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

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. © 2018 A. Zeifman et al.

Авторы
Zeifman A.1, 2 , Razumchik R. 4, 5 , Satin Y.1 , Kiseleva K. 1, 5 , Korotysheva A.1 , Korolev V.4, 3
Издательство
Walter de Gruyter GmbH
Номер выпуска
1
Язык
Английский
Страницы
141-154
Статус
Опубликовано
Том
28
Год
2018
Организации
  • 1 Department of Applied Mathematics, Vologda State University, S. Orlova 6, Vologda, Russian Federation
  • 2 Institute of Socio-Economic Development of Territories, Russian Academy of Sciences, 56A Gorky Street, Vologda, Russian Federation
  • 3 Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russian Federation
  • 4 Institute of Informatics Problems, Russian Academy of Sciences, Vavilova 44-2, Moscow, 119333, Russian Federation
  • 5 Applied Probability and Informatics Department, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya, Moscow, 117198, Russian Federation
Ключевые слова
Inhomogeneous birth and death processes; Logarithmic norm forward Kolmogorov system; Rate of convergence; Sharp bounds; Weak ergodicity
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6825/