Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-29T00:48:00.605Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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