{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T06:39:42Z","timestamp":1721716782686},"reference-count":35,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2019,10,28]],"date-time":"2019-10-28T00:00:00Z","timestamp":1572220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2018,9,8]]},"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:p>An explicit expression for time-dependent system size probabilities is obtained for the general state-dependent discrete-time queue with system disaster. Using generating function for the<jats:italic>n<\/jats:italic>th state transient probabilities, the underlying difference equation of system size probabilities are transformed into three-term recurrence relation which is then expressed as a continued fraction. The continued fractions are converted into formal power series which yield the time-dependent system size probabilities in closed form. Further, the busy period distribution is obtained for the considered model. As a special case, the system size probabilities and busy period distribution of Geo\/Geo\/1 queue are deduced. Finally, numerical illustrations are presented to visualize the system effect for various values of the parameters.<\/jats:p>","DOI":"10.1051\/ro\/2018078","type":"journal-article","created":{"date-parts":[[2018,9,11]],"date-time":"2018-09-11T08:23:53Z","timestamp":1536654233000},"page":"1915-1927","source":"Crossref","is-referenced-by-count":1,"title":["Analysis of state-dependent discrete-time queue with system disaster"],"prefix":"10.1051","volume":"53","author":[{"given":"Ramupillai","family":"Sudhesh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arumugam","family":"Vaithiyanathan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2019,10,28]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1023\/A:1012796517394","volume":"39","author":"Anisimov","year":"2001","journal-title":"Queueing Syst."},{"key":"R2","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1016\/S0305-0548(03)00107-2","volume":"31","author":"Atencia","year":"2004","journal-title":"Comput. 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