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A queue with poisson input and semi-Markov service times: busy period analysis

Published online by Cambridge University Press:  14 July 2016

Peter Purdue
Peter Purdue*
Affiliation:
University of Kentucky
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Abstract

We discuss here an extension of a queueing model studied by Neuts and also by Çinlar. We obtain a matrix form of Takács' equations and exhibit the equilibrium conditions. We also show that the conditions imposed by Neuts and by Çinlar in order to obtain their results concerning the busy period are not necessary.

Keywords

QUEUEING THEORYVOLTERRA TYPE INTEGRAL EQUATIONSMATRIC FUNCTIONSQUEUES WITH DIFFERENT CUSTOMER TYPES
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 353 - 357
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Çinlar, E. (1967) Time dependence of queues with semi-Markovian services. J. Appl. Prob. 4, 356–364.Google Scholar
[2] Çinlar, E. (1967) Queues with semi-Markovian arrivals. J. Appl. Prob. 4, 365–379.Google Scholar
[3] Çinlar, E. (1969) Markov renewal theory. Adv. Appl. Prob. 1, 123–187.Google Scholar
[4] Neuts, M. F. (1966) The single server queue with Poisson input and semi-Markovian service times. J. Appl. Prob. 3, 202–230.Google Scholar
[5] Neuts, M. F. (1968) Two servers in series, treated in terms of a Markov renewal branching process. Adv. Appl. Prob. 2, 110–149.Google Scholar
[6] Neuts, M. F. (1971) A queue subject to extraneous phase changes. Adv. Appl. Prob. 3, 78–119.Google Scholar
[7] Neuts, M. F. and Purdue, P. (1971) Multivariate semi-Markovian matrices. J. Austral. Math. Soc. 13, 107–113.Google Scholar
[8] Purdue, P. (1973) Non-linear matrix integral equations of Volterra type in queueing theory. J. Appl. Prob. 10, 644–651.Google Scholar