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The caudal characteristic curve of queues

Published online by Cambridge University Press:  01 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
University of Delaware
*
∗Present address: Dept. of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA.
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Abstract

Many queues and related stochastic models, and in particular those that have a matrix-geometric stationary probability vector, have steady-state queue-length densities that are asymptotically geometric. The graph of the asymptotic rate η of these densities as a function of the traffic intensity ρ is the caudal characteristic curve. This is an informative graph from which a number of qualitative inferences about the behavior of the queue may be drawn.

The caudal characteristic curve may be computed (by elementary algorithms) for several useful models for which a complete exact numerical solution is not practically feasible. These include queues with certain types of superimposed arrival processes and/or multiple non-exponential servers. The necessary theorems which lead to the algorithmic procedures as well as the interpretation of several numerical examples are discussed.

Keywords

ASYMPTOTIC BEHAVIORSUPERIMPOSED ARRIVAL PROCESSESMULTIPLE SERVERSCOMPUTATIONAL PROBABILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 1 , March 1986 , pp. 221 - 254
Copyright
Copyright © Applied Probability Trust 1986 

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