Setwise and filtered Gibbs samplers for teletraffic analysis

A setwise Gibbs sampler (SGS) method is developed to simulate stationary distributions and performance measures of network occupancy of Baskett-Chandy-Muntz-Palacios (BCMP) telecommunication models. It overcomes the simulation difficulty encountered in applying the standard Gibbs sampler to closed BCMP networks with constant occupancy constraints. We show Markov chains induced by SGS converge to the target stationary distributions. This article also investigates the filtered Gibbs sampler (FGS) as an efficient method for estimating various network performance measures. It shows that FGS's efficiency is considerable, but may be improperly overestimated. A more conservative performance estimator is then presented.