{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T21:51:38Z","timestamp":1761947498177},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,6,24]],"date-time":"2008-06-24T00:00:00Z","timestamp":1214265600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2009,8]]},"DOI":"10.1007\/s00186-008-0232-y","type":"journal-article","created":{"date-parts":[[2008,6,23]],"date-time":"2008-06-23T15:50:38Z","timestamp":1214236238000},"page":"77-98","source":"Crossref","is-referenced-by-count":5,"title":["Transient solution of a non-empty chemical queueing system"],"prefix":"10.1007","volume":"70","author":[{"given":"Ahmed M.K.","family":"Tarabia","sequence":"first","affiliation":[]},{"given":"Hideaki","family":"Takagi","sequence":"additional","affiliation":[]},{"given":"A.H.","family":"El-Baz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,6,24]]},"reference":[{"key":"232_CR1","first-page":"83","volume":"22","author":"BW Conolly","year":"1997","unstructured":"Conolly BW, Parthasarathy PR, Dharmaraja S (1997) A chemical queue. Math Sci 22: 83\u201391","journal-title":"Math Sci"},{"key":"232_CR2","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1063\/1.1703954","volume":"4","author":"RJ Glauber","year":"1963","unstructured":"Glauber RJ (1963) Time-dependent statistics of the Ising model. J Math Phys 4: 495\u2013508","journal-title":"J Math Phys"},{"key":"232_CR3","volume-title":"Fundamentals of queueing theory","author":"D Gross","year":"1998","unstructured":"Gross D, Harris CM (1998) Fundamentals of queueing theory, 3rd edn. Wiley, New York","edition":"3"},{"key":"232_CR4","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1002\/nav.3800200210","volume":"20","author":"MF Neuts","year":"1973","unstructured":"Neuts MF (1973) The single server queue in discrete time\u2014numerical analysis 1. Naval Res Logist Q 20: 297\u2013304","journal-title":"Naval Res Logist Q"},{"key":"232_CR5","volume-title":"Combinatorial identities","author":"J Riordan","year":"1968","unstructured":"Riordan J (1968) Combinatorial identities. Wiley, New York"},{"key":"232_CR6","volume-title":"Stochastic processes","author":"SM Ross","year":"1995","unstructured":"Ross SM (1995) Stochastic processes, 2nd edn. Wiley, New York","edition":"2"},{"key":"232_CR7","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1080\/02331939708844299","volume":"40","author":"OP Sharma","year":"1997","unstructured":"Sharma OP, Bunday DB (1997) A simple formula for transient state probabilities of an M\/M\/1\/ \u221e queue. Optimization 40: 79\u201384","journal-title":"Optimization"},{"key":"232_CR8","first-page":"273","volume":"62","author":"OP Sharma","year":"2000","unstructured":"Sharma OP, Tarabia AMK (2000a) A simple transient analysis of an M\/M\/1\/N queue. Sankhy\u0101, Ser A 62: 273\u2013281","journal-title":"Sankhy\u0101, Ser A"},{"issue":"5","key":"232_CR9","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/07362990008809700","volume":"18","author":"OP Sharma","year":"2000","unstructured":"Sharma OP, Tarabia AMK (2000b) On the busy period of a multichannel Markovian queue. Stoch Anal Appl 18(5): 859\u2013869","journal-title":"Stoch Anal Appl"},{"key":"232_CR10","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1351\/pac197126030537","volume":"26","author":"WH Stockmayer","year":"1971","unstructured":"Stockmayer WH, Gobush W, Norvice R (1971) Local-jump models for chain dynamics. Pure Appl Chem 26: 555\u2013561","journal-title":"Pure Appl Chem"},{"key":"232_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0096-3003(01)00145-X","volume":"132","author":"AMK Tarabia","year":"2002","unstructured":"Tarabia AMK (2002) A new formula for the transient behaviour of a non-empty M\/M\/1\/ \u221e queue. Appl Math Comput 132: 1\u201310","journal-title":"Appl Math Comput"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-008-0232-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00186-008-0232-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-008-0232-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T19:29:35Z","timestamp":1709062175000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-008-0232-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6,24]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,8]]}},"alternative-id":["232"],"URL":"https:\/\/doi.org\/10.1007\/s00186-008-0232-y","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6,24]]}}}