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Sensitivity analysis for stationary and ergodic queues: additional results

Part of: Stability theory Special processes

Published online by Cambridge University Press:  01 July 2016

P. Konstantopoulos  and
M. Zazanis
P. Konstantopoulos*
Affiliation:
University of Texas at Austin
M. Zazanis*
Affiliation:
Northwestern University
*
** Postal address. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60628, USA.
** Postal address. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60628, USA.
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Abstract

Perturbation analysis estimators for expectations of possibly discontinuous functions of the time-stationary workload were derived in [2]. The expressions obtained may, however, not be valid if the customer-stationary distribution of the workload has atoms (at points other than zero). This was pointed out by Brémaud and Lasgouttes in [1]. In this note we clearly state the additional condition required for the validity of the expressions in [2]. We furthermore show how our approximation scheme can also be used to obtain the correct expressions for the right and left derivatives given in [1].

Keywords

STATIONARY PROCESSESPERFORMANCE EVALUATION AND QUEUEINGNON-MARKOVIAN PROCESSES ESTIMATION

MSC classification

Primary: 60K25: Queueing theory
Secondary: 34D10: Perturbations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 556 - 560
Copyright
Copyright © Applied Probability Trust 1994 

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References

[1] Bremaud, P. and Lasgouttes, J.-M. (1992) Stationary IPA estimates for non-smooth functions of the GI/G/1/8 workload. Rapp. de Rech. INRIA No. 1677.Google Scholar
[2] Konstantopoulos, P. and Zazanis, M. (1992) Sensitivity analysis for stationary and ergodic queues. Adv. Appl. Prob. 24, 738–750.Google Scholar
[3] Rudin, W. (1976) Principles of Mathematical Analysis. McGraw-Hill, New York.Google Scholar