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Elastic Optical Network (EON) has been considered as a promising opticalnetworking technology to architect the next-generation backbone networks.Routing and Spectrum Assignment (RSA) is the fundamental problem in EONs torealize service provisioning. Generally, the RSA is solved by routing therequests with lightpaths first and then assigning spectrum resources to thelightpaths to optimize the spectrum usage. Thus, the spectrum assignmentexplicitly decide the final spectrum usage of EONs. However, besides thespectrum assignment, there are three other factors, the network topology,traffic distribution and routing scheme, implicitly impact on the spectrumusage. Few related work involves in the implicit impact mechanism. In thispaper, we aim to provide a thoroughly theoretical analysis on the impact of thethree key factors on the spectrum usage. To this end, two theoretical chainsare proposed: (1) The optimal spectrum usage can be measured by the chromaticnumber of the conflict graph, which is positively correlated to theintersecting probability, \emph{i.e.}, the smaller the intersectingprobability, the smaller the optimal spectrum usage; (2) The intersectingprobability is decided by the network topology, traffic distribution androuting scheme via a quadratic programming parameterized with a matrix ofconflict coefficients. The effectiveness of our theoretical analysis has beenvalidated by extensive numerical results. Meanwhile, our theoretical deductionsalso permit to give several constant approximation ratios for RSA algorithms.

How the Network Topology, Traffic Distribution, and Routing Scheme Impact on the Spectrum Usage in Elastic Optical Networks