{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T06:01:42Z","timestamp":1741068102707,"version":"3.38.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2011,4]]},"DOI":"10.1007\/s11134-011-9215-4","type":"journal-article","created":{"date-parts":[[2011,3,9]],"date-time":"2011-03-09T19:04:01Z","timestamp":1299697441000},"page":"295-304","source":"Crossref","is-referenced-by-count":6,"title":["Convergence of the all-time supremum of a L\u00e9vy process in the heavy-traffic regime"],"prefix":"10.1007","volume":"67","author":[{"given":"K. M.","family":"Kosi\u0144ski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"O. J.","family":"Boxma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Zwart","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,3,10]]},"reference":[{"key":"9215_CR1","volume-title":"Applied Probability and Queues","author":"S. Asmussen","year":"2003","unstructured":"Asmussen, S.: Applied Probability and Queues. Springer, Berlin (2003)"},{"key":"9215_CR2","volume-title":"L\u00e9vy Processes","author":"J. Bertoin","year":"1990","unstructured":"Bertoin, J.: L\u00e9vy Processes. Cambridge University Press, Cambridge (1990)"},{"key":"9215_CR3","doi-asserted-by":"crossref","first-page":"705","DOI":"10.2307\/1426397","volume":"7","author":"N.H. Bingham","year":"1975","unstructured":"Bingham, N.H.: Fluctuation theory in continuous time. Adv. Appl. Probab. 7, 705\u2013766 (1975)","journal-title":"Adv. Appl. Probab."},{"key":"9215_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511721434","volume-title":"Regular Variation","author":"N.H. Bingham","year":"1987","unstructured":"Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)"},{"key":"9215_CR5","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1023\/A:1019124112386","volume":"33","author":"O.J. Boxma","year":"1999","unstructured":"Boxma, O.J., Cohen, J.W.: Heavy-traffic analysis for the GI\/G\/1 queue with heavy-tailed distributions. Queueing Syst. 33, 177\u2013204 (1999)","journal-title":"Queueing Syst."},{"key":"9215_CR6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1023\/A:1017992329699","volume":"40","author":"J.W. Cohen","year":"2002","unstructured":"Cohen, J.W.: Random walk with a heavy-tailed jump distribution. Queueing Syst. 40, 35\u201373 (2002)","journal-title":"Queueing Syst."},{"key":"9215_CR7","first-page":"109","volume":"27","author":"M. Czysto\u0142owski","year":"2007","unstructured":"Czysto\u0142owski, M., Szczotka, T.: Tightness of stationary waiting times in Heavy Traffic for GI\/GI\/1 queues with thick tails. Probab. Math. Stat. 27, 109\u2013123 (2007)","journal-title":"Probab. Math. Stat."},{"key":"9215_CR8","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s11134-009-9160-7","volume":"64","author":"M. Czysto\u0142owski","year":"2010","unstructured":"Czysto\u0142owski, M., Szczotka, T.: Queueing approximation of suprema of spectrally positive L\u00e9vy process. Queueing Syst. 64, 305\u2013323 (2010)","journal-title":"Queueing Syst."},{"key":"9215_CR9","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1214\/009117904000000315","volume":"32","author":"R.A. Doney","year":"2004","unstructured":"Doney, R.A.: Stochastic bounds for L\u00e9vy processes. Ann. Probab. 32, 1545\u20131552 (2004)","journal-title":"Ann. Probab."},{"key":"9215_CR10","unstructured":"Furrer, H.: Risk theory and heavy-tailed L\u00e9vy processes. Ph.D. thesis, ETH, Zurich (1997)"},{"key":"9215_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02514-7","volume-title":"Limit Theorems for Stochastic Processes","author":"J. Jacod","year":"1987","unstructured":"Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochastic Processes. Springer, Berlin (1987)"},{"key":"9215_CR12","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1214\/aoap\/1177005983","volume":"1","author":"O. Kella","year":"1991","unstructured":"Kella, O., Whitt, W.: Queues with server vacations and L\u00e9vy processes with secondary jump input. Ann. Appl. Probab. 1, 104\u2013117 (1991)","journal-title":"Ann. Appl. Probab."},{"key":"9215_CR13","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1017\/S0305004100036094","volume":"57","author":"J.F.C. Kingman","year":"1961","unstructured":"Kingman, J.F.C.: The single server queue in heavy traffic. Proc. Camb. Philol. Soc. 57, 902\u2013904 (1961)","journal-title":"Proc. Camb. Philol. Soc."},{"key":"9215_CR14","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1111\/j.2517-6161.1962.tb00465.x","volume":"24","author":"J.F.C. Kingman","year":"1962","unstructured":"Kingman, J.F.C.: On queues in heavy traffic. J. R. Stat. Soc., Ser. B, Stat. Methodol. 24, 383\u2013392 (1962)","journal-title":"J. R. Stat. Soc., Ser. B, Stat. Methodol."},{"key":"9215_CR15","first-page":"137","volume-title":"Proceedings of Symposium on Congestion Theory","author":"J.F.C. Kingman","year":"1965","unstructured":"Kingman, J.F.C.: The heavy traffic approximation in the theory of queues. In: Smith, W.L., Wilkinson, W.E. (eds.) Proceedings of Symposium on Congestion Theory, pp. 137\u2013159. University of North Carolina Press, Chapel Hill (1965)"},{"key":"9215_CR16","volume-title":"Introductory Lectures on Fluctuations of L\u00e9vy Processes with Applications","author":"A.E. Kyprianou","year":"2006","unstructured":"Kyprianou, A.E.: Introductory Lectures on Fluctuations of L\u00e9vy Processes with Applications. Springer, Berlin (2006)"},{"key":"9215_CR17","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.spa.2005.09.002","volume":"116","author":"K. Maulik","year":"2006","unstructured":"Maulik, K., Zwart, B.: Tail asymptotics for exponential functionals of L\u00e9vy processes. Stoch. Process. Appl. 116, 156\u2013177 (2006)","journal-title":"Stoch. Process. Appl."},{"key":"9215_CR18","first-page":"199","volume":"9","author":"Ju.V. Prokhorov","year":"1963","unstructured":"Prokhorov, Ju.V., Transition phenomena in queueing processes. I. Liet. Mat. Rink. 9, 199\u2013205 (1963)","journal-title":"Liet. Mat. Rink."},{"key":"9215_CR19","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1214\/aop\/1176994266","volume":"9","author":"W.E. Pruitt","year":"1981","unstructured":"Pruitt, W.E.: The growth of random walks and L\u00e9vy processes. Ann. Probab. 9, 948\u2013956 (1981)","journal-title":"Ann. Probab."},{"key":"9215_CR20","doi-asserted-by":"crossref","first-page":"1236","DOI":"10.1287\/mnsc.46.9.1236.12234","volume":"46","author":"S. Resnick","year":"2000","unstructured":"Resnick, S., Samorodnitsky, G.: A heavy traffic limit theorem for workload processes with heavy tailed service requirements. Manag. Sci. 46, 1236\u20131248 (2000)","journal-title":"Manag. Sci."},{"key":"9215_CR21","unstructured":"Shneer, S., Wachtel, V.: Heavy-traffic analysis of the maximum of an asymptotically stable random walk. Technical Report 2009-005, EURANDOM (2009)"},{"key":"9215_CR22","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1137\/1102011","volume":"11","author":"A.V. Skorokhod","year":"1957","unstructured":"Skorokhod, A.V.: Limit theorems for stochastic processes with independent increments. Theory Probab. Appl. 11, 138\u2013171 (1957)","journal-title":"Theory Probab. Appl."},{"key":"9215_CR23","first-page":"251","volume":"23","author":"T. Szczotka","year":"2003","unstructured":"Szczotka, T., Woyczy\u0144ski, W.A.: Distributions of suprema of L\u00e9vy processes via heavy traffic invariance principle. Probab. Math. Stat. 23, 251\u2013272 (2003)","journal-title":"Probab. Math. Stat."},{"key":"9215_CR24","first-page":"67","volume":"24","author":"T. Szczotka","year":"2004","unstructured":"Szczotka, T., Woyczy\u0144ski, W.A.: Heavy-tailed dependent queues in heavy traffic. Probab. Math. Stat. 24, 67\u201396 (2004)","journal-title":"Probab. Math. Stat."},{"key":"9215_CR25","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0304-4149(87)90058-5","volume":"26","author":"E. Willekens","year":"1987","unstructured":"Willekens, E.: On the supremum of an infinitely divisible process. Stoch. Process. Appl. 26, 173\u2013175 (1987)","journal-title":"Stoch. Process. Appl."}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s11134-011-9215-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T23:17:13Z","timestamp":1741043833000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-011-9215-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,10]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,4]]}},"alternative-id":["9215"],"URL":"https:\/\/doi.org\/10.1007\/s11134-011-9215-4","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[2011,3,10]]}}}