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Regenerative rare events simulation via likelihood ratios

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Søren Asmussen ,
Reuven Y. Rubinstein  and
Chia-Li Wang
Søren Asmussen*
Affiliation:
Aalborg University
Reuven Y. Rubinstein*
Affiliation:
Technion — Israel Institute of Technology
Chia-Li Wang*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Institute of Electronic Systems, Aalborg University, Fr. Bajersvej 7, DK-9220 Aalborg, Denmark.
∗∗ Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel.
∗∗∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
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Abstract

In this paper we obtain some new theoretical and numerial results on estimation of small steady-state probabilities in regenerative queueing models by using the likelihood ratio (score function) method, which is based on a change of the probability measure. For simple GI/G/1 queues, this amounts to simulating the regenerative cycles by a suitable change of the interarrival and service time distribution, typically corresponding to a reference traffic intensity ρ0 which is < 1 but larger than the given one ρ. For the M/M/1 queue, the resulting gain of efficiency is calculated explicitly and shown to be considerable. Simulation results are presented indicating that similar conclusions hold for gradient estimates and in more general queueing models like queueing networks.

Keywords

QUEUEING THEORYQUEUEING NETWORKSREGENERATIVE QUEUEING MODELS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 797 - 815
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported by the Technion V.P.R. Fund — B.R.L. Bloomfield Industrial Management R.F.

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