Approximate/perfect samplers for closed Jackson networks

Authors:
Shuji Kijima;Tomomi Matsui
Affiliations:
University of Tokyo, Bunkyo-ku, Tokyo, Japan;University of Tokyo, Bunkyo-ku, Tokyo, Japan
Venue:
WSC '05 Proceedings of the 37th conference on Winter simulation
Year:
2005

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Abstract

In this paper, we propose two samplers for the productform solution of basic queueing networks, closed Jackson networks with multiple servers. Our approach is sampling via Markov chain, but it is NOT a simulation of behavior of customers in queueing networks. We propose two of new ergodic Markov chains both of which have a unique stationary distribution that is the product form solution of closed Jackson networks. One of them is for approximate sampling, and we show it mixes rapidly. To our knowledge, this is the first approximate polynomial-time sampler for closed Jackson networks with multiple servers. The other is for perfect sampling based on monotone CFTP (coupling from the past) algorithm proposed by Propp and Wilson, and we show the monotonicity of the chain.