{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:31:12Z","timestamp":1751365872494},"reference-count":0,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"3","license":[{"start":{"date-parts":[[2014,9,1]],"date-time":"2014-09-01T00:00:00Z","timestamp":1409529600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p> A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. The criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined. Some key performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn and waiting time distributions of priority and non-priority customers are derived. A numerical example illustrating the importance of taking into account the correlation in the arrival process is presented<\/jats:p>","DOI":"10.2478\/amcs-2014-0036","type":"journal-article","created":{"date-parts":[[2014,9,26]],"date-time":"2014-09-26T12:13:08Z","timestamp":1411733588000},"page":"485-501","source":"Crossref","is-referenced-by-count":18,"title":["Analysis of an <i>MMAP\/PH<sub>1<\/sub>, PH<sub>2<\/sub>\/N\/\u221e <\/i> queueing system operating in a random environment"],"prefix":"10.61822","volume":"24","author":[{"given":"Chesoong","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Business Administration Sangji University, Wonju, Kangwon, 220-702, Korea"}]},{"given":"Alexander","family":"Dudin","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus"}]},{"given":"Sergey","family":"Dudin","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus"}]},{"given":"Olga","family":"Dudina","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science Belarusian State University, 4, Nezavisimosti Ave., Minsk, 220030, Belarus"}]}],"member":"37438","published-online":{"date-parts":[[2014,9,25]]},"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/24\/3\/article-p485.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/pdf\/10.2478\/amcs-2014-0036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:28:40Z","timestamp":1709202520000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.2478\/amcs-2014-0036"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,9,25]]},"published-print":{"date-parts":[[2014,9,1]]}},"alternative-id":["10.2478\/amcs-2014-0036"],"URL":"https:\/\/doi.org\/10.2478\/amcs-2014-0036","relation":{},"ISSN":["2083-8492"],"issn-type":[{"value":"2083-8492","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,1]]}}}