{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:17:02Z","timestamp":1759637822884,"version":"3.43.0"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2002,4,1]],"date-time":"2002-04-01T00:00:00Z","timestamp":1017619200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,4,1]],"date-time":"2002-04-01T00:00:00Z","timestamp":1017619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Queueing Systems"],"published-print":{"date-parts":[[2002,4]]},"DOI":"10.1023\/a:1014786928831","type":"journal-article","created":{"date-parts":[[2002,12,28]],"date-time":"2002-12-28T16:18:52Z","timestamp":1041092332000},"page":"233-245","source":"Crossref","is-referenced-by-count":16,"title":["An Exact Solution for an M(t)\/M(t)\/1 Queue with Time-Dependent Arrivals and Service"],"prefix":"10.1007","volume":"40","author":[{"given":"Charles","family":"Knessl","sequence":"first","affiliation":[]},{"given":"Yongzhi Peter","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"398496_CR1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF01158520","volume":"10","author":"J. Abate","year":"1992","unstructured":"J. Abate and W. Whitt, The Fourier-series method for inverting transforms of probability distributions, Queueing Systems 10 (1992) 5-88.","journal-title":"Queueing Systems"},{"key":"398496_CR2","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1214\/aoms\/1177728268","volume":"27","author":"A.B. Clarke","year":"1956","unstructured":"A.B. Clarke, A waiting line process of Markov type, Ann. Math. Statist. 27 (1956) 452-459.","journal-title":"Ann. Math. Statist."},{"key":"398496_CR3","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1287\/opre.24.4.760","volume":"24","author":"T. Collings","year":"1976","unstructured":"T. Collings and C. Stoneman, The M\/M\/\u221e queue with varying arrival and departure rates, Oper. Res. 24 (1976) 760-773.","journal-title":"Oper. Res."},{"key":"398496_CR4","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1287\/mnsc.35.2.127","volume":"35","author":"L. Green","year":"1989","unstructured":"L. Green and P. Kolesar, Testing the validity of a queueing model of police patrol, Managm. Sci. 35 (1989) 127-148.","journal-title":"Managm. Sci."},{"key":"398496_CR5","doi-asserted-by":"crossref","unstructured":"J.B. Keller, Time-dependent queues, SIAM Rev. (1982) 401-412.","DOI":"10.1137\/1024098"},{"key":"398496_CR6","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1239\/aap\/1013540033","volume":"32","author":"C. Knessl","year":"2000","unstructured":"C. Knessl, Exact and asymptotic solutions to a PDE that arises in time-dependent queues, Adv. in Appl. Probab. 32 (2000) 256-283.","journal-title":"Adv. in Appl. Probab."},{"key":"398496_CR7","doi-asserted-by":"crossref","first-page":"281","DOI":"10.3233\/ASY-2001-458","volume":"27","author":"C. Knessl","year":"2001","unstructured":"C. Knessl and Y. Yang, Analysis of a Brownian particle moving in a time-dependent drift field, Asymptotic Analysis 27 (2001) 281-319.","journal-title":"Asymptotic Analysis"},{"key":"398496_CR8","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1287\/inte.14.6.16","volume":"14","author":"P. Kolesar","year":"1984","unstructured":"P. Kolesar, Stalking the endangered CAT: A queueing analysis of congestion at automatic teller machines, Interfaces 14 (1984) 16-26.","journal-title":"Interfaces"},{"key":"398496_CR9","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1287\/opre.20.6.1089","volume":"20","author":"B.O. Koopman","year":"1972","unstructured":"B.O. Koopman, Air-terminal queues under time-dependent conditions, Oper. Res. 20 (1972) 1089-1114.","journal-title":"Oper. Res."},{"key":"398496_CR10","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1287\/inte.19.5.57","volume":"19","author":"E.G. Landauer","year":"1989","unstructured":"E.G. Landauer and L.C. Becker, Reducing waiting time at security checkpoints, Interfaces 19(1989) 57-65.","journal-title":"Interfaces"},{"key":"398496_CR11","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1023\/A:1019145927891","volume":"31","author":"B.H. Margolius","year":"1999","unstructured":"B.H. Margolius, A sample path analysis of the M\nt\n\/M\nt\n\/\nc queue, Queueing Systems 31 (1999) 59-93.","journal-title":"Queueing Systems"},{"key":"398496_CR12","doi-asserted-by":"crossref","first-page":"436","DOI":"10.2307\/3212264","volume":"5","author":"G.F. Newell","year":"1968","unstructured":"G.F. Newell, Queues with time-dependent arrival rates I: The transition through saturation, J. Appl. Probab. 5 (1968) 436-451.","journal-title":"J. Appl. Probab."},{"key":"398496_CR13","doi-asserted-by":"crossref","first-page":"579","DOI":"10.2307\/3211923","volume":"5","author":"G.F. Newell","year":"1968","unstructured":"G.F. Newell, Queues with time-dependent arrival rates II: The maximum queue and the return to equilibrium, J. Appl. Probab. 5 (1968) 579-590.","journal-title":"J. Appl. Probab."},{"key":"398496_CR14","doi-asserted-by":"crossref","first-page":"591","DOI":"10.2307\/3211924","volume":"5","author":"G.F. Newell","year":"1968","unstructured":"G.F. Newell, Queues with time-dependent arrival rates III: A mild rush hour, J. Appl. Probab. 5 (1968) 591-606.","journal-title":"J. Appl. Probab."},{"key":"398496_CR15","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1023\/A:1019116804750","volume":"26","author":"Y. Yang","year":"1997","unstructured":"Y. Yang and C. Knessl, Asymptotic analysis of the M\/G\/1 queue with a time-dependent arrival rate, Queueing Systems 26 (1997) 23-68.","journal-title":"Queueing Systems"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014786928831.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1014786928831\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014786928831.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T04:34:08Z","timestamp":1754454848000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1014786928831"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,4]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["398496"],"URL":"https:\/\/doi.org\/10.1023\/a:1014786928831","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[2002,4]]}}}