Dimensioning an OBS switch with partial wavelength conversion and fiber delay lines via a mean field model

In this paper we introduce a mean field model to analyze an optical switch equipped with both wavelength converters (WCs) and fiber delay lines (FDLs) to resolve contention in OBS networks. Under some very general conditions, that is, a general burst size distribution and any Markovian burst arrival process at each wavelength, this model determines the minimum number of WCs required to achieve a zero loss rate as the number of wavelengths becomes large. The mean field result is exact as the number of wavelengths goes to infinity and turns out to be very accurate for systems with (a few) hundred wavelengths, commonly occurring when using wavelength division multiplexing (WDM). Moreover, we show that if the number of WCs is underdimensioned, (i) periodic system behavior may occur (with the period being the greatest common divisor of the burst lengths) and (ii) increasing the number of WCs may even worsen the loss rate under the often studied minimum horizon allocation policy (as opposed to the minimum gap policy). Finally, we further demonstrate that in terms of the loss rate, including (more) FDLs may have little or no effect on the number of WCs required to achieve a near-zero loss, especially for higher loads.