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December, 1976 Random Overlapping Intervals--A Generalization of Erlang's Loss Formula
David Oakes
Ann. Probab. 4(6): 940-946 (December, 1976). DOI: 10.1214/aop/1176995938


Consider a queueing system with infinitely many servers, a general distribution of service times and an instantaneous rate $\alpha_k$ of new arrivals, where $\alpha_k$ depends only on the number of busy servers. This is called a generalized Erlang model (GEM) since if $\alpha_k = \alpha (k < N), \alpha_k = 0 (k \geqq N)$, then Erlang's model for a telephone exchange with $N$ lines is recovered. The synchronous and asynchronous stationary distributions of the GEM are determined and several interesting properties of the process are discussed. In particular the stationary GEM is shown to be reversible.


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David Oakes. "Random Overlapping Intervals--A Generalization of Erlang's Loss Formula." Ann. Probab. 4 (6) 940 - 946, December, 1976.


Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0351.60085
MathSciNet: MR423589
Digital Object Identifier: 10.1214/aop/1176995938

Primary: 60K30
Secondary: 60K20 , 60K25

Keywords: Erlang's formula , infinite server queues , pure loss queueing systems , random intervals , reversibility , semi-Markov process , state-dependent arrival rates , synchronous and asynchronous distributions

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 6 • December, 1976
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