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The Quasi-Stationary Distributions of Queues in Heavy Traffic

E. K. Kyprianou
Journal of Applied Probability
Vol. 9, No. 4 (Dec., 1972), pp. 821-831
DOI: 10.2307/3212618
Stable URL: http://www.jstor.org/stable/3212618
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Quasi-Stationary Distributions of Queues in Heavy Traffic
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Abstract

This paper demonstrates that, when in heavy traffic, the quasi-stationary distribution of the virtual waiting time process of both the M/G/1 and GI/M/1 queues as well as the quasi-stationary distribution of the waiting times {Wn} of the M/G/1 queue can be approximated by the same gamma distribution. What characterises this approximating gamma distribution are the first two moments of the service time and inter-arrival time distributions only. A similar approximating behaviour is demonstrated for the queue size process.

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