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On two stationary distributions for the stable GI/G/1 queue

Published online by Cambridge University Press:  14 July 2016

Austin J. Lemoine
Austin J. Lemoine*
Affiliation:
Clemson University, South Carolina
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Abstract

This paper provides simple proofs of two standard results for the stable GI/G/1 queue on the structure of the distribution functions of the stationary virtual waiting time and the stationary queue-length Our argument is applicable to more general single server systems than the queue GI/G/1.

Keywords

STABLE G//G/1 QUEUESTATIONARY VIRTUAL WAITING TIMESTATIONARY QUEUE-LENGTHSTATIONARY ACTUAL WAITING TIME
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 849 - 852
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

Research supported by N.S.F. Grant No. GK-39073.

References

[1]Cohen, J. W. (1969) The Single Server Queue. North Holland, Amsterdam.Google Scholar
[2]Lemoine, A. J. (1974) Limit theorems for generalized single server queues. Adv. Appl. Prob. 6, 159–174.Google Scholar
[3]Lemoine, A. J. (1974) Limit theorems for generalized single server queues: the exceptional system. SIAM J. Appl. Math. To appear.Google Scholar
[4]Takács, L. (1963) The limiting distribution of the virtual waiting time and the queue size for a single-server queue with recurrent input and general service times. Sankyha A 25, 91–100.Google Scholar