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September, 1953 On the Stochastic Matrices Associated with Certain Queuing Processes
F. G. Foster
Ann. Math. Statist. 24(3): 355-360 (September, 1953). DOI: 10.1214/aoms/1177728976


We shall be concerned with an irreducible Markov chain, which we shall call "the system." For simplicity we shall assume that the system is aperiodic, but this is not essential. The reader is referred to [1] for explanations of the terminology used. We first state some general theorems which provide criteria for determining whether the system is transient, recurrent-null or ergodic (recurrent-nonnull). These are then applied to the Markov chains associated with certain queuing processes recently studied by D. G. Kendall [4], [5]; most of the results have already been obtained by Kendall using direct methods, and the main purpose of the present paper is to illustrate the application of general theorems to this type of problem.


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F. G. Foster. "On the Stochastic Matrices Associated with Certain Queuing Processes." Ann. Math. Statist. 24 (3) 355 - 360, September, 1953.


Published: September, 1953
First available in Project Euclid: 28 April 2007

zbMATH: 0051.10601
MathSciNet: MR56232
Digital Object Identifier: 10.1214/aoms/1177728976

Rights: Copyright © 1953 Institute of Mathematical Statistics

Vol.24 • No. 3 • September, 1953
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