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Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Naoto Miyoshi  and
Toshiharu Hasegawa
Naoto Miyoshi*
Affiliation:
Kyoto University
Toshiharu Hasegawa*
Affiliation:
Kyoto University
*
∗ Address for both authors: Division of Applied Systems Science, Faculty of Engineering, Kyoto University, Kyoto 606-01, Japan.
∗ Address for both authors: Division of Applied Systems Science, Faculty of Engineering, Kyoto University, Kyoto 606-01, Japan.
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Abstract

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

Keywords

SENSITIVITY ANALYSISSMOOTHED PERTURBATION ANALYSISSTRONG CONSISTENCYSINGLE-RUN ESTIMATIONFCFSLCFSPREEMPTIVE LIFONON-PREEMPTIVE PRIORITY QUEUEPREEMPTIVE-RESUME PRIORITY QUEUE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 2 , June 1997 , pp. 545 - 566
Copyright
Copyright © Applied Probability Trust 1997 

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