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On the convergence to stationarity of birth-death processes.

Coolen-Schrijner, P. and Van Doorn, E. A. (2001) 'On the convergence to stationarity of birth-death processes.', Journal applied probability., 38 (3). pp. 696-706.


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.

Item Type:Article
Keywords:Birth-death process, Speed of convergence.
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Record Created:01 May 2007
Last Modified:15 Feb 2010 12:42

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