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Stationary joint distributions arising in the analysis of the M/G/1 queue by the method of the imbedded markov chain

Published online by Cambridge University Press:  14 July 2016

J. H. Jenkins
J. H. Jenkins*
Affiliation:
Birkbeck College and West Ham College of Technology
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Summary

Probability generating functions are used to relate the joint distribution of the numbers of customers left behind by two successive departing customers to the marginal distribution of the number left behind by each departing customer. A probability generating function is then found for the joint distribution of the numbers of customers arriving in two successive departure intervals using the joint distribution of the numbers of customers left behind by three successive departing customers. The results could be obtained from general Markov chain theory but the method used in this paper is quicker.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 512 - 520
Copyright
Copyright © Applied Probability Trust 

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References

Burke, P. J. (1956) The output of a queueing system. Operat. Res. 4, 699–704.Google Scholar
Finch, P. D. (1959) The output process of the queueing system M/G/1. J. R. Statist. Soc. B, 21, 375–380.Google Scholar
Kendall, D. G. (1951) Some problems in the theory of queues. J. R. Statist. Soc. B, 13, 151–185.Google Scholar