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Paper details
Number 1 - March 2018
Volume 28 - 2018
Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services
Alexander Zeifman, Rostislav Razumchik, Yacov Satin, Ksenia Kiseleva, Anna Korotysheva, Victor Korolev
Abstract
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.
Keywords
inhomogeneous birth and death processes, weak ergodicity, rate of convergence, sharp bounds, logarithmic norm, forward Kolmogorov system