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

Shuji Kijima, Tomomi Matsui

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)35-55
Number of pages21
JournalAnnals of Operations Research
Volume162
Issue number1
DOIs
Publication statusPublished - Sep 1 2008

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Approximation
Polynomials
Markov chain Monte Carlo methods
Markov chain
Stationary distribution
Markov chain Monte Carlo

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research

Cite this

Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers. / Kijima, Shuji; Matsui, Tomomi.

In: Annals of Operations Research, Vol. 162, No. 1, 01.09.2008, p. 35-55.

Research output: Contribution to journalArticle

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