The M/M /∞ queue in a random environment

The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state d...

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Bibliographic Details
Published in:Journal of applied probability 1986-03, Vol.23 (1), p.175-184
Main Authors: O'Cinneide, C. A., Purdue, P.
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Factorials
Markov chains
Markov processes
Mathematical moments
Matrices
Operational research and scientific management
Operational research. Management science
Queuing theory. Traffic theory
Random variables
Rational functions
Research Papers
Steady states
Stochastic processes
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Summary:The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state distribution is demonstrated and two numerical examples are presented.
ISSN:0021-9002
1475-6072
DOI:10.2307/3214126