{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:00:52Z","timestamp":1746802852483,"version":"3.40.5"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001321","name":"National Research Foundation","doi-asserted-by":"publisher","award":["2013S1A5A8022372"],"award-info":[{"award-number":["2013S1A5A8022372"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"We consider the discrete-timeGeo<\/mml:mtext><\/mml:mrow>X<\/mml:mi><\/mml:mrow><\/mml:msup>\/<\/mml:mo>G<\/mml:mi>\/<\/mml:mo>1<\/mml:mn><\/mml:math>queue underN<\/jats:italic>-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold valueN<\/jats:italic>. Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner. In addition, we derive their busy as well as idle-period distributions. Some classical vacation models are considered as special cases.<\/jats:p>","DOI":"10.1155\/2013\/587163","type":"journal-article","created":{"date-parts":[[2013,12,26]],"date-time":"2013-12-26T21:01:19Z","timestamp":1388091679000},"page":"1-6","source":"Crossref","is-referenced-by-count":4,"title":["On the Discrete-TimeGeo<\/mml:mtext><\/mml:mrow>X<\/mml:mi><\/mml:mrow><\/mml:msup>\/<\/mml:mo>G<\/mml:mi>\/<\/mml:mo>1<\/mml:mn><\/mml:math>Queues underN<\/mml:mi><\/mml:mrow><\/mml:math>-Policy with Single and Multiple Vacations"],"prefix":"10.1155","volume":"2013","author":[{"given":"Sung J.","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Management Engineering, Sangmyung University, Cheonan 330-720, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nam K.","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Chonnam National University, Gwangju 500-757, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hyun-Min","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Business Administration, Pai Chai University, Daejeon 302-735, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyung Chul","family":"Chae","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, KAIST, Daejon 305-701, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dae-Eun","family":"Lim","sequence":"additional","affiliation":[{"name":"Division of Business and Commerce, Baekseok University, Cheonan 330-704, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01149327"},{"year":"1991","key":"2","first-page":"xii+487"},{"year":"1993","key":"3"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010947911863"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1020571814186"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024028722553"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0305-0548(94)E0015-Y"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.2307\/3215040"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019170817355"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2009.09.007"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/793801"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.09.037"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2009.06.003"},{"key":"14","doi-asserted-by":"crossref","first-page":"131","DOI":"10.3934\/jimo.2014.10.131","volume":"10","year":"2014","journal-title":"Journal of Industrial and Management Optimization"},{"year":"2006","key":"15","first-page":"xii+385"},{"key":"16"},{"first-page":"xii+286","year":"1983","series-title":"Operations Research and Industrial Engineering","key":"17"},{"year":"1993","key":"18"},{"year":"1989","key":"19","first-page":"xx+556"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1040.0116"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/587163.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/587163.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/587163.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T22:36:46Z","timestamp":1597271806000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/587163\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":20,"alternative-id":["587163","587163"],"URL":"https:\/\/doi.org\/10.1155\/2013\/587163","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}