June 2011 Exact Monte Carlo simulation for fork-join networks
Hongsheng Dai
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Adv. in Appl. Probab. 43(2): 484-503 (June 2011).


In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to $K$ parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.


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Hongsheng Dai. "Exact Monte Carlo simulation for fork-join networks." Adv. in Appl. Probab. 43 (2) 484 - 503, June 2011.


Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1220.65010
MathSciNet: MR2848387

Primary: 65C05 , 65C50
Secondary: 60K20 , 60K25

Keywords: Coupling from the past , fork-join network , perfect sampling , read-once coupling from the past

Rights: Copyright © 2011 Applied Probability Trust


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Vol.43 • No. 2 • June 2011
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