期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2018
卷号：28
期号：1
页码：1-14
DOI：10.2478/amcs-2018-0011
出版社：De Gruyter Open
摘要：In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing
systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing
system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch
service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on
the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of
numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics
(the idle probability and the mean number of customers in the system) of the systems considered with a given approximation
error.
关键词：inhomogeneous birth and death processes; weak ergodicity; rate of convergence; sharp bounds; logarithmic
norm; forward Kolmogorov system;
