Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T01:22:25.155Z Has data issue: false hasContentIssue false
  • English
  • Français

The M/G/k loss system with servers subject to breakdown

Published online by Cambridge University Press:  14 July 2016

D. Fakinos
D. Fakinos*
Affiliation:
Air Force General Staff, Athens
*
∗ Postal address: 45 Trivonianou Street, T. T. 407, Athens, Greece.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies the equilibrium behaviour of the M/G/k loss system with servers subject to breakdown. Such a system has k servers, whose customers arrive in a Poisson process. They are served if there is an idle server, otherwise they leave and do not return. Each server is subject to breakdown with probability of occurrence depending on the length of the time the server has been busy since his last repair. On a breakdown the customer waits and his service is continued just after the repair of the server. Among other things, a generalization of the Erlang B-formula is given and it is shown that the equilibrium departure process is Poisson. In fact these results are obtained for the more general case where customers may balk and service and repair rates are state dependent.

Keywords

M/G/k LOSS SYSTEMSERVER'S BREAKDOWNEQUILIBRIUM DISTRIBUTIONDEPARTURE PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 706 - 712
Copyright
Copyright © Applied Probability Trust 1983 

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

Fakinos, D. (1980) The M/G/k blocking system with heterogeneous servers. J. Operat. Res. Soc. 31, 919–927.CrossRefGoogle Scholar
Fakinos, D. (1982a) The generalized M/G/k blocking system with heterogeneous servers. J. Operat. Res. Soc. 33, 801–810.CrossRefGoogle Scholar
Fakinos, D. (1982b) The M/G/k group-arrival group-departure loss system. J. Appl. Prob. 19, 826–834.CrossRefGoogle Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Shanbhag, D. N. and Tambouratzis, D. G. (1973) Erlang's formula and some results on the departure process for a loss system. J. Appl. Prob. 10, 233–240.CrossRefGoogle Scholar
Takács, L. (1969) On Erlang's formula. Ann. Math. Statist. 40, 71–78.CrossRefGoogle Scholar