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The Trivariate Distribution of the Maximum Queue Length, the Number of Customers Served and the Duration of the Busy Period for the M/G/1 Queueing System

Published online by Cambridge University Press:  14 July 2016

E.G. Enns
E.G. Enns*
Affiliation:
University of Queensland
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Extract

In the study of the busy period for a single server queueing system, three variables that have been investigated individually or at most in pairs are:

  1. 1. The duration of the busy period.

  2. 2. The number of customers served during the busy period.

  3. 3. The maximum number of customers in the queue during the busy period.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 154 - 161
Copyright
Copyright © Applied Probability Trust 

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References

[1] Cohen, J. W. (1967) The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1. J. Appl. Prob. 4, 162–179.Google Scholar
[2] Heathcote, C. R. (1965) On the maximum of the queue GI/M/1. J. Appl. Prob. 2, 206–214.Google Scholar
[3] Neuts, M. F. (1964) The distribution of the maximum length of a Poisson queue during a busy period. Operat. Res. 12, 281–285.Google Scholar
[4] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[5] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. John Wiley, New York.Google Scholar
[6] Seneta, E. (1967) On the maxima of absorbing Markov chains. Aust. J. Statist. 9, 93–102.CrossRefGoogle Scholar
[7] Rao, C. R. (1962) A note on a generalized inverse of a matrix with applications to problems in Mathematical Statistics. J. R. Statist. Soc. B 24, 152–158.Google Scholar