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Steady state solution of a single-server queue with linear repeated requests

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

J. R. Artalejo  and
A. Gomez-Corral
J. R. Artalejo*
Affiliation:
Universidad Complutense de Madrid
A. Gomez-Corral*
Affiliation:
Universidad Complutense de Madrid
*
∗Postal address: Departamento de Estadistica e I.O., Facultad de Matematicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
∗Postal address: Departamento de Estadistica e I.O., Facultad de Matematicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
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Abstract

Queueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.

Keywords

QUEUES WITH REPEATED REQUESTSHYPERGEOMETRIC FUNCTIONS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 223 - 233
Copyright
Copyright © Applied Probability Trust 1997 

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