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Sensitivity analysis for stationary and ergodic queues

Part of: Special processes Stability theory

Published online by Cambridge University Press:  01 July 2016

P. Konstantopoulos  and
Michael A. Zazanis
P. Konstantopoulos
Affiliation:
INRIA
Michael A. Zazanis*
Affiliation:
Northwestern University
*
∗∗Postal address: Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA.
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Abstract

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

Keywords

PERTURBATION ANALYSISQUEUEING NETWORKS

MSC classification

Primary: 60K25: Queueing theory
Secondary: 34D10: Perturbations
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 738 - 750
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

∗

Present address: Electrical Engineering and Computer Science Department, University of California, Berkeley, CA 94720, USA.

Supported in part by NSF Grants ECS-88110033 and DDM-8905638.

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