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On the estimation of probabilities for birth and death processes
Part of
A. I. Zeifman
Journal:

Journal of Applied Probability / Volume 32 / Issue 3 / September 1995

Published online by Cambridge University Press:

14 July 2016, pp. 623-634

Print publication:

September 1995
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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.

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On the estimation of probabilities for birth and death processes