{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T00:12:15Z","timestamp":1759104735116},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,7,16]],"date-time":"2010-07-16T00:00:00Z","timestamp":1279238400000},"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":[[2010,10]]},"DOI":"10.1007\/s00186-010-0321-6","type":"journal-article","created":{"date-parts":[[2010,7,15]],"date-time":"2010-07-15T13:30:10Z","timestamp":1279200610000},"page":"311-326","source":"Crossref","is-referenced-by-count":10,"title":["Asymptotic expansions of defective renewal equations with applications to perturbed risk models and processor sharing queues"],"prefix":"10.1007","volume":"72","author":[{"given":"Jose","family":"Blanchet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bert","family":"Zwart","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,7,16]]},"reference":[{"key":"321_CR1","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0167-6377(94)90081-7","volume":"15","author":"J Abate","year":"1994","unstructured":"Abate J, Whitt W (1994) A Heavy-traffic expansion for the asymptotic decay rates of tail probabilities in multi-channel queues. Oper Res Lett 15: 223\u2013230","journal-title":"Oper Res Lett"},{"key":"321_CR2","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1239\/aap\/1198177240","volume":"39","author":"J Blanchet","year":"2007","unstructured":"Blanchet J, Glynn P (2007) Uniform renewal theory with applications to expansions of geometric sums. Adv Appl Probab 39: 1070\u20131097","journal-title":"Adv Appl Probab"},{"key":"321_CR3","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1137\/S0040585X97977537","volume":"44","author":"A Borovkov","year":"2000","unstructured":"Borovkov A, Foss S (2000) Estimates for overshooting and arbitrary boundary by a random walk and their applications. Theor Probab Appl 44: 231\u2013253","journal-title":"Theor Probab Appl"},{"key":"321_CR4","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0167-6687(91)90023-Q","volume":"10","author":"F Dufresne","year":"1991","unstructured":"Dufresne F, Gerber H (1991) Risk theory for the compound Poisson process that is perturbed by diffusion. Insur Math Econom 10: 51\u201359","journal-title":"Insur Math Econom"},{"key":"321_CR5","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s11134-006-9007-4","volume":"55","author":"R Egorova","year":"2007","unstructured":"Egorova R, Zwart AP (2007) Tail behavior of conditional sojourn times in processor-sharing queues. Queueing Syst 55: 107\u2013121","journal-title":"Queueing Syst"},{"key":"321_CR6","volume-title":"An introduction to probability theory and its applications, vol 2","author":"W Feller","year":"1968","unstructured":"Feller W (1968) An introduction to probability theory and its applications, vol 2. Wiley, New York"},{"key":"321_CR7","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1214\/105051604000000260","volume":"14","author":"C Fuh","year":"2004","unstructured":"Fuh C (2004) Uniform renewal theorems and ruin probabilities in Markov random walks. Ann Appl Prob 14: 1202\u20131241","journal-title":"Ann Appl Prob"},{"key":"321_CR8","doi-asserted-by":"crossref","first-page":"653","DOI":"10.2307\/1427484","volume":"24","author":"S Grishechkin","year":"1992","unstructured":"Grishechkin S (1992) On a relationship between processor-sharing queues and Crump-Mode-Jagers branching processes. Adv Appl Probab 24: 653\u2013698","journal-title":"Adv Appl Probab"},{"key":"321_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0304-4149(99)00084-8","volume":"86","author":"M Gyllenberg","year":"2000","unstructured":"Gyllenberg M, Silvestrov D (2000) Nonlinearly perturbed regenerative processes and pseudo-stationary phenomena for stochastic systems. Stoch Proc Appl 86: 1\u201327","journal-title":"Stoch Proc Appl"},{"key":"321_CR10","first-page":"75","volume":"26","author":"M Gyllenberg","year":"2000","unstructured":"Gyllenberg M, Silvestrov D (2000) Cram\u00e9r\u2013Lundberg approximation for nonlinearly perturbed risk processes. Insurance: Mathematics and Economics 26: 75\u201390","journal-title":"Insurance: Mathematics and Economics"},{"key":"321_CR11","doi-asserted-by":"crossref","DOI":"10.1515\/9783110208252","volume-title":"Quasi-stationary phenomena in nonlinearly perturbed stochastic systems","author":"M Gyllenberg","year":"2008","unstructured":"Gyllenberg M, Silvestrov D (2008) Quasi-stationary phenomena in nonlinearly perturbed stochastic systems. De Gruyter, Berlin"},{"key":"321_CR12","volume-title":"Lundberg approximations for compound distributions with insurance applications","author":"S Lin","year":"2000","unstructured":"Lin S, Willmot G (2000) Lundberg approximations for compound distributions with insurance applications. Springer, New York"},{"key":"321_CR13","doi-asserted-by":"crossref","first-page":"360","DOI":"10.2307\/3213646","volume":"21","author":"TJ Ott","year":"1984","unstructured":"Ott TJ (1984) The sojourn-time distribution in the M\/G\/1 queue with processor sharing. J Appl Probab 21: 360\u2013378","journal-title":"J Appl Probab"},{"key":"321_CR14","volume-title":"Adventures in stochastic processes","author":"S Resnick","year":"1992","unstructured":"Resnick S (1992) Adventures in stochastic processes. McGraw-Hill, New York"},{"key":"321_CR15","doi-asserted-by":"crossref","first-page":"701","DOI":"10.2307\/1426855","volume":"11","author":"D Siegmund","year":"1979","unstructured":"Siegmund D (1979) Corrected diffusion approximations in certain random walk problems. Adv Appl Probab 11: 701\u2013719","journal-title":"Adv Appl Probab"},{"key":"321_CR16","first-page":"133","volume":"12","author":"SF Yashkov","year":"1983","unstructured":"Yashkov SF (1983) A derivation of response time distribution for a M\/G\/1 processor-sharing queue. Probl Control Inf Theor 12: 133\u2013148","journal-title":"Probl Control Inf Theor"},{"key":"321_CR17","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1080\/15326349308807276","volume":"9","author":"SF Yashkov","year":"1993","unstructured":"Yashkov SF (1993) On a heavy traffic limit theorem for the M\/G\/1 processor-sharing queue. Stoch Model 9: 467\u2013471","journal-title":"Stoch Model"},{"key":"321_CR18","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00186-009-0290-9","volume":"71","author":"Q Zhen","year":"2010","unstructured":"Zhen Q, Knessl C (2010) Asymptotic expansions for the sojourn time distribution in the M\/G\/1-PS queue. Math Methods Oper Res 71: 201\u2013244","journal-title":"Math Methods Oper Res"},{"key":"321_CR19","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1023\/A:1019142010994","volume":"35","author":"AP Zwart","year":"2000","unstructured":"Zwart AP, Boxma OJ (2000) Sojourn time asymptotics in the M\/G\/1 processor sharing queue. Queueing Syst 35: 141\u2013166","journal-title":"Queueing Syst"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-010-0321-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00186-010-0321-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-010-0321-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T14:33:29Z","timestamp":1558622009000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-010-0321-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,16]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,10]]}},"alternative-id":["321"],"URL":"https:\/\/doi.org\/10.1007\/s00186-010-0321-6","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,16]]}}}