The quasi-stationary distributions of queues in heavy traffic
- 1 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 9 (04) , 821-831
- https://doi.org/10.1017/s0021900200036184
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.Keywords
This publication has 5 references indexed in Scilit:
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- On the quasi-stationary distribution of the virtual waiting time in queues with Poisson arrivalsJournal of Applied Probability, 1971
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