Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer

This paper deals with queueing models, in which the number of customers is described by a (inhomogeneous, in general) birth–death process. Depending on the choice of the type of intensities for the arrival and service of customers, the system can either have impatience (in which, as the queue length...

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Main Authors: Alexander Zeifman, Yacov Satin, Ilia Usov, Janos Sztrik
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Computation
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Online Access:https://www.mdpi.com/2079-3197/13/6/150
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author Alexander Zeifman
Yacov Satin
Ilia Usov
Janos Sztrik
author_facet Alexander Zeifman
Yacov Satin
Ilia Usov
Janos Sztrik
author_sort Alexander Zeifman
collection DOAJ
description This paper deals with queueing models, in which the number of customers is described by a (inhomogeneous, in general) birth–death process. Depending on the choice of the type of intensities for the arrival and service of customers, the system can either have impatience (in which, as the queue length increases, the intensities of arrival decrease and the intensities of service increases) or attraction (in which, on the contrary, as the queue length increases, the intensities of the arrival of customers increase and service intensities decrease). In this article, various types of such models are considered, and their transient and limiting characteristics are computed. Furthermore, the rate of convergence and related bounds are also dealt with. Several numerical examples illustrate the proposed procedures.
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issn 2079-3197
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publishDate 2025-06-01
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series Computation
spelling doaj-art-8d5dbdd4455b4e41aea7c769117fb5e02025-08-20T03:27:28ZengMDPI AGComputation2079-31972025-06-0113615010.3390/computation13060150Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of CustomerAlexander Zeifman0Yacov Satin1Ilia Usov2Janos Sztrik3Department of Applied Mathematics, Vologda State University, 160000 Vologda, RussiaDepartment of Applied Mathematics, Vologda State University, 160000 Vologda, RussiaDepartment of Applied Mathematics, Vologda State University, 160000 Vologda, RussiaFaculty of Informatics, University of Debrecen, 4032 Debrecen, HungaryThis paper deals with queueing models, in which the number of customers is described by a (inhomogeneous, in general) birth–death process. Depending on the choice of the type of intensities for the arrival and service of customers, the system can either have impatience (in which, as the queue length increases, the intensities of arrival decrease and the intensities of service increases) or attraction (in which, on the contrary, as the queue length increases, the intensities of the arrival of customers increase and service intensities decrease). In this article, various types of such models are considered, and their transient and limiting characteristics are computed. Furthermore, the rate of convergence and related bounds are also dealt with. Several numerical examples illustrate the proposed procedures.https://www.mdpi.com/2079-3197/13/6/150inhomogeneous continuous-time Markov chainsbirth–death processergodicitylogarithmic norm
spellingShingle Alexander Zeifman
Yacov Satin
Ilia Usov
Janos Sztrik
Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer
Computation
inhomogeneous continuous-time Markov chains
birth–death process
ergodicity
logarithmic norm
title Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer
title_full Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer
title_fullStr Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer
title_full_unstemmed Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer
title_short Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer
title_sort computation of transient and steady state characteristics of queueing systems with different types of customer
topic inhomogeneous continuous-time Markov chains
birth–death process
ergodicity
logarithmic norm
url https://www.mdpi.com/2079-3197/13/6/150
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