Worst-case analysis of dynamic wavelength allocation in optical networks

This paper proposes algorithms for allocating wavelengths to connections (lightpaths) in optical wavelength division multiplexed networks, predominantly for ring topologies. A worst-case model is considered, where no blocking of lightpaths is allowed, and there are no assumptions made on the traffic arrival and holding times. The traffic is characterized only by its load L, which is the maximum number of lightpaths that can be present on any link, assuming no blocking. A dynamic traffic model is considered where requests to set up lightpaths arrive over time and must be accommodated without rerouting existing lightpaths, and lightpaths may be terminated over time as well. For networks without wavelength conversion, we show that at least 0.5Llog(2) N wavelengths are required by any dynamic algorithm for rings of N nodes and present an algorithm that uses at most Llog(2) N + L wavelengths for rings and 2(L - I) log, N for trees, We also study the worst-case behavior of the well-known first-fit algorithm, and show that it requires at most 2.52Llog(2) N + 5L wavelengths (small variants of these constants are proven as well). When limited wavelength conversion is allowed, we first show how to use expanders to insure no blocking in arbitrary topologies. Then, we present conversion patterns for rings with conversion degree d = 2, which require Llog(2) L + 4L or 2Llog(2) log(2) L + 4L wavelengths, thereby eliminating the dependence (that exists without wavelength conversion) between the number of wavelengths and N. We also consider different traffic models where lightpath setup requests arrive over time, but once set up, lightpaths are never taken down. For this model the number of wavelengths needed is shown to be only max{0, L - d} + L for a conversion degree of d.