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A single-server queue with limited virtual waiting time

Published online by Cambridge University Press:  14 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Case Western Reserve University, Cleveland, Ohio
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Abstract

The limiting distributions of the actual waiting time and the virtual waiting time are determined for a single-server queue with Poisson input and general service times in the case where there are two types of services and no customer can stay in the system longer than an interval of length m.

Keywords

FINITE QUEUESINGLE SERVERPOISSON INPUTGENERAL SERVICE TIMESACTUAL WAITING TIMEVIRTUAL WAITING TIMELIMITING DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 612 - 617
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Daley, D. J. (1964) Single-server queuing systems with uniformly limited queuing time. J. Austral. Math. Soc. 4, 489–505.Google Scholar
[2] Takács, L. (1960) The transient behavior of a single server queueing process with a Poisson input. Proc. 4th Berkeley Symp. Math. Statist. Prob. 535–567. University of California Press.Google Scholar
[3] 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. Sankya A 25, 91–100.Google Scholar
[4] Takács, L. (1967) The distribution of the content of finite dams. J. Appl. Prob. 4, 151–161.Google Scholar