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A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded Markov chain and total probability law. The solution of the corresponding system written for Laplace transforms is obtained via an algebraic approach in a compact form. Numerical illustration results are attached as well.<\/jats:p>","DOI":"10.3390\/s22249909","type":"journal-article","created":{"date-parts":[[2022,12,16]],"date-time":"2022-12-16T08:55:39Z","timestamp":1671180939000},"page":"9909","source":"Crossref","is-referenced-by-count":4,"title":["Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9476-2070","authenticated-orcid":false,"given":"Wojciech M.","family":"Kempa","sequence":"first","affiliation":[{"name":"Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 23 Kaszubska Str., 44-100 Gliwice, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3870-7509","authenticated-orcid":false,"given":"Iwona","family":"Paprocka","sequence":"additional","affiliation":[{"name":"Department of Engineering Processes Automation and Integrated Manufacturing Systems, Faculty of Mechanical Engineering, Silesian University of Technology, Konarskiego 18A Str., 44-100 Gliwice, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1080\/00207543.2018.1472404","article-title":"Applying data mining technique to disassembly sequence planning: A method to assess effective disassembly time of industrial products","volume":"57","author":"Marconi","year":"2019","journal-title":"Int. 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