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On the busy period of the modified GI/G/1 queue

Published online by Cambridge University Press:  14 July 2016

A. G. Pakes
A. G. Pakes*
Affiliation:
Monash University
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Abstract

Proceeding from duality results for the GI/G/1 queue, this paper obtains the probability of the number served in a busy period of a GI/G/1 system where customers initiating a busy period have a different service time distribution from other customers. Using duality arguments for processes with interchangeable increments, the Laplace transform of the busy period duration is found for a modified GI/M/1 queue.

Keywords

QUEUESMODIFIED SERVICE DISCIPLINENUMBERS SERVED INLENGTH OFBUSY PERIODS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 192 - 197
Copyright
Copyright © Applied Probability Trust 1973 

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References

Bhat, U. N. (1964) On the busy period of a single server bulk queue with modified service mechanism. Calcutta Statist. Assoc. Bull. 13, 163–171.CrossRefGoogle 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
Kingman, J. F. C. (1966) On the algebra of queues. J. Appl. Prob. 3, 285–326.CrossRefGoogle Scholar
Pakes, A. G. (1972) A GI/M/1 queue with a modified service mechanism. Ann. Inst. Statist. Math. To appear.Google Scholar
Prabhu, N. U. (1965) Queues and Inventories. Wiley, New York.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar
Welch, P. D. (1964) On a generalised queueing process in which the first customer of each busy period receives exceptional service. Operations Res. 12, 736–752.CrossRefGoogle Scholar
Yeo, G. F. (1962) Single server queues with modified service mechanisms. J. Austral. Math. Soc. 3, 491–502.Google Scholar