{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:15:54Z","timestamp":1773656154816,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2006,1]]},"DOI":"10.1007\/s11134-006-3753-1","type":"journal-article","created":{"date-parts":[[2006,1,19]],"date-time":"2006-01-19T01:59:22Z","timestamp":1137635962000},"page":"49-104","source":"Crossref","is-referenced-by-count":4,"title":["On the Erlang Loss Model with Time Dependent Input"],"prefix":"10.1007","volume":"52","author":[{"given":"Charles","family":"Knessl","sequence":"first","affiliation":[]},{"given":"Yongzhi Peter","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"3753_CR1","volume-title":"Handbook of Mathematical Functions","author":"M. Abramowitz","year":"1972","unstructured":"M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972)."},{"key":"3753_CR2","volume-title":"Asymptotic Expansions of Integrals","author":"N. Bleistein","year":"1986","unstructured":"N. Bleistein and R.A. Handelsman, Asymptotic Expansions of Integrals (Dover, New York, 1986)."},{"key":"3753_CR3","volume-title":"Methods of Mathematical Physics, Volume II","author":"R. Courant","year":"1962","unstructured":"R. Courant and D. Hilbert, Methods of Mathematical Physics, Volume II (Interscience, New York, 1962)."},{"key":"3753_CR4","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1287\/opre.41.4.731","volume":"41","author":"S. Eick","year":"1993","unstructured":"S. Eick, W.A. Massey and W. Whitt, The physics of the M(t)\/G\/\u221e queue, Operations Research 41 (1993) 400\u2013408.","journal-title":"Operations Research"},{"key":"3753_CR5","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1287\/mnsc.39.2.241","volume":"39","author":"S. Eick","year":"1993","unstructured":"S. Eick, W.A. Massey and W. Whitt, Infinite-server queues with sinusoidal arrival rates, Management Science 39 (1993) 241\u2013252.","journal-title":"Management Science"},{"key":"3753_CR6","first-page":"189","volume":"10","author":"A.K. Erlang","year":"1918","unstructured":"A.K. Erlang, Solutions of some problems in the theory of probabilities of significance in automatic telephone exchanges, The Post Office Electrical Engineers\u2019 Journal 10 (1918) 189\u2013197.","journal-title":"The Post Office Electrical Engineers\u2019 Journal"},{"key":"3753_CR7","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1002\/j.1538-7305.1974.tb02756.x","volume":"53","author":"D.L. Jagerman","year":"1974","unstructured":"D.L. Jagerman, Some properties of the Erlang loss function, Bell System Technical Journal 53 (1974) 525\u2013551.","journal-title":"Bell System Technical Journal"},{"key":"3753_CR8","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1002\/j.1538-7305.1975.tb02858.x","volume":"54","author":"D.L. Jagerman","year":"1975","unstructured":"D.L. Jagerman, Nonstationary blocking in telephone traffic, Bell System Technical Journal 54 (1975) 625\u2013661.","journal-title":"Bell System Technical Journal"},{"key":"3753_CR9","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1137\/1024098","volume":"24","author":"J.B. Keller","year":"1982","unstructured":"J.B. Keller, Time-dependent queues, SIAM Review 24 (1982) 401\u2013412.","journal-title":"SIAM Review"},{"key":"3753_CR10","volume-title":"Queueing Systems, Volume I: Theory","author":"L. Kleinrock","year":"1975","unstructured":"L. Kleinrock, Queueing Systems, Volume I: Theory (John Wiley, New York, 1975)."},{"key":"3753_CR11","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1080\/15326349908807172","volume":"6","author":"C. Knessl","year":"1990","unstructured":"C. Knessl, On the transient behavior of the Erlang loss model, Comm. Statist. Stochastic Models 6 (1990) 749\u2013776.","journal-title":"Comm. Statist. Stochastic Models"},{"key":"3753_CR12","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, Advances in Applied Probability 32 (2000) 256\u2013283.","journal-title":"Advances in Applied Probability"},{"key":"3753_CR13","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\u2013319.","journal-title":"Asymptotic Analysis"},{"key":"3753_CR14","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1287\/moor.20.1.33","volume":"20","author":"A. Mandelbaum","year":"1995","unstructured":"A. Mandelbaum and W.A. Massey, Strong approximations for time dependent queues, Math. of Operations Research 20 (1995) 305\u2013327.","journal-title":"Math. of Operations Research"},{"key":"3753_CR15","first-page":"183","volume":"13","author":"W.A. Massey","year":"1993","unstructured":"W.A. Massey and W. Whitt, Networks of infinite server queues with nonstationary Poisson input, QUESTA 13 (1993) 183\u2013250.","journal-title":"QUESTA"},{"key":"3753_CR16","unstructured":"D. Mitra and A. Weiss, The transient behavior in: Erlang's model for large trunk groups and various traffic conditions, in Proceedings 12th International Teletraffic Congress (Torino, Italy, June 1988) pp. 5.1B4.1\u20135.1B4.8."},{"key":"3753_CR17","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. Applied Probability 5 (1968) 436\u2013451.","journal-title":"J. Applied Probability"},{"key":"3753_CR18","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. Applied Probability 5 (1968) 579\u2013590.","journal-title":"J. Applied Probability"},{"key":"3753_CR19","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. Applied Probability 5 (1968) 591\u2013606.","journal-title":"J. Applied Probability"},{"key":"3753_CR20","volume-title":"Boundary Value Problems of Mathematical Physics, Volume I","author":"I. Stakgold","year":"1967","unstructured":"I. Stakgold, Boundary Value Problems of Mathematical Physics, Volume I (MacMillan, New York, 1967)."},{"key":"3753_CR21","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1137\/0153030","volume":"53","author":"S. Xie","year":"1993","unstructured":"S. Xie and C. Knessl, On the transient behavior of the Erlang loss model: Heavy usage asymptotics, SIAM J. Appl. Math. 53 (1993) 555\u2013599.","journal-title":"SIAM J. Appl. Math."},{"key":"3753_CR22","first-page":"23","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, QUESTA 26 (1997) 23\u201368.","journal-title":"QUESTA"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-006-3753-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-006-3753-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-006-3753-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T06:34:29Z","timestamp":1736231669000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-006-3753-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["3753"],"URL":"https:\/\/doi.org\/10.1007\/s11134-006-3753-1","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}