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Queues with paired customers

Published online by Cambridge University Press:  14 July 2016

Guy Latouche
Guy Latouche*
Affiliation:
Université Libre de Bruxelles
*
∗ Postal address: Université Libre de Bruxelles, Faculté des Sciences, Laboratoire d'informatique Théorique, Campus Plaine, Boulevard du Triomphe, C.P. 212, B–1050 Bruxelles, Belgium.
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Abstract

Queueing systems with a special service mechanism are considered. Arrivals consist of two types of customers, and services are performed for pairs of one customer from each type. The state of the queue is described by the number of pairs and the difference, called the excess, between the number of customers of each class. Under different assumptions for the arrival process, it is shown that the excess, considered at suitably defined epochs, forms a Markov chain which is either transient or null recurrent. A system with Poisson arrivals and exponential services is then considered, for which the arrival rates depend on the excess, in such a way that the excess is bounded. It is shown that the queue is stable whenever the service rate exceeds a critical value, which depends in a simple manner on the arrival rates. For stable queues, the stationary probability vector is of matrix-geometric form and is easily computable.

Keywords

QUEUEING THEORYSERVICES BY PAIRSEXCESSCOMPUTATIONAL PROBABILITY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981, pp. 684 - 696
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Research conducted in part while the author was visiting the University of Delaware.

References

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