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If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer\u2019s service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace\u2013Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.<\/jats:p>","DOI":"10.1515\/amcs-2017-0009","type":"journal-article","created":{"date-parts":[[2017,4,2]],"date-time":"2017-04-02T10:00:29Z","timestamp":1491127229000},"page":"119-131","source":"Crossref","is-referenced-by-count":8,"title":["Analysis of an MAP\/PH\/1 Queue with Flexible Group Service"],"prefix":"10.61822","volume":"27","author":[{"given":"Arianna","family":"Brugno","sequence":"first","affiliation":[{"name":"Department of Information Engineering, Electrical Engineering and Applied Mathematics University of Salerno, Via Giovanni Paolo II, 132, 84084 , Fisciano (SA) , Italy"}]},{"given":"Ciro","family":"D\u2019Apice","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Electrical Engineering and Applied Mathematics University of Salerno, Via Giovanni Paolo II, 132, 84084 , Fisciano (SA) , Italy"}]},{"given":"Alexander","family":"Dudin","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science Belarusian State University, 4, Nezavisimosti Av ., Minsk , 220030 , Belarus"}]},{"given":"Rosanna","family":"Manzo","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Electrical Engineering and Applied Mathematics University of Salerno, Via Giovanni Paolo II, 132, 84084 , Fisciano (SA) , Italy"}]}],"member":"37438","published-online":{"date-parts":[[2017,5,4]]},"reference":[{"key":"2021040623033684326_j_amcs-2017-0009_ref_001_w2aab2b8c17b1b7b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Atencia, I. (2014). A discrete-time system with service control and repairs, International Journal of Applied Mathematics and Computer Science24(3): 471\u2013484, DOI: 10.2478\/amcs-2014-0035.","DOI":"10.2478\/amcs-2014-0035"},{"key":"2021040623033684326_j_amcs-2017-0009_ref_002_w2aab2b8c17b1b7b1ab1ab2Aa","doi-asserted-by":"crossref","unstructured":"Bailey, N. (1954). On queueing processes with bulk service, Journal of the Royal Statistical Society B16(1): 80\u201387.","DOI":"10.1111\/j.2517-6161.1954.tb00149.x"},{"key":"2021040623033684326_j_amcs-2017-0009_ref_003_w2aab2b8c17b1b7b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"Banerjee, A., Gupta, U. and Chakravarthy, S. (2015). 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