Grid Job Routing Algorithms - Phosphorus

Grid Job Routing AlgorithmsAppendix B Linear Programming Formulation toSolve the RWA Problem when Users Demandmore than one Wavelengths over the samePathIn this Appendix we present extentions to the LP formulation presented in Appendix A, when there areconnection requests that demand more that one wavelength over the same paths.Assume that we have a request of m=2 wavelengths. We define a new variableof two consecutive wavelengths ' ( , )path p occupies wavelengthsc = cici + 1, ci∈ C . Moreover,c ' of link l . Then we define new constraints:c1. The condition ∑ λpl≤ 1 is transformed topc'λplas follows: c ' is a groupc'λplis an indicator variable, equal to 1 ifcc'∑λpl+ ∑∑ λpl≤1, where c c 'p p c'or c ' = ( c − 1, c)). This condition means that a wavelength c (subset of 'wavelengths c ' , in a link l , can be used only once by any path p .⊂ ( c ' = ( c, c + 1)c ) or a group of2.3.c'c'c cλpl= λpl 'and λpl= λpl ', where l and l ' are consecutive links in path p . This conditionmeans that a path p must occupy the same wavelength c (or wavelengths c ' ) through the links ittraverses.c'∑ ∑ λpl= 1, where l is the first link of the path p and R sd= 2p∈Pc'sd. This condition means that theconnection will use only one path p and only one wavelength pair from the first link l of this path p .On the other hand if 1∑ ∑ pl.p∈PccR sd= , then λ = 1sdProject:PHOSPHORUSDeliverable Number: D.5.3Date of Issue: 31/06/07EC Contract No.: 034115Document Code: Phosphorus-WP5-D5.399