Filtered Gibbs sampler for estimating blocking probabilities in WDM optical networks

Blocking probabilities in Wavelength Division Multiplex optical networks are hard to compute for realistic sized systems, even though analytical formulas for the distribution exist (under maximal packing of wavelengths) . This computational difficulty is mainly due to the structure of the state space, which imposes strong coupling constraints amongst components of the occupancy vector. Direct simulation is often used to estimate the blocking probabilities. This paper presents a new method based on the Gibbs sampler, for which the estimation is 'localised' (distributed computation) and carried out conditioning on an appropriate filtration. The filtered estimators benefit from the variance reduction of conditional expectations as well as a reduction in computational effort due to the local estimation. Our simulation results suggest that that these methods dramatically outperform the currently used computational methods. For some systems, other techniques may prove impossible to implement whilst our method is not subject to the curse of dimensionality.