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On the convergence to stationarity of birth-death processes

Coolen-Schrijner, P.; Van Doorn, E.A.

Authors

P. Coolen-Schrijner

E.A. Van Doorn



Abstract

Taking up a recent proposal by Stadje and Parthasarathy in the setting of the many-server Poisson queue, we consider the integral ∫0∞[limu→∞E(X(u))-E(X(t))]dt as a measure of the speed of convergence towards stationarity of the process {X(t) , t≥0}, and evaluate the integral explicitly in terms of the parameters of the process in the case that {X(t) , t≥0} is an ergodic birth-death process on {0,1,....} starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.

Citation

Coolen-Schrijner, P., & Van Doorn, E. (2001). On the convergence to stationarity of birth-death processes. Journal of Applied Probability, 38(3), 696-706. https://doi.org/10.1239/jap/1005091033

Journal Article Type Article
Publication Date 2001-09
Deposit Date May 1, 2007
Journal Journal of Applied Probability
Print ISSN 0021-9002
Electronic ISSN 1475-6072
Publisher Applied Probability Trust
Peer Reviewed Peer Reviewed
Volume 38
Issue 3
Pages 696-706
DOI https://doi.org/10.1239/jap/1005091033
Keywords Birth-death process, Speed of convergence.

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