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Stochastic inequalities for an overflow model

Published online by Cambridge University Press:  14 July 2016

Arie Hordijk  and
Ad Ridder
Arie Hordijk*
Affiliation:
University of Leiden
Ad Ridder*
Affiliation:
University of Leiden
*
∗Postal address: University of Leiden, Department of Mathematics and Computer Science, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
∗Postal address: University of Leiden, Department of Mathematics and Computer Science, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
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Abstract

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

Keywords

QUEUEING NETWORKSSTATIONARY DISTRIBUTIONINSENSITIVE BOUNDS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 696 - 708
Copyright
Copyright © Applied Probability Trust 1987 

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