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An extension of Erlang's formulas which distinguishes individual servers

Published online by Cambridge University Press:  14 July 2016

Jan M. Chaiken  and
Edward Ignall
Jan M. Chaiken
Affiliation:
New York City — Rand Institute
Edward Ignall
Affiliation:
Columbia University, New York
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Abstract

For a particular kind of finite-server loss system in which the number and identity of servers depends on the type of the arriving call and on the state of the system, the limits of the state probabilities (as t → ∞) are found for an arbitrary service-time distribution.

Keywords

ERLANG'S FORMULASSTATE PROBABILITIES FOR INDIVIDUAL SERVERSN SERVER QUEUEEMERGENCY UNITS
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 192 - 197
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. John Wiley, New York.Google Scholar
[2] Carter, G., Chaiken, J. M. and Ignall, I. (1971) Response areas for two emergency units. Tech. Report R-532, New York City — Rand Institute.Google Scholar
[3] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. 2. John Wiley, New York.Google Scholar
[4] Sevast'Yanov, B. A. (1957) An ergodic theorem for Markov processes and its application to telephone systems with refusals. Theor. Probability Appl. 2, 104–112.Google Scholar