Polynomial-time Perfect Sampler for Closed Jackson Networks with Single Servers

In this paper, we propose a sampler for the product-form solution of basic queueing networks, closed Jackson networks with single servers. Our approach is sampling via Markov chain, but it is NOT a simulation of behavior of customers in queueing networks. We propose a new ergodic Markov chain whose unique stationary distribution is the product form solution of a closed Jackson Network, thus we can sample from the product form solution without knowing the value of its normalizing constant. The sampler is based on monotone Coupling from the Past (monotone CFTP) and realizes the sampling from the target distribution exactly. We show that the chain is monotone and rapidly mixing, and that the expected running time of the sampling algorithm is O(n ln(Kn)) where n is the number of nodes in the network and K is the number of customers.