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An explicit solution to a particular Markov chain of M/G/1 type

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts
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Abstract

A Markov chain of M/G/1 type, which arose in a problem of communications engineering, is analyzed by a combination of matrix analysis and appropriate series expansions. The highly explicit results obtainable for this model owe much to analytic methods introduced by Professor Takács. Special features of the numerical implementation of the proposed solution are also discussed. The simplifications proper to this model can also be used in some related, more complex models to be discussed elsewhere.

Keywords

QUEUESALGORITHMIC PROBABILITY

MSC classification

Primary: 60K25: Queueing theory
Type
Part 6 Stochastic Processes
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 337 - 342
Copyright
Copyright © Applied Probability Trust 1994 

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References

[1] Heimann, D. and Neuts, M. F. (1973) The single server in discrete time - numerical analysis IV. Naval Res. Logist. Quart. 20, 753–766.CrossRefGoogle Scholar
[2] Neuts, M. F. (1989) Structured Stochastic Matrices of M/G/1 Type and their Applications. Marcel Dekker, New York.Google Scholar
[3] Neuts, M. F. (1991) The joint distribution of arrivals and departures in quasi-birth-and-death processes. In Numerical Solution of Markov Chains , ed. Stewart, William J., pp. 147–159. Marcel Dekker, New York.Google Scholar
[4] Ramaswami, V. (1988) A stable recursion for the steady state vector in Markov chains of M/G/1 type. Stoch. Models 4, 183–188.CrossRefGoogle Scholar
[5] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[6] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar