Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services-Reference-Cited by-同舟云学术

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

Published:2018-03-01 Issue:1 Volume:28 Page:141-154
ISSN:2083-8492
Container-title:International Journal of Applied Mathematics and Computer Science
language:en
Short-container-title:

Author:

Zeifman Alexander¹²,Razumchik Rostislav³⁴,Satin Yacov¹,Kiseleva Ksenia⁴¹,Korotysheva Anna¹,Korolev Victor⁵³

Affiliation:

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. Institute of Informatics Problems Russian Academy of Sciences, Vavilova 44-2, Moscow , 119333, Russian Federation

4. Applied Probability and Informatics Department Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya, Moscow , 117198, Russian Federation

5. Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University, Leninskie Gory, Moscow , Russian Federation

Abstract

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

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.sciendo.com/pdf/10.2478/amcs-2018-0011

Reference32 articles.

1. Almasi, B., Roszik, J. and Sztrik, J. (2005). Homogeneous finite-source retrial queues with server subject to breakdowns and repairs, Mathematical and Computer Modelling 42(5): 673-682.10.1016/j.mcm.2004.02.046

2. Chen, A., Pollett, P., Li, J. and Zhang, H. (2010). Markovian bulk-arrival and bulk-service queues with state-dependent control, Queueing Systems 64(3): 267-304.10.1007/s11134-009-9162-5

3. Daleckij, J. and Krein,M. (1974). Stability of Solutions of Differential Equations in Banach Space, American Mathematical Society, Providence, RI.

4. Doorn, E.V., Zeifman, A. and Panfilova, T. (2010). Bounds and asymptotics for the rate of convergence of birth-death processes, Theory of Probability and Its Applications 54(1): 97-113.10.1137/S0040585X97984097

5. Granovsky, B. and Zeifman, A. (2000). The n-limit of spectral gap of a class of birthdeath Markov chains, Applied Stochastic Models in Business and Industry 16(4): 235-248.10.1002/1526-4025(200010/12)16:4<235::AID-ASMB415>3.0.CO;2-S

Cited by 16 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the Study of Forward Kolmogorov System: the Corresponding Problems and Bounds for Inhomogeneous Continuous-time Markov Chains and Models;2022 International Conference on Information, Control, and Communication Technologies (ICCT);2022-10-03

2. A Multi-Source Fluid Queue Based Stochastic Model of the Probabilistic Offloading Strategy in a MEC System With Multiple Mobile Devices and a Single MEC Server;INT J AP MAT COM-POL;2022

3. Bounds on the rate of convergence for Markovian queuing models with catastrophes;Statistics & Probability Letters;2021-09

4. Ergodicity bounds for the Markovian queue with time-varying transition intensities, batch arrivals and one queue skipping policy;Applied Mathematics and Computation;2021-04

5. On obtaining sharp bounds of the rate of convergence for a class of continuous-time Markov chains;Statistics & Probability Letters;2020-06