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Exact Monte Carlo simulation for fork-join networks

Part of: Probabilistic methods, simulation and stochastic differential equations Special processes

Published online by Cambridge University Press:  01 July 2016

Hongsheng Dai
Hongsheng Dai*
Affiliation:
University of Brighton
*
∗ Postal address: Department of Mathematics, School of Computing, Engineering and Mathematics, University of Brighton, Lewes Road, Brighton BN2 4GJ, UK. Email address: h.dai@brighton.ac.uk
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Abstract

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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.

Keywords

Coupling from the pastfork-join networkperfect samplingread-once coupling from the past

MSC classification

Primary: 65C05: Monte Carlo methods 65C50: Other computational problems in probability
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 2 , June 2011 , pp. 484 - 503
Copyright
Copyright © Applied Probability Trust 2011 

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