Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T09:28:51.675Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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