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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MDPI AG
2025-06-01
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| 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. |
| format | Article |
| id | doaj-art-8d5dbdd4455b4e41aea7c769117fb5e0 |
| institution | Kabale University |
| issn | 2079-3197 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| 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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