{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T20:37:39Z","timestamp":1771015059261,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2005,7,1]],"date-time":"2005-07-01T00:00:00Z","timestamp":1120176000000},"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":[[2005,7]]},"DOI":"10.1007\/s11134-005-0926-2","type":"journal-article","created":{"date-parts":[[2005,8,18]],"date-time":"2005-08-18T05:16:28Z","timestamp":1124342188000},"page":"299-323","source":"Crossref","is-referenced-by-count":3,"title":["Tail Behaviour of the Area Under the Queue Length Process of the Single Server Queue with Regularly Varying Service Times"],"prefix":"10.1007","volume":"50","author":[{"given":"Rafa\u0142","family":"Kulik","sequence":"first","affiliation":[]},{"given":"Zbigniew","family":"Palmowski","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"926_CR1","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1019104402024","volume":"Systems","author":"J. Abate","year":"1997","unstructured":"J. Abate and W. Whitt, Asymptotics for M\/G\/1 low-priority waiting-time tail probabilities, Queueing Systems (1997) 173\u2013233.","journal-title":"Queueing"},{"key":"926_CR2","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1214\/aoap\/1028903531","volume":"8","author":"S. Asmussen","year":"1998","unstructured":"S. Asmussen, Subexponential asymptotics for stochastic processes: Extremal behaviour, stationary distributions and first passage times, Annals of Applied Probability 8 (1998) 354\u2013374.","journal-title":"Annals of Applied Probability"},{"key":"926_CR3","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1023\/A:1009970005784","volume":"1","author":"S. Asmussen","year":"1998","unstructured":"S. Asmussen, Extreme value theory for queues via cycle maxima, Extremes 1 (1998) 137\u2013168.","journal-title":"Extremes"},{"key":"926_CR4","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0304-4149(96)00087-7","volume":"64","author":"S. Asmussen","year":"1996","unstructured":"S. Asmussen and C. Kl\u00fcppelberg, Large deviations results for subexponential tails, with applications to insurance risk, Stochastic Processes and their Applications 64 (1996) 103\u2013125.","journal-title":"Stochastic Processes and their Applications"},{"key":"926_CR5","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S0304-4149(98)00064-7","volume":"79","author":"S. Asmussen","year":"1999","unstructured":"S. Asmussen, C. Kl\u00fcppelberg and K. Sigman, Sampling at subexponential times, with queueing applications, Stochastic Processes and their Applications 79 (1999) 265\u2013286.","journal-title":"Stochastic Processes and their Applications"},{"key":"926_CR6","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1023\/A:1019172028316","volume":"33","author":"S. Asmussen","year":"1999","unstructured":"S. Asmussen and J. M\u00f8ller, Tail asymptotics for M\/G\/1 type queueing processes with subexponential increments, Queueing Systems 33 (1999) 153\u2013176.","journal-title":"Queueing Systems"},{"key":"926_CR7","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.2307\/3214995","volume":"33","author":"S. Asmussen","year":"1996","unstructured":"S. Asmussen and J.L. Teugels, Convergence rates for M\/G\/1 queues and ruin problems with heavy tails, Journal of Applied Probability 33 (1996) 1181\u20131190.","journal-title":"Journal of Applied Probability"},{"key":"926_CR8","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.spa.2004.01.005","volume":"111","author":"A. Baltrunas","year":"2004","unstructured":"A. Baltrunas, D.J. Daley and C. Kl\u00fcppelberg, Tail behaviour of the busy period of a GI\/GI\/1 queue with subexponential service times, Stochastic Processes and their Applications 111 (2004) 237\u2013258.","journal-title":"Stochastic Processes and their Applications"},{"key":"926_CR9","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511721434","volume-title":"Regular Variation","author":"N.H. Bingham","year":"1987","unstructured":"N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation (Cambridge University Press, Cambridge, 1987)."},{"key":"926_CR10","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1239\/jap\/1044476835","volume":"40","author":"A.A. Borovkov","year":"2003","unstructured":"A.A. Borovkov, O.J. Boxma and Z. Palmowski, On the integral of the workload process of the single server queue, Journal of Applied Probability 40 (2003) 200\u2013225.","journal-title":"Journal of Applied Probability"},{"key":"926_CR11","doi-asserted-by":"crossref","first-page":"550","DOI":"10.2307\/3212101","volume":"6","author":"D.J. Daley","year":"1969","unstructured":"D.J. Daley, The total waiting time in a busy period of a stable single-server queue. I, Journal of Applied Probability 6 (1969) 550\u2013564.","journal-title":"Journal of Applied Probability"},{"key":"926_CR12","doi-asserted-by":"crossref","first-page":"565","DOI":"10.2307\/3212102","volume":"6","author":"D.J. Daley","year":"1969","unstructured":"D.J. Daley and D.R. Jacobs Jr., The total waiting time in a busy period of a stable single-server queue. II, Journal of Applied Probability 6 (1969) 565\u2013572.","journal-title":"Journal of Applied Probability"},{"key":"926_CR13","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1214\/aoap\/1042765662","volume":"13","author":"S. Foss","year":"2003","unstructured":"S. Foss and S. Zachary, The maximum on a random time interval of a random walk with long-tailed increments and negative drift, Annals of Applied Probability 13 (2003) 37\u201353.","journal-title":"Annals of Applied Probability"},{"key":"926_CR14","doi-asserted-by":"crossref","unstructured":"S. Foss, Z. Palmowski and S. Zachary, The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk, to appear in Annals of Applied Probability (2005).","DOI":"10.1214\/105051605000000269"},{"key":"926_CR15","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1137\/1116071","volume":"16","author":"D.K. Fuk","year":"1971","unstructured":"D.K. Fuk and S.V. Nagaev, Probability inequalities for sums of independent random variables, Th. Prob. Appl. 16 (1971) 643\u2013660.","journal-title":"Th. Prob. Appl."},{"key":"926_CR16","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1023\/A:1019100617896","volume":"29","author":"F. Guillemin","year":"1998","unstructured":"F. Guillemin and D. Pinchon, On the area swept under the occupation process of an M\/M\/1 queue in a busy period, Queueing Systems 29 (1998) 383\u2013398.","journal-title":"Queueing Systems"},{"key":"926_CR17","doi-asserted-by":"crossref","first-page":"862","DOI":"10.2307\/1428137","volume":"27","author":"F. Guillemin","year":"1997","unstructured":"F. Guillemin and A. Simonian, Transient characteristics of an M\/M\/\u221e system, Advances in Applied Probability 27 (1997) 862\u2013888.","journal-title":"Advances in Applied Probability"},{"key":"926_CR18","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0167-7152(97)00028-X","volume":"35","author":"A. Gut","year":"1997","unstructured":"A. Gut, Stopped two-dimensional perturbed random walks and L\u00e9vy processes, Statistics and Probability Letters 35 (1997) 317\u2013325.","journal-title":"Statistics and Probability Letters"},{"key":"926_CR19","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1214\/aoap\/1043862423","volume":"7","author":"D. Heath","year":"1997","unstructured":"D. Heath, S. Resnick and G. Samorodnitsky, Patterns of buffer overflow in a class of queues with long memory in the input stream, Annals of Applied Probability 7 (1997) 1021\u20131057.","journal-title":"Annals of Applied Probability"},{"key":"926_CR20","first-page":"253","volume":"30","author":"C.C. Heyde","year":"1968","unstructured":"C.C. Heyde, On large deviation probabilities in the case of attraction to a non-normal law, Sankhya Ser. A 30 (1968) 253\u2013258.","journal-title":"Sankhya Ser. A"},{"key":"926_CR21","doi-asserted-by":"crossref","first-page":"269","DOI":"10.2307\/1426171","volume":"3","author":"D.L. Iglehart","year":"1971","unstructured":"D.L. Iglehart, Functional limit theorems for the queue GI\/G\/1 in light traffic, Advances in Applied Probability 3 (1971) 269\u2013281.","journal-title":"Advances in Applied Probability"},{"issue":"2","key":"926_CR22","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1287\/moor.1030.0082","volume":"29","author":"P. Jelenkovic","year":"2004","unstructured":"P. Jelenkovic and P. Momcilovic, Large deviations for square root insensitive random sums, Mathematics of Operations Research 29(2) (2004), 398\u2013406.","journal-title":"Mathematics of Operations Research"},{"key":"926_CR23","first-page":"325","volume":"35","author":"C. Kl\u00fcppelberg","year":"1988","unstructured":"C. Kl\u00fcppelberg, Subexponential distributions and integrated tails, Journal of Applied Probability 35 (1988) 325\u2013347.","journal-title":"Journal of Applied Probability"},{"key":"926_CR24","doi-asserted-by":"crossref","unstructured":"A.De Meyer and J.L. Teugels, On the asymptotic behaviour of the distributions of the busy period and service time in M\/G\/1, Journal of Applied Probability (1980), 802\u2013813.","DOI":"10.2307\/3212973"},{"key":"926_CR25","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1137\/1114006","volume":"14","author":"A.V. Nagaev","year":"1969","unstructured":"A.V. Nagaev, Integral limit theorems taking large deviations into account when Cram\u00e9r\u2019s condition does not hold. I, Th. Prob. Appl. 14 (1969) 51\u201364.","journal-title":"Th. Prob. Appl."},{"key":"926_CR26","unstructured":"A.V. Nagaev, Probabilities of large deviations of sums of independent random variables, Doctor of Science Thesis (1970)."},{"key":"926_CR27","unstructured":"I.F. Pinelis, Asymptotics equivalence of the probabilities of large deviations for sums and maximum of independent random variables. Limit theorems of probability theory, Trudy Inst. Mat. 5 (1985), \u201cNauka\u201d Sibirsk. Otdel., Novosybirsk, pp. 144\u2013173."},{"key":"926_CR28","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1287\/moor.26.3.485.10584","volume":"26","author":"A.P. Zwart","year":"2001","unstructured":"A.P. Zwart, Tail asymptotics for the busy period in the GI\/G\/1 queue, Mathematics of Operations Research 26 (2001) 485\u2013493.","journal-title":"Mathematics of Operations Research"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-005-0926-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-005-0926-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-005-0926-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T02:07:00Z","timestamp":1586398020000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-005-0926-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,7]]},"references-count":28,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2005,7]]}},"alternative-id":["926"],"URL":"https:\/\/doi.org\/10.1007\/s11134-005-0926-2","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,7]]}}}