Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-27T04:40:04.067Z Has data issue: false hasContentIssue false
  • English
  • Français

A proof of simple insensitive bounds for a pure overflow system

Published online by Cambridge University Press:  14 July 2016

Nico M. Van Dijk
Nico M. Van Dijk*
Affiliation:
Twente University
*
∗Present address: Faculty of Economical Sciences and Econometrics, Free University, P.O. Box 7161, 1007 MC Amsterdam, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

In [1], [4] and [6] simple and intuitively obvious bounds were suggested for various overflow systems and claimed to be insensitive, that is to be valid also in the non-exponential case. This insensitivity was formalized in [4] and [6] when the service distributions have a monotone failure rate. This technical note provides another proof which for the case of a pure overflow system with one customer class extends the insensitivity to the general case.

Keywords

LOSS PROBABILITYBOUNDINSENSITIVITYMARKOV CHAIN
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 113 - 120
Copyright
Copyright © Applied Probability Trust 1989 

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] Van Dijk, N. M. (1987) Simple and insensitive bounds for a grading and an overflow model. Operat. Res. Letters 6, 73–76.CrossRefGoogle Scholar
[2] Van Dijk, N. M. (1988) A formal proof for the insensitivity of simple bounds for finite multiserver non-exponential tandem queues. Stoch. Proc. Appl. 27, 261–277.Google Scholar
[3] Van Dijk, N. M. and Lamond, B. F. (1988) Bounds for the call congestion of finite single-server exponential tandem queues. Operat. Res. 36, 470–477.Google Scholar
[4] Hordijk, A. and Ridder, A. (1987) Stochastic inequalities for an overflow model. J. Appl. Prob. 25, 9–20.Google Scholar
[5] Hordijk, A. and Schassberger, R. (1982) Weak convergence of generalized semi-Markov processes. Stoch. Proc. Appl. 2, 271–291.Google Scholar
[6] Ridder, A. (1987) Stochastic Inequalities for Queues. Ph.D. Thesis, University of Leiden.Google Scholar
[7] Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
[8] Whitt, W. (1981) Comparing counting processes and queues. Adv. Appl. Prob. 13, 207–220.CrossRefGoogle Scholar