Rejection rules in the M/G/1 queue

Rejection rules in the M/G/1 queue

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Article ID: iaor19971599
Country: United States
Volume: 19
Issue: 1/2
Start Page Number: 105
End Page Number: 130
Publication Date: May 1995
Journal: Queueing Systems
Authors: ,
Keywords: queues
Abstract:

The authors consider a M/G/1 queue modified such that an arriving customer may be totally or partially rejected dependong on a r.v. (the barricade) describing his impatience and on the state of the system. Three main variants of this scheme are studied. The steady-state distribution is expressed in terms of Volterra equations and the relation to storage processes, dams and queues with state-dependent Poisson arrival rate is discussed. For exponential service times, the authors further find the busy period Laplace transform in the case of a deterministic barricade, whereas for exponential barricade it is shown by a coupling argument that the busy period can be identified with a first passage time in an associated birth-death process.

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