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Steady-state Markov chain models for the Heine and Euler distributions

Part of: Basic hypergeometric functions Markov processes

Published online by Cambridge University Press:  14 July 2016

A. W. Kemp
A. W. Kemp*
Affiliation:
University of St Andrews
*
∗ Postal address: Department of Mathematical and Computational Sciences, University of St Andrews, St Andrews KY16 9SS, UK.
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Abstract

The paper puts forward steady-state Markov chain models for the Heine and Euler distributions. The models for oil exploration strategies that were discussed by Benkherouf and Bather (1988) are reinterpreted as current-age models for discrete renewal processes. Steady-state success-runs processes with non-zero probabilities that a trial is abandoned, Foster processes, and equilibrium random walks corresponding to elective M/M/1 queues are also examined.

Keywords

q-ANALOGUESSUCCESS-RUNSFOSTER PROCESSELECTIVE M/M/1 QUEUE

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 869 - 876
Copyright
Copyright © Applied Probability Trust 1992 

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References

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