Grid Job Routing Algorithms - Phosphorus

Grid Job Routing AlgorithmsAppendix A Linear Programming Formulation toSolve the RWA problemIn this Appendix a detailed description of the Linear Formulation for Routing and Wavelength Assignmentproblem is presented. The following parameters are considered to be known beforehand and are given as inputto the algorithm for the routing of a given set of connections.G(V,A) a unidirectional graph, where V is the set of vertices describing the nodes of the network and A the setof edges describing the links of the network.N = |V| the number of the nodes of the network.L = |A| the number of the edges of the network.C the set of the available wavelengths.W = |C| the total number of the available wavelengths.R the traffic matrix in units of lightpaths, i.e. R 12 = 2 indicates that there are 2 connection/lightpath requestsbetween nodes 1 and 2 of the network.U the total number of the distinct source-destination pairs.k the total number of paths (main and alternate/protection) that have to be selected for each request.P the set of all paths (main and alternate/protection) of all the connections.Z the set of all nodes that have wavelength conversion capabilities.Q the set of all available wavelength conversions at all the nodes of the network.Project:PHOSPHORUSDeliverable Number: D.5.3Date of Issue: 31/06/07EC Contract No.: 034115Document Code: Phosphorus-WP5-D5.396