{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:24:20Z","timestamp":1760059460933,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,14]],"date-time":"2025-06-14T00:00:00Z","timestamp":1749859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper deals with queueing models, in which the number of customers is described by a (inhomogeneous, in general) birth\u2013death 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.<\/jats:p>","DOI":"10.3390\/computation13060150","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T04:06:24Z","timestamp":1750046784000},"page":"150","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computation of Transient and Steady-State Characteristics of Queueing Systems with Different Types of Customer"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7855-3364","authenticated-orcid":false,"given":"Alexander","family":"Zeifman","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia"},{"name":"Federal Research Center \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, 119133 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4168-1071","authenticated-orcid":false,"given":"Yacov","family":"Satin","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia"}]},{"given":"Ilia","family":"Usov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5303-818X","authenticated-orcid":false,"given":"Janos","family":"Sztrik","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"345","DOI":"10.2307\/3212755","article-title":"On the transient state probabilities for a queueing model where potential customers are discouraged by queue length","volume":"11","author":"Natvig","year":"1974","journal-title":"J. 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On Queues with Impatient Customers [Research Report] RR-0094. INRIA. 1981. inria-00076467. Available online: https:\/\/inria.hal.science\/inria-00076467\/document."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, K., Li, N., and Jiang, Z. (2010, January 15\u201317). Queueing system with impatient customers: A review. Proceedings of the 2010 IEEE International Conference on Service Operations and Logistics, and Informatics, QingDao, China.","DOI":"10.1109\/SOLI.2010.5551611"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s11134-010-9186-x","article-title":"Transient analysis of a queue with system disasters and customer impatience","volume":"66","author":"Sudhesh","year":"2010","journal-title":"Queueing Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Dudin, A.N., Dudin, S.A., Klimenok, V.I., and Dudina, O.S. (2024). Stability of queueing systems with impatience, balking and non-persistence of customers. 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