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Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers

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Abstract

In this paper, we propose a fully polynomial-time randomized approximation scheme (FPRAS) for a closed Jackson network. Our algorithm is based on the Markov chain Monte Carlo (MCMC) method. Thus our scheme returns an approximate solution, for which the size of the error satisfies a given bound. To our knowledge, this algorithm is the first polynomial time MCMC algorithm for closed Jackson networks with multiple servers. We propose two new ergodic Markov chains, both of which have a unique stationary distribution that is the product form solution for closed Jackson networks. One of them is for an approximate sampler, and we show that it mixes rapidly. The other is for a perfect sampler based on the monotone coupling from the past (CFTP) algorithm proposed by Propp and Wilson, and we show that it has a monotone update function.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Shuji Kijima

  2. Department of Information and System Engineering, Faculty of Science and Engineering, Chuo University, Chuo, Japan

    Tomomi Matsui

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  1. Shuji Kijima
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  2. Tomomi Matsui
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Correspondence to Shuji Kijima.

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Kijima, S., Matsui, T. Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers. Ann Oper Res 162, 35–55 (2008). https://doi.org/10.1007/s10479-008-0317-2

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  • DOI: https://doi.org/10.1007/s10479-008-0317-2

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