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On the estimation of probabilities for birth and death processes

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1995 

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