Martingale Methods for Analysing Single-Server Queues |
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Authors: | Roughan M Pearce CEM |
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Institution: | (1) AT&T Labs – Research, 180 Park Av, Florham Park, NJ 07932, USA;(2) Department of Applied Mathematics, University of Adelaide, Adelaide, 5005, Australia |
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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. |
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Keywords: | M/G/1 queue martingale queueing phase overload control |
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