis of RWA algorithms on large WDM networks. In this paper, we use modeling/simulation to analyze proposed algorithms for RWA problem for large WDM networks under static and dynamic traffic conditions. The related work necessary for this paper are described in the section 2.

2. Related Work

There has been a great amount of work done related to Routing and Wavelength Assignment (RWA) in recent times. In [2], a review of all the routing techniques and the wavelength assignment heuristics is given under static and dynamic traffic models. In [10], the RWA problem has been solved using several linear programming formulations for different kinds of network topologies to find a near optimal routing solution. The work in [12] researches about the recent advances that took place in the field of optical networks and how the RWA problem of WDM network has been modified to find the most optimal solution. In [9], there has been work on the RWA problem under static and dynamic traffic conditions, using ILP for static case and heuristics for dynamic case. The routing schemes that were mostly considered in the previous studies were: Fixed routing, Fixed alternate routing and Adaptive routing [2]. In this paper, we have used the fixed routing [2] for the static traffic model, where the fixed route is the shortest path in the network for each s-d pair. In case of dynamic traffic model, we have used fixed routing and fixed alternate routing [2]. In fixed routing, the path chosen for each s-d pair is the shortest possible path in the network. The shortest path is found using Dijkstra's algorithm. In fixed alternate routing, one secondary path (second shortest path) is chosen which is link disjoint to the primary path (shortest path). If a wavelength is not available in the primary path, then the secondary path is considered for the wavelength assignment.

In case of static traffic model, where the lightpaths are known in advance, the wavelengths required to route the traffic is formulated using Integer Linear Programming [2]. But this can be used to solve the wavelength assignment problem for small networks only. For larger networks, heuristics have to be used to get an optimal solution. One of the most important heuristic for static traffic model is greedy heuristic [12]. In this paper, greedy heuristic has been used to solve the wavelength assignment problem for static traffic model. For Dynamic traffic model, several wavelength assignment heuristics are used in the recent years. Some of the important wavelength assignment heuristics include first-fit, random-fit, most-used and least-used [2]. In the first-fit heuristic [2][19], the first available wavelength is assigned to the incoming lightpath request, where the wavelengths are numbered sequentially and the lower numbered wavelength is given the highest priority. In the most-used heuristic [2][19], the wavelength which is used by most of the links of network is assigned to the incoming request. The first-fit and the most-used heuristics try to pack the lightpaths into lesser number of wavelengths possible, whereas the remaining heuristics spreads the lightpaths among the wavelengths available. In this paper, we have considered firstfit heuristic and most-used heuristic as the wavelength assignment schemes in case of dynamic traffic model.

The work in [3][8][ 13][ 14] researches survivability in WDM networks. There are certain path and link protection/restoration schemes that were proposed for the survivability of the WDM Networks [3][8][13]. The

protection schemes are found to be more advantageous than the restoration schemes, as more time and complexity is needed for recovery in the restoration schemes [13]. The protection schemes include: path protection and link protection. The studies in [5][6] show that the path protection is more efficient than the link protection. The path protection again includes: Dedicated-path protection and Shared-path protection [13]. In dedicated path protection, a backup path for the primary path and wavelength are reserved in advance. The backup path is node disjoint to primary path. The wavelength of the backup path is not shared with any other backup path, whereas in shared path protection, the wavelength of the backup path can be shared among backup paths of other lightpath requests [8]. In this paper, the dedicated path protection scheme has been considered for the protection of primary route, as it takes less recovery time and data loss is minimal for this scheme.

Figure 1: Graph showing the number of lightpath requests occurring each hour (slot) for set of 495 lightpath requests

3. Simulation

The network model used for simulation is similar to the model used in [3]. The network is randomly generated by fixing the number of nodes 'n' and average node degree 'k' of the network. Each fibre has twice the number of wavelengths (2*A), since each fibre in the network is bidirectional. The networks used in the simulation are 100, 200, 300 and 400 node networks with average node degrees 6, 7 and 8. There exists wavelength for every lightpath request.

The traffic models that are used for simulation are: Static traffic model and Dynamic traffic model. The set of lightpaths are chosen randomly and each source-destination pair is chosen with uniform probability for both the models. The lightpaths considered for dynamic model are periodic, that means, they occur once in a day, once in a week or once in a month. In this simulation, we assume that the lightpath requests occur once in a day, and they occur uniformly over a day. The time is divided into slots of one hour each. A distribution of set of 495 lightpath requests over a day is shown in figure 1. The number of lightpath requests that occur in each hour (slot) is shown in the figure 1. The time slot is plotted on horizontal axis (X-axis) and the number of lightpath requests that occur in each time slot is plotted on vertical axis (Y-axis). The duration of each lightpath is estimated in terms of slots and the duration of the lightpath request is chosen randomly.

The number of lightpath requests (traffic load) is increased from 10%E to 40%E (where 'E' is the maximum possible edges of a connected bidirectional network, given by E = n(n-1)/2) and the wavelength requirement was estimated using routing and wavelength assignment schemes for each network under static and dynamic traffic models.

For static traffic model, given a network and set of lightpath requests 'greedy heuristic' is used to assign the wavelengths for the incoming lightpath requests. In this heuristic, a wavelength packs the maximum number of

lightpath requests before moving to next wavelength. The path chosen for each lightpath is the shortest possible path in the network. The shortest path is found using Dijkstra's algorithm. The number of wavelengths required for different loads in each network can be seen in the table 1.

For dynamic traffic model, given a network and a set of lightpath requests, two wavelength assignment schemes 'first-fit' and 'most-used' are used to assign the wavelengths for the incoming lightpath requests. The routing schemes used to estimate the wavelength requirement are fixed routing, fixed alternate routing and dedicated path protection. The number of wavelengths required for different loads in each network for dynamic traffic model using first-fit and most-used heuristic can be seen in table 2 and table 3 respectively.

Table 1: The wavelength requirement of the networks for Static traffic model using fixed routing and greedy heuristic

# of nodes Load Node degree=6 Node degree=7 Node degree=8

100 495 (10%E) 38 33 31

990 (20%E) 71 63 57

1485 (30%E) 106 92 81

1980 (40%E) 134 120 107

200 1990 (10%E) 126 110 92

3980 (20%E) 255 213 182

5980 (30%E) 382 314 272

7960 (40%E) 501 424 356

300 4485(10%E) 198 192 156

8970 (20%E) 410 300 286

13455 (30%E) 580 569 462

17940(40%E) 812 764 581

400 7980(10%E) 268 225 207

15960(20%E) 602 512 489

23960(30%E) 801 768 703

31920(40%E) 1134 1067 1034

Table 2: The wavelength requirement of the networks for dynamic traffic model using first-fit heuristic where FR is Fixed routing, and FA is Fixed alternate routing, and PR is routing when protection is provided.

# of nodes Load Node de; gree=6 Node dej gree=7 Node dej gree=8

FR FA PR FR FA PR FR FA PR

100 495 (10%E) 22 19 28 21 17 26 18 12 23

990 (20%E) 34 30 53 31 26 48 28 22 45

1485 (30%E) 49 40 72 43 32 70 38 30 66

1980 (40%E) 62 54 92 56 49 90 50 44 89

200 1990 (10%E) 57 39 98 50 37 73 43 31 72

3980 (20%E) 109 81 187 94 76 156 79 59 127

5980 (30%E) 161 152 297 133 121 237 116 103 199

7960 (40%E) 198 181 362 170 158 301 156 123 239

300 4485(10%E) 88 75 147 86 71 137 71 60 119

8970 (20%E) 172 153 301 150 123 269 132 119 231

13455(30%E) 257 231 431 241 227 401 194 172 354

17940(40%E) 342 329 623 325 298 559 255 234 443

400 7980(10%E) 186 175 324 136 123 223 106 98 187

15960(20%E) 324 301 587 289 267 508 236 203 367

23960(30%E) 687 634 992 576 556 935 516 498 932

31920(40%E) 814 783 1413 803 748 1387 723 686 1208

Table 3: The wavelength requirement of the networks for dynamic traffic model using most-used heuristic where FR is Fixed routing, FA is Fixed alternate routing, and PR is routing when protection is provided.

# of nodes Load Node degree=6 Node degree=7 Node degre e=8

FR FA PR FR FA PR FR FA PR

100 495 (10%E) 20 15 25 16 14 22 15 10 20

990 (20%E) 31 25 46 29 24 43 23 18 39

1485 (30%E) 43 30 69 40 29 64 30 22 57

1980 (40%E) 56 49 87 51 41 86 42 36 76

200 1990 (10%E) 50 35 91 46 30 71 39 27 63

3980 (20%E) 98 79 178 87 73 149 67 51 121

5980 (30%E) 153 145 289 127 119 211 105 96 197

7960 (40%E) 179 168 345 164 151 283 143 127 251

300 4485(10%E) 83 68 128 79 65 122 61 52 106

8970 (20%E) 167 151 287 137 115 247 123 103 209

13455(30%E) 239 223 409 229 209 367 176 157 323

17940(40%E) 329 318 597 301 287 518 231 218 401

400 7980(10%E) 167 154 301 128 116 214 94 87 173

15960(20%E) 297 269 503 274 254 479 218 197 334

23960(30%E) 558 521 913 496 483 897 454 397 880

31920(40%E) 783 731 1321 723 693 1123 701 628 1098

4. Simulation Analysis

The result from our simulation and analysis are summrized below.

• For a given network, under a routing and wavelength assignment scheme, as the load increases, the wavelength required to accommodate those requests increases. In table 1, for 100 node network with node degree 8, the wavelengths required are 31, 57, 81 and 107 when the load is 495, 990, 1485 and 1980. Similar behavior is observed for dynamic traffic model.

• In dynamic traffic model, the fixed alternate routing requires less number of wavelengths to accommodate a set of lightpath requests compared to fixed routing, for a given load and wavelength assignment scheme. And the protection scheme requires more wavelengths than the fixed and the fixed alternate routing because a backup path and wavelength is assigned for each lightpath request. For 400 node network, node deg.= 6 and load= 20%E; the fixed alternate routing requires 7% less number of wavelengths compared to fixed routing, when first fit was used. The comparison of wavelength requirement with respect to routing schemes for 400 node network with node degree 6 can be seen in figure 2.

• For a network, the higher the node degree, the number of wavelengths satisfying a given set of lightpath requests decreases. In table 1, for a 400 node network with 10%E load, the wavelengths required are 268, 225 and 207 when the node degrees are 6, 7 and 8 respectively, when static traffic model is used. This behavior can also be seen for dynamic traffic model. The comparison of the wavelength requirement with respect to the node degree for 400 node network when static traffic model was used, can be seen below in figure 3.

• From tables 2 and 3, it can be seen that for a given load and routing scheme in a network, most-used wavelength assignment heuristic performs slightly better than the first-fit wavelength assignment heuristic. The most-used requires less number of wavelengths to satisfy the lightpath requests. For 100 node network with node degree 8, when the load is 30%E and routing scheme is fixed routing, the wavelengths required by the most-used heuristic and first-fit heuristic is 30 and 38 respectively. The comparison of the wavelengths required by the first-fit and most-used heuristics for 100 node network with node degree 8 can be seen below in figure 4.

• In a network, static traffic model always requires higher number of wavelengths compared to dynamic model with fixed routing and fixed alternate routing. For 300 node network, node degree = 8, load = 30%E, the static model requires 113% more number of wavelengths compared to dynamic model with fixed routing using most-used heuristic.

1600 1400 1200 1000 800 600 400 200 0

Fixed Routing

Fixed Alternate routing

In case of protection

7980(10%E) 15960(20%E) 23960(30%E) 31920(40%E) No. of s-d pairs(lightpath requests)

Figure 2: Comparison of the wavelength requirement for n=400, k=6 with respect to routing schemes when first-fit heuristic is used as

wavelength assignment scheme.

Figure 3: Comparison of wavelength requirement for 400 node network with respect to node degree of network-Static traffic model

Figure 4: Comparison of wavelength requirement for most-used and first-fit heuristics for 100 node network with average node degree '8' under fixed routing

5. Conclusion and Future work

There has been a great deal of work done on design of algorithms to solve RWA problem for small WDM Networks, but there has not been much work done on the analysis of RWA algorithms in large WDM networks such as, 100, 200, 300 and 400 node networks. In this paper, we analyse proposed algorithms for RWA problem in large WDM networks under static and dynamic traffic conditions. For this purpose, the simulations were done on randomly generated 100, 200, 300 and 400 node networks with average node degrees 6, 7 and 8.The traffic was increased -- 10%E, 20%E, 30%E and 40%E -- where 'E' is the maximum possible edges of a connected bidirectional network; and the wavelength requirement was estimated for each network under static and dynamic traffic models. The wavelength requirement for static traffic model was estimated using greedy heuristic with fixed routing. And the wavelength requirement for dynamic traffic model was estimated using first-fit wavelength assignment heuristic and most-used wavelength assignment heuristic under fixed routing, fixed alternate routing, and when protection is provided. The results showed that:

• The fixed alternate routing packs lightpaths into less number of wavelengths compared to fixed routing.

• The 'most-used' wavelength assignment heuristic performs 'slightly' better than 'first-fit' wavelength assignment heuristic.

• The static traffic model always requires higher number of wavelengths compared to dynamic model with fixed routing and fixed alternate routing.

• The higher the node degree decreases wavelength requirements.

• The wavelength requirement increases, as the number of nodes of network increases.

In this paper, we have done analysis on randomly generated large networks. However, to be more realistic, similar analysis can be done on large scale-free networks. We have seen the wavelength requirements for the dedicated path protection scheme in this paper. It would be interesting to see the wavelength requirements for the shared path protection scheme, where the backup wavelength is shared by the backup path of other lightpath requests. These investigations are work in progress.

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