{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:41:06Z","timestamp":1760190066568,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T00:00:00Z","timestamp":1561680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This manuscript starts with a detailed analysis of the current solution for the queueing system M\/Er\/1\/\u221e. In the existing solution, Erlang\u2019s service is caused by Poisson\u2019s arrival process of groups, but not individual clients. The service of individual clients is still exponentially distributed, contrary to the declaration in Kendall\u2019s notation. From the related theory of the Hidden Markov Model (HMM), for the advancement of queueing theory, the idea of \u201chidden Markov states\u201d (HMS) was taken. In this paper, the basic principles of application of HMS have first been established. The abstract HMS states have a catalytic role in the standard procedure of solving the non-Markovian queueing systems. The proposed solution based on HMS exceeds the problem of accessing identical client groups in the current solution of the M\/Er\/r queueing system. A detailed procedure for the new solution of the queueing system M\/Er\/1\/\u221e is implemented. Additionally, a new solution to the queueing system M\/N\/1\/\u221e with a normal service time N(\u03bc, \u03c3) based on HMS is also implemented.<\/jats:p>","DOI":"10.3390\/a12070133","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T11:20:26Z","timestamp":1561720826000},"page":"133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Method for Markovian Adaptation of the Non-Markovian Queueing System Using the Hidden Markov Model"],"prefix":"10.3390","volume":"12","author":[{"given":"Ilija","family":"Tanackov","sequence":"first","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi\u2019ca 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0910-591X","authenticated-orcid":false,"given":"Olegas","family":"Prentkovskis","sequence":"additional","affiliation":[{"name":"Department of Mobile Machinery and Railway Transport, Faculty of Transport Engineering, Vilnius Gediminas Technical University, Plytin\u0117sg.27, LT-10105 Vilnius, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u017darko","family":"Jevti\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi\u2019ca 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7972-3292","authenticated-orcid":false,"given":"Gordan","family":"Stoji\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi\u2019ca 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pamela","family":"Ercegovac","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, TrgDositejaObradovi\u2019ca 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/BF01194620","article-title":"Uebereine Aufgabe der Wahrscheinlichkeits theory","volume":"32","author":"Pollaczek","year":"1930","journal-title":"Math. 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