Martingale methods for analysing single-server queues

Martingale methods for analysing single-server queues

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Article ID: iaor20041314
Country: Netherlands
Volume: 41
Issue: 3
Start Page Number: 205
End Page Number: 239
Publication Date: Jul 2002
Journal: Queueing Systems
Authors: ,
Keywords: M/G/1 queues
Abstract:

In this paper we present a martingale method for analysing queues of M/G/1 type, which have been generalised so that the system passes through a series of phases on which the service behaviour may differ. The analysis uses the process embedded at departures to create a martingale, which makes possible the calculation of the probability generating function of the stationary occupancy distribution. Specific examples are given, for instance, a model of an unreliable queueing system, and an example of a queue-length-threshold overload-control system.

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