Upper bound on the rate of convergence and truncation bound for non-homogeneous birth and death processes on Z

Y.A. Satin, R.V. Razumchik, A.I. Zeifman and I.A. Kovalev

Applied Mathematics and Computation, 2022, vol. 423, issue C

Abstract: We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on Z with the time–varying and possibly state-dependent intensities. First in the literature upper bounds on the rate of convergence are provided. Upper bounds for the truncation errors are also given. The condition under which a limiting (time-dependent) distribution exists is formulated but relies on the quantities that need to be guessed in each use-case. The developed theory is illustrated by two numerical examples within the queueing theory context.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322000959

DOI: 10.1016/j.amc.2022.127009

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