Martingale Methods for Analysing Single-Server Queues

Authors:
M. Roughan;C. E. M. Pearce
Affiliations:
AT&T Labs – Research, 180 Park Av. Florham Park, NJ 07932, USA roughan@research.att.com;Department of Applied Mathematics, University of Adelaide, Adelaide 5005, Australia cpearce@maths.adelaide.edu.au
Venue:
Queueing Systems: Theory and Applications
Year:
2002

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Abstract

In this paper we presents 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.