A perfect sampling algorithm of random walks with forbidden arcs

International audienceIn this paper we show how to construct an algorithm to sample the stationary distribution of a random walk over ${1,...,N}^d$ with forbidden arcs. This algorithm combines the rejection method and coupling from the past of a set of trajectories of the Markov chain that generalizes the classical sandwich approach. We also provide a complexity analysis of this approach in several cases showing a coupling time in $O(N^2 d log d )$ when no arc is forbidden and an experimental study of its performance

A perfect sampling algorithm of random walks with forbidden arcs

In this paper we show how to construct an algorithm to sample the stationary distribution of a random walk over a grid with forbidden arcs. This algorithm combines the rejection method and coupling from the past of a set of trajectories of the Markov chain that generalizes the classical sandwich approach. We also provide a complexity analysis of this approach in several cases showing a coupling time that is logarithmic in the size of the grid, when no arc is forbidden, and an experimental study of its performance

Perfect Sampling of Networks with Finite and Infinite Capacity Queues

International audienceWe consider open Jackson queueing networks with mixed finite and infinite buffers and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain has a large or even infinite state space. The main idea is to use a Jackson network with infinite buffers (that has a product form stationary distribution) to bound the number of initial conditions to be considered in the coupling from the past scheme. We also provide bounds on the sampling time of this new perfect sampling algorithm under hyper-stability conditions (to be defined in the paper) for each queue. These bounds show that the new algorithm is considerably more efficient than existing perfect samplers even in the case where all queues are finite. We illustrate this efficiency through numerical experiments