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On the busy period of discrete-time queues

Published online by Cambridge University Press:  14 July 2016

T. Gergely  and
T. L. Török
T. Gergely
Affiliation:
Central Research Institute for Physics, Budapest
T. L. Török
Affiliation:
Central Research Institute for Physics, Budapest
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Abstract

This paper obtains the probability and the expectation of the length of the busy and idle periods in a discrete-time service system by means of two-component Markov chains and their first passage times. The M/G/1 model is discussed as a special case.

Keywords

QUEUESDISCRETE TIMEGI/G/1BUSY PERIODIDLE PERIODMARKOV CHAINS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 853 - 857
Copyright
Copyright © Applied Probability Trust 1974 

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References

Cohen, J. W. (1969) The Single Server Queue. North Holland, Amsterdam.Google Scholar
Dafermos, S. C. and Neuts, M. F. (1971) A single server queue in discrete time. Cahiers Centre Rech. Opérat. 13, 23–40.Google Scholar
Finch, P. D. (1961) On the busy period in the queueing system GI/G/1. J. Austral. Math. Soc. 2, 217–228.Google Scholar
Gergely, T. and Yezhow, I. I. (1972) Markov-chains homogeneous in second component. European Meeting of Statisticians, Budapest.Google Scholar