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On the estimation of probabilities for birth and death processes

Part of: General theory in ordinary differential equations Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

A. I. Zeifman
A. I. Zeifman*
Affiliation:
Vologda State Pedagogical Institute
*
∗Postal address: Vologda State Pedagogical Institute, Vologda, S. Orlova, 6, 160600, Russia.
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Abstract

Let X(t) be a non-homogeneous birth and death process. In this paper we develop a general method of estimating bounds for the state probabilities for X(t), based on inequalities for the solutions of the forward Kolmogorov equations. Specific examples covered include simple estimates of Pr(X(t) < j | X(0) = k) for the M(t)/M(t)/N/0 and M(t)/M(t)/N queue-length processes.

Keywords

DIFFERENTIAL EQUATIONSESTIMATES OF STATE PROBABILITIES

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60K25: Queueing theory 34A30: Linear equations and systems, general
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 623 - 634
Copyright
Copyright © Applied Probability Trust 1995 

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References

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