Dai, Hongsheng (2011) 'Exact Monte Carlo simulation for fork-join networks.' Advances in Applied Probability, 43 (2). pp. 484-503. ISSN 0001-8678

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Abstract

<jats:p>In a fork-join network each incoming job is split into <jats:italic>K</jats:italic> tasks and the <jats:italic>K</jats:italic> tasks are simultaneously assigned to <jats:italic>K</jats:italic> 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 <jats:italic>coupling from the past</jats:italic> 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.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	Coupling from the past; fork-join network; perfect sampling; read-once coupling from the past
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science and Health Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor:	Elements
Depositing User:	Elements
Date Deposited:	12 Feb 2013 07:44
Last Modified:	15 Jan 2022 00:54
URI:	http://repository.essex.ac.uk/id/eprint/5495

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