Wavelength division multiplexing (WDM) technology transmits multiple optical communication channels in an optical fiber. Routing and wavelength assignment (RWA) problems on WDM network have widely attracted interest of many researchers. Recently, so called sub-wavelength paths which are smaller granular paths than the wavelength-paths are discussed. In this paper, we deal with the RWA problem with considering sub-wavelength assignment on optical networks. One of the purpose of our study is to investigate active rates for optical networks. We formulate a sub-wavelength path assignment problem maximizing accommodated traffic demands by integer programming and solve it by a cutting plane algorithm. Since, in actuality, RWA is done individually for each demand on the time when the demand occurs, we consider a greedy type on-line algorithm. Numerical experiments show the efficiency of our algorithms and give some observation for active rates. Moreover, we verify the efficiency of our greedy-type algorithm on realistic situations which follow 10/40/100 Gbps system used for the current communication on optical networks. Our experimental results conclude that the active rates are depending on the configurations of the underlying graphs, and that our greedy-type algorithm is efficient for several kinds of instances.
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