{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T21:53:37Z","timestamp":1759701217014},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,6,14]],"date-time":"2012-06-14T00:00:00Z","timestamp":1339632000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s11424-012-9154-0","type":"journal-article","created":{"date-parts":[[2012,6,18]],"date-time":"2012-06-18T06:08:03Z","timestamp":1339999683000},"page":"759-777","source":"Crossref","is-referenced-by-count":12,"title":["Analysis of batch arrival queue with randomized vacation policy and an un-reliable server"],"prefix":"10.1007","volume":"25","author":[{"given":"Jau Chuan","family":"Ke","sequence":"first","affiliation":[]},{"given":"Kai Bin","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,6,14]]},"reference":[{"key":"9154_CR1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF01149327","volume":"1","author":"B. T. Doshi","year":"1986","unstructured":"B. T. Doshi, Queueing systems with vacations \u2014 A survey, Queueing Systems, 1986, 1: 29\u201366.","journal-title":"Queueing Systems"},{"key":"9154_CR2","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1287\/mnsc.22.2.202","volume":"22","author":"Y. Levy","year":"1975","unstructured":"Y. Levy and U. Yechiali, Utilization of idle time in an M\/G\/1 queueing system, Management Science, 1975, 22: 202\u2013211.","journal-title":"Management Science"},{"key":"9154_CR3","volume-title":"Queueing Analysis: A Foundation of Performance Evaluation","author":"H. Takagi","year":"1991","unstructured":"H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, Vol. I, vacation and priority systems, part I, North-Holland, Amsterdam, 1991."},{"key":"9154_CR4","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0167-6377(86)90110-0","volume":"5","author":"Y. Baba","year":"1986","unstructured":"Y. Baba, On the M[x]\/G\/1 queue with vacation time, Operations Research Letters, 1986, 5: 93\u201398.","journal-title":"Operations Research Letters"},{"key":"9154_CR5","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1002\/1520-6750(198902)36:1<111::AID-NAV3220360109>3.0.CO;2-3","volume":"36","author":"O. Kella","year":"1989","unstructured":"O. Kella, The threshold policy in the M\/G\/1 queue with server vacations, Naval Research Logistics, 1989, 36: 111\u2013123.","journal-title":"Naval Research Logistics"},{"key":"9154_CR6","first-page":"467","volume":"31","author":"H. W. Lee","year":"1994","unstructured":"H. W. Lee, S. S. Lee, J. O. Park, and K. C. Chae, Analysis of M[x]\/G\/1 queue with N policy and multiple vacations, Journal of Applied Probability, 1994, 31: 467\u2013496.","journal-title":"Journal of Applied Probability"},{"key":"9154_CR7","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0305-0548(94)E0015-Y","volume":"22","author":"S. S. Lee","year":"1995","unstructured":"S. S. Lee, H. W. Lee, and K. C. Chae, Batch arrival queue with N policy and single vacation, Computers and Operations Research, 1995, 22: 173\u2013189.","journal-title":"Computers and Operations Research"},{"issue":"3","key":"9154_CR8","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s001860100167","volume":"54","author":"J. C. Ke","year":"2001","unstructured":"J. C. Ke, The control policy of an M[x]\/G\/1 queueing system with server startup and two vacation types, Mathematical Methods of Operations Research, 2001, 54(3): 471\u2013490.","journal-title":"Mathematical Methods of Operations Research"},{"key":"9154_CR9","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/S0307-904X(03)00074-X","volume":"27","author":"S. Hur","year":"2003","unstructured":"S. Hur, J. Kim, and C. Kang, An analysis of the M\/G\/1 system with N and T policy, Applied Mathematical Modelling, 2003, 27: 665\u2013675.","journal-title":"Applied Mathematical Modelling"},{"key":"9154_CR10","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1057\/palgrave.jors.2601536","volume":"54","author":"L. Tadj","year":"2003","unstructured":"L. Tadj, A quorum queueing system under T-policy, J. Operat. Res. Soc., 2003, 54: 466\u2013471.","journal-title":"J. Operat. Res. Soc."},{"issue":"2","key":"9154_CR11","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/mma.905","volume":"31","author":"J. C. Ke","year":"2008","unstructured":"J. C. Ke, Two thresholds of a batch arrival queueing system under modified T vacation policy with startup and closedown, Mathematical Methods in the Applied Sciences, 2008, 31(2): 229\u2013247.","journal-title":"Mathematical Methods in the Applied Sciences"},{"issue":"2","key":"9154_CR12","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/BF02579061","volume":"13","author":"L. Tadj","year":"2005","unstructured":"L. Tadj and G. Choudhury, Optimal design and control of queues, TOP, 2005, 13(2): 359\u2013412.","journal-title":"TOP"},{"key":"9154_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/07362990500397277","volume":"24","author":"G. Choudhury","year":"2006","unstructured":"G. Choudhury and M. Paul, A batch arrival queue with a second optional service channel under N-policy, Stochastic Analysis and Applications, 2006, 24: 1\u201321.","journal-title":"Stochastic Analysis and Applications"},{"key":"9154_CR14","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1023\/A:1010947911863","volume":"38","author":"Z. G. Zhang","year":"2001","unstructured":"Z. G. Zhang and N. Tian, Discrete time Geo\/G\/1 queue with multiple adaptive vacations, Queueing Systems, 2001, 38: 419\u2013429.","journal-title":"Queueing Systems"},{"key":"9154_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/asmb.607","volume":"22","author":"J. C. Ke","year":"2006","unstructured":"J. C. Ke and Y. K. Chu, A modified vacation model M[x]\/G\/1 system, Appl. Stochastic Models Bus. Ind., 2006, 22: 1\u201316.","journal-title":"Appl. Stochastic Models Bus. Ind."},{"issue":"7","key":"9154_CR16","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1016\/j.apm.2006.02.012","volume":"31","author":"J. C. Ke","year":"2007","unstructured":"J. C. Ke, Operating characteristic analysis on the M[x]\/G\/1 system with a variant vacation policy and balking, Applied Mathematical Modelling, 2007, 31(7): 1321\u20131337.","journal-title":"Applied Mathematical Modelling"},{"key":"9154_CR17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1111\/1475-3995.00350","volume":"9","author":"K. H. Wang","year":"2002","unstructured":"K. H. Wang and J. C. Ke, Control policies of an M\/G\/1 queueing system with a removable and non-reliable server, Intl. Trans in Op. Res., 2002, 9: 195\u2013212.","journal-title":"Intl. Trans in Op. Res."},{"key":"9154_CR18","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/S0360-8352(02)00235-8","volume":"44","author":"J. C. Ke","year":"2003","unstructured":"J. C. Ke, The optimal control of an M\/G\/1 queueing system with server vacations, startup and breakdowns, Comput. Ind. Eng., 2003, 44: 567\u2013579.","journal-title":"Comput. Ind. Eng."},{"key":"9154_CR19","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s001860300279","volume":"58","author":"J. C. Ke","year":"2003","unstructured":"J. C. Ke, Optimal strategy policy in batch arrival queue with server breakdowns and multiple vacations, Math. Meth. Oper. Res., 2003, 58: 41\u201356.","journal-title":"Math. Meth. Oper. Res."},{"key":"9154_CR20","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.apm.2005.03.022","volume":"30","author":"J. C. Ke","year":"2006","unstructured":"J. C. Ke, On M\/G\/1 system under NT policies with breakdowns, startup and closedown, Applied Mathematical Modelling, 2006, 30: 49\u201366.","journal-title":"Applied Mathematical Modelling"},{"issue":"2","key":"9154_CR21","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s00186-005-0046-0","volume":"63","author":"J. C. Ke","year":"2006","unstructured":"J. C. Ke, An M\/G\/1 queue under hysteretic vacation policy with an early startup and un-reliable server, Mathematical Methods of Operations Research, 2006, 63(2): 357\u2013369.","journal-title":"Mathematical Methods of Operations Research"},{"key":"9154_CR22","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1016\/j.mcm.2004.08.009","volume":"41","author":"J. C. Ke","year":"2005","unstructured":"J. C. Ke, Modified T vacation policy for an M\/G\/1 queueing system with an un-reliable server and startup, Mathematical and Computer Modelling, 2005, 41: 1267\u20131277.","journal-title":"Mathematical and Computer Modelling"},{"issue":"7","key":"9154_CR23","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1016\/j.apm.2006.02.010","volume":"31","author":"J. C. Ke","year":"2007","unstructured":"J. C. Ke, Batch arrival queues under vacation policies with server breakdowns and startup\/closedown times, Applied Mathematical Modelling, 2007, 31(7): 1282\u20131292.","journal-title":"Applied Mathematical Modelling"},{"issue":"8","key":"9154_CR24","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1108\/02644400810909616","volume":"25","author":"D. Y. Yang","year":"2008","unstructured":"D. Y. Yang, K. H. Wang, J. C. Ke, and W. L. Pearn, Optimal randomized control policy of an unreliable server system with second optional service and startup, Engineering Computations: International Journal for Computer-Aided Engineering and Software, 2008, 25(8): 783\u2013800.","journal-title":"Engineering Computations: International Journal for Computer-Aided Engineering and Software"},{"issue":"6","key":"9154_CR25","doi-asserted-by":"crossref","first-page":"2699","DOI":"10.1016\/j.apm.2008.08.006","volume":"33","author":"G. Choudhury","year":"2009","unstructured":"G. Choudhury and L. Tadj, An M\/G\/1 queue with two phases of service subject to the server breakdown and delayed repair, Applied Mathematical Modelling, 2009, 33(6): 2699\u20132709.","journal-title":"Applied Mathematical Modelling"},{"issue":"1","key":"9154_CR26","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.cam.2009.02.101","volume":"231","author":"G. Choudhury","year":"2009","unstructured":"G. Choudhury, J. C. Ke, and L. Tadj, The N-policy for an unreliable server with delaying repair and two phases of service, Journal of Computational and Applied Mathematics, 2009, 231(1): 349\u2013364.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"9154_CR27","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1017\/S0305004100030437","volume":"51","author":"D. R. Cox","year":"1955","unstructured":"D. R. Cox, The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables, Proceedings Cambridge Philosophical Society, 1955, 51: 433\u2013441.","journal-title":"Proceedings Cambridge Philosophical Society"},{"key":"9154_CR28","doi-asserted-by":"crossref","first-page":"1941","DOI":"10.1016\/S0305-0548(01)00059-4","volume":"29","author":"G. Choudhury","year":"2002","unstructured":"G. Choudhury, A batch arrival queue with a vacation time under single vacation policy, Computers and Operations Research, 2002, 29: 1941\u20131955.","journal-title":"Computers and Operations Research"},{"key":"9154_CR29","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1287\/opre.30.2.223","volume":"30","author":"R. W. Wolff","year":"1982","unstructured":"R. W. Wolff, Poisson arrival see time average, Oper. Res., 1982, 30: 223\u2013231.","journal-title":"Oper. Res."},{"key":"9154_CR30","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/S0026-2714(96)00018-2","volume":"37","author":"Y. H. Tang","year":"1997","unstructured":"Y. H. Tang, A single-server M\/G\/1 queueing system subject to breakdowns \u2014 Some reliability and queueing problem, Microelectronics and Reliability, 1997, 37: 315\u2013321.","journal-title":"Microelectronics and Reliability"},{"key":"9154_CR31","doi-asserted-by":"crossref","first-page":"546","DOI":"10.2307\/3215393","volume":"34","author":"W. Li","year":"1997","unstructured":"W. Li, D. Shi, and X. Chao, Reliability analysis of M\/G\/1 queueing system with server breakdowns and vacations, Journal of Applied Probability, 1997, 34: 546\u2013555.","journal-title":"Journal of Applied Probability"},{"key":"9154_CR32","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/0377-2217(86)90298-5","volume":"23","author":"Y. T. Park","year":"1986","unstructured":"Y. T. Park and K. S. Park, Generalized spare ordering policies with random lead time, European Journal of Operational Research, 1986, 23: 320\u2013330.","journal-title":"European Journal of Operational Research"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-012-9154-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-012-9154-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-012-9154-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T10:54:04Z","timestamp":1559386444000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-012-9154-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,14]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["9154"],"URL":"https:\/\/doi.org\/10.1007\/s11424-012-9154-0","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,14]]}}}