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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.
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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 

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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