Prioritized scheduling in WDM packet switching networks with limited range wavelength conversion

In this paper we study scheduling problems in unbuffered WDM packet switching networks when the packets have different priorities. The WDM packet switching networks we consider have wavelength conversion ability. We focus on limited range wavelength conversion since it is easier to implement and more cost effective than full range wavelength conversion and also contains the latter as a special case. We formalize the problem of optimal scheduling as a problem of finding an optimal matching in a weighted bipartite graph. The optimal matching is capable of both maximizing network throughput and providing good service differentiation. We give a simple algorithm called Zig-Zag Path Insertion Algorithm which solves the problem in O(NK log(Nk) + NkD) time, where N is the number of input/output fibers of the switching network, k is the number of wavelengths per fiber and D is the conversion degree, as compared to O(N(2)k(2)) time if directly adopting other existing algorithms.