Creator:

Zeifman, Alexander ; Razumchik, Rostislav ; Satin, Yacov ; Kiseleva, Ksenia ; Korotysheva, Anna ; Korolev, Victor

Contributor:

Aitouche, Abdel - ed.

Title:

Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

Subtitle:

.

Group publication title:

AMCS, volume 28 (2018)

Subject and Keywords:

inhomogeneous birth and death processes ; weak ergodicity ; rate of convergence ; sharp bounds ; logarithmic norm ; forward Kolmogorov system

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.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Date:

2018

Resource Type:

artykuł

DOI:

10.2478/amcs-2018-0011

Pages:

141-154

Source:

AMCS, volume 28, number 1 (2018) ; click here to follow the link

Language:

eng

License CC BY 4.0:

click here to follow the link

Rights:

Biblioteka Uniwersytetu Zielonogórskiego