Algorithm for wavelength assignment in optical networks

Wavelength division multiplexing (WDM) is a technology which multiplexes many optical carrier signals onto a single optical fiber by using different wavelengths. Wavelength assignment is one of the important components of routing and wavelength assignment (RWA) problem in WDM networks. In this article, to decrease the blocking probability, a new algorithm for wavelength assignmentLeast Used Wavelength Conversion algorithm is introduced and is an enhancement to the previously used Least Used Wavelength assignment algorithm. The performance of this wavelength assignment algorithm is evaluated in terms of blocking probability and the results show that the proposed technique is very promising in future. The Least Used Wavelength Conversion algorithm is compared with algorithms such as first-fit, best-fit, random and most-used wavelength assignment algorithm.


INTRODUCTION
Wavelength division multiplexing (WDM) is a very promising technology to meet the ever increasing demands of high capacity and bandwidth.The term wavelength-division multiplexing is commonly applied to an optical carrier.In a WDM network several optical signals are sent on the same fiber using different wavelength channels.WDM is used to address routing and wavelength assignment (RWA) problem.The first part of this problem is to route the network and the second is wavelength assignment.Wavelength assignment is one of the important issues in RWA.In general, if there are multiple feasible wavelengths between a source node and a destination node, then a wavelength assignment algorithm is required to select a wavelength for a given light path.Either distinct wavelength is assigned on each link of path or the same wavelength on each link can be used.When the wavelength conversion is not possible at intermediate routing nodes a light path must occupy the same wavelength on each link over its physical route.The clever algorithms are needed in order to ensure that RWA function is performed using a minimum number of wavelengths (Dar and Saini, 2013;Wason and Kaler, 2010).
The Least Used Wavelength Conversion Algorithm (LUWC) is an improvement over least used wavelength assignment algorithm.In LUWC, least-used wavelength assignment algorithm is executed until blocking.Also the *Corresponding author.E-mail: drmushtaqpbg@gmail.com.Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License concept of wavelength conversion is used in this model.When the call is blocked, wavelength conversion is introduced and hence blocking probability is reduced.If the full wavelength conversion is used after least-used wavelength assignment algorithm, the blocking probability is reduced to a very large extent and its value reduces to a minimum possible value.Hence, the overall performance of the network increases.The Least Used Wavelength Conversion algorithm is compared with algorithms such as first-fit, best-fit, random and mostused wavelength assignment algorithm.Simulation results proved that the proposed approach is very effective for minimization of blocking probability of optical wavelength division multiplexed networks (Mukherjee, et al., 2004).All the results are taken using MATLAB.

WAVELENGTH ASSIGNMENT
There are two constraints that need to keep in mind while trying to solve RWA.One is distinct wavelength assignment constraint that is, all light paths sharing a common fiber must be assigned distinct wavelengths to avoid interference (Arun and Azizoglu, 2000).This applies not only with in alloptical networks but in access links as well.Another is wavelength continuity constraint which means the wavelength assigned to each light path remains the same on all the links while it traverses from source end-node to destination end-node (Murthy and Gurusamy, 2002;Qi and Chen, 2006).The most important wavelength assignment algorithms are as follows: (i) First-fit algorithm: In this algorithm, firstly the wavelengths of the traffic matrix are sorted in non decreasing order.Then algorithm steps through this sorted list for selecting candidate chains joined.This process is carried on until all chains are considered to form a single chain representing linear topology.The idea of the first-fit scheme is to pack the usage of the wavelengths toward the lower end of the wavelengths so that high numbered wavelengths can contain longer continuous paths.By using first fit algorithm blocking can be reduced to a great extent as compared to random algorithm (Alyatama, 2005;Yuan and Zhou, 2000).(ii) Random algorithm: In this algorithm, wavelength is selected randomly from available wavelengths.A number is generated randomly and the wavelength is assigned to this randomly generated number.As this technique chooses a random wavelength from the set of all wavelengths that are available along the path, the blocking probability cannot be minimized as much as compared to other wavelength assignment algorithms (Alyatama, 2005).(iii) Most-used: The most-used scheme furthers the idea of the first-fit scheme in packing the usage of wavelengths.In this scheme, all the available wavelength that can be used to establish a connection are considered, the wavelength that has been used the most is selected for the connection.The wavelength usage using the most-used scheme is more compact than that using the first-fit scheme.Studies have shown that with precise global network state information, the most used scheme performs slightly better than the first-fit scheme (Yuan and Zhou, 2000).(iv) Best-fit algorithm: Among all the wavelengths from the list, this algorithm chooses an efficient wavelength for the assignment and is known to be the best fit wavelength assignment.According to the previous study the best fit algorithm performs better than other existing algorithms.Depending upon the number of wavelengths and load given to the path per unit link, the blocking probability of the best fit increases and decreases respectively (Yuan and Zhou, 2000).

BLOCKING PROBABILITY
If there is no free wavelength available on any link, the call will be blocked.In simple terms blocking probability as per Poisson's formula can be calculated as the ratio of calls blocked to the total number of calls generated as given below The network performance of any network can be measured through blocking probability, which is the statistical probability that a telephone connection cannot be connected due to insufficient transmission resources in the network.Also, the blocking probability on the link can be calculated by famous Erlang-B formula as given by Wan et al. (2003) Equation ( 2). (2) Where, P b(L,W) is blocking probability for L load and W wavelengths.

MODELING SETUP
Here, the enhanced algorithm is given and is evaluated in terms of blocking probability.Following assumptions are made to design the model: (i) The network is connected in an arbitrary topology.Each link has a fixed number of wavelengths.(ii) Point to point traffic.(iii) There is no queuing of the connection request.The connection blocked will suddenly be discarded.Firstly, a source to destination pair is selected.Then using the shortest path routing algorithm, a route is selected.After that with the help of proposed algorithm, wavelength is assigned to the route.Until blocking, leastused wavelength assignment algorithm is executed.If the call is blocked, the concept of wavelength conversion is introduced which is done with the help of wavelength converters and hence blocking probability is reduced.

RESULTS AND DISCUSSION
Here, the simulation results of proposed algorithm are shown.constant.The results prove that the blocking probability of the proposed algorithm decreases with the increase in the number of wavelengths.In the second phase, the load per unit link is increased keeping the other