{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:03:30Z","timestamp":1760058210114,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"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>In this study, we consider a multi-server priority queueing model with batch arrivals of two types of customers, a finite buffer, and two input finite buffers for storing customers that cannot be admitted for service immediately upon arrival. The transition of a customer from an input buffer to the main buffer can occur after an exponentially distributed time. Customers residing in the input and main buffers are impatient. The four-dimensional Markov chain is used to describe the dynamics of the system under consideration. It is analyzed via the derivation of its generator and providing an effective algorithm for computing its steady-state probabilities. Formulas for calculating the system\u2019s major performance metrics are established. Numerical results demonstrating the suggested methods\u2019 viability and the effect of variation of transition rates of customers from the input buffers are presented.<\/jats:p>","DOI":"10.3390\/computation13030077","type":"journal-article","created":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T10:43:51Z","timestamp":1742294631000},"page":"77","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of a Queueing Model with Flexible Priority, Batch Arrival, and Impatient Customers"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2881-0227","authenticated-orcid":false,"given":"Alexander","family":"Dudin","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus"},{"name":"R&D Center, Baku Engineering University, Hasan Aliyev Str., 120, Khirdalan City AZ0101, Absheron, Azerbaijan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6788-8783","authenticated-orcid":false,"given":"Olga","family":"Dudina","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus"}]},{"given":"Sergei","family":"Dudin","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus"}]},{"given":"Agassi","family":"Melikov","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Baku Engineering University, Hasan Aliyev Str., 120, Khirdalan City AZ0101, Absheron, Azerbaijan"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"ref_1","unstructured":"Jaiswal, N.K. 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