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Sensitivity analysis for stationary and ergodic queues

Part of: Stability theory Special processes

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.

References

[1] Asmussen, S. (1987) Applied Probability and Queues. Wiley, New York.Google Scholar
[2] Bartle, R. G. (1979) The Elements of Real Analysis. Wiley, New York.Google Scholar
[3] Baccelli, F. and Bremaud, P. (1987) Palm Probabilities and Stationary Queues. Lectures Notes in Statistics 41, Springer-Verlag, Berlin.CrossRefGoogle Scholar
[4] Brémaud, P. (1991) An elementary proof of Sengupta's invariance relation and a remark on Miyazawa's conservation principle. J. Appl. Prob. 28, 950–954.CrossRefGoogle Scholar
[5] Cao, X. R. (1987) Realization probability in closed Jackson queueing networks and its application. Adv. Appl. Prob. 19, 708–738.CrossRefGoogle Scholar
[6] Cao, X. R. (1988) A sample performance function of closed Jackson queueing networks. Operat. Res. 36, 1, 128–136.CrossRefGoogle Scholar
[7] Glasserman, P. (1990) Gradient Estimation via Perturbation Analysis. Kluwer Academic, Boston.Google Scholar
[8] Glasserman, P., Hu, J. Q. and Strickland, S. G. (1990) Strongly consistent steady-state derivative estimates. Technical Report, Division of Applied Sciences, Harvard University.Google Scholar
[9] Gut, A. (1988) Stopped Random Walks. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[10] Heidelberger, P., Cao, X. R., Zazanis, M. A. and Suri, R. (1988) Convergence properties of infinitesimal perturbation analysis. Management Sci. 34, 1281–1302.CrossRefGoogle Scholar
[11] Ho, Y. C. (1987) Performance evaluation and perturbation analysis of discrete event dynamic systems. IEEE Trans. Autom. Control 32, 563–572.Google Scholar
[12] Hu, J. Q. (1990) Convexity of sample path performance and strong consistency of infinitesimal perturbation analysis estimates. IEEE Trans. Autom. Control. Google Scholar
[13] Konstantopoulos, P. and Zazanis, M. (1990) Extensions of perturbation analysis to stationary queues. Allerton Conference, October 1990.Google Scholar
[14] Neveu, J. (1976) Sur les mesures de Palm de deux processus ponctuels stationnaires. Z. Wahrscheinlichkeitsth. 34, 199–203.CrossRefGoogle Scholar
[15] Suri, R. and Zazanis, M. (1988) Perturbation analysis gives strongly consistent estimates for the M/G/1 queue. Management Sci. 34, 39–64.CrossRefGoogle Scholar
[16] Walrand, J. (1988) An Introduction to Queueing Networks. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[17] Zazanis, M. and Suri, R. (1989) Perturbation analysis of the GI/G/1 queue. QUESTA. Submitted.Google Scholar