<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov...

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

Published Online: Mar 31, 2018

Page range: 141 - 154

Received: Apr 24, 2017

Accepted: Aug 09, 2017

DOI: https://doi.org/10.2478/amcs-2018-0011

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

© by Alexander Zeifman

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Mar 31, 2018

Page range: 141 - 154

Received: Apr 24, 2017

Accepted: Aug 09, 2017

DOI: https://doi.org/10.2478/amcs-2018-0011

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

© by Alexander Zeifman

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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