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A note on Belyaev's limiting distribution of the intervals between losses in an n-server system

Published online by Cambridge University Press:  14 July 2016

D. G. Tambouratzis
D. G. Tambouratzis*
Affiliation:
University of Manchester
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Summary

The aim of the present note is to give an alternative simpler proof to a result of Belyaev [1], namely that in a loss system of n servers with recurrent input and negative exponential service times the intervals between losses, suitably scaled to have constant mean, tend to a negative exponential distribution as n tends to infinity.

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 457 - 464
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Belyaev, Yu. K. (1963) Limit theorems for dissipative flows. Theor. Probability Appl. 8, 165–173.Google Scholar
[2] Khintchine, A. Y. (1960) Mathematical Methods in the Theory of Queuing. Griffin, London.Google Scholar
[3] Takács, L. (1959) On the limiting distribution of the number of coincidences concerning telephone traffic. Ann. Math. Statist. 30, 134–142.CrossRefGoogle Scholar
[4] Takács, L. (1962) An Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar