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The waiting-time process of a queueing system with gamma-type input and blocking

Published online by Cambridge University Press:  14 July 2016

C. Langaris
C. Langaris*
Affiliation:
University of Ioannina
*
∗Postal address: Department of Mathematics, University of Ioannina, Ioannina 45332, Greece.
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Abstract

In this work the first-come-first-served waiting-time process of a customer in a two-stage queueing network without intermediate waiting space is analysed. We assume that the arrivals follow the gamma distribution, the service times in the first stage are arbitrarily distributed, and the service times in the second stage are again of gamma type.

Connecting the waiting time of the (n + 1)th customer with that of the nth and locating the zeros of a certain function we derive expressions for the Laplace transform of the waiting-time distribution both in the transient and the steady state.

Keywords

TANDEM QUEUESFINITE WAITING SPACEERLANG DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 166 - 174
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Avi-Itzhak, B. and Yadin, M. (1965) A sequence of two servers with no intermediate queue. Management Sci. 11, 553–564.Google Scholar
[2] Langaris, C. and Conolly, B. (1984) On the waiting time of a two-stage queueing system with blocking. J. Appl. Prob. 21, 628–638.Google Scholar
[3] Neuts, M. F. (1968) Two queues in series with a finite, intermediate waiting room. J. Appl. Prob. 5, 123–147.Google Scholar
[4] Prabhu, N. U. (1967) Transient behaviour of a tandem queue. Management Sci. 13, 631–639.Google Scholar
[5] Suzuki, T. (1964) On a tandem queue with blocking. J. Operat. Res. Soc. Japan 6, 137–157.Google Scholar
[6] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar