{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:23:11Z","timestamp":1775470991264,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,6,18]],"date-time":"2011-06-18T00:00:00Z","timestamp":1308355200000},"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":[[2011,9]]},"DOI":"10.1007\/s11134-011-9231-4","type":"journal-article","created":{"date-parts":[[2011,6,17]],"date-time":"2011-06-17T22:58:44Z","timestamp":1308351524000},"page":"29-44","source":"Crossref","is-referenced-by-count":13,"title":["The on\u2013off network traffic model under intermediate scaling"],"prefix":"10.1007","volume":"69","author":[{"given":"Cl\u00e9ment","family":"Dombry","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ingemar","family":"Kaj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,6,18]]},"reference":[{"key":"9231_CR1","doi-asserted-by":"crossref","DOI":"10.1142\/9789812779311","volume-title":"Ruin Probabilities","author":"S. Asmussen","year":"2000","unstructured":"Asmussen, S.: Ruin Probabilities. World Scientific, Singapore (2000)"},{"key":"9231_CR2","doi-asserted-by":"crossref","first-page":"1790","DOI":"10.1214\/EJP.v14-675","volume":"14","author":"L. Beghin","year":"2009","unstructured":"Beghin, L., Orsingher, E.: Fractional Poisson processes and related planar random motions. Electron. J. Probab. 14, 1790\u20131826 (2009)","journal-title":"Electron. J. Probab."},{"key":"9231_CR3","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1214\/EJP.v15-762","volume":"15","author":"L. Beghin","year":"2010","unstructured":"Beghin, L., Orsingher, E.: Poisson-type processes governed by fractional and higher-order recursive differential equations. Electron. J. Probab. 15, 684\u2013709 (2010)","journal-title":"Electron. J. Probab."},{"key":"9231_CR4","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1007\/s10959-009-0259-x","volume":"23","author":"H. Bierm\u00e9","year":"2010","unstructured":"Bierm\u00e9, H., Estrade, A., Kaj, I.: Self-similar random fields and rescaled random balls models. J. Theor. Probab. 23, 1110\u20131141 (2010)","journal-title":"J. Theor. Probab."},{"key":"9231_CR5","volume-title":"Convergence of Probability Measures","author":"P. Billingsley","year":"1968","unstructured":"Billingsley, P.: Convergence of Probability Measures, 2nd\u00a0edn. Wiley, New York (1968)","edition":"2"},{"key":"9231_CR6","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.H.: Regular Variation. Cambridge University Press, Cambridge (1987)"},{"issue":"1","key":"9231_CR7","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1214\/aoap\/1015961155","volume":"12","author":"T. Mikosch","year":"2002","unstructured":"Mikosch, T., Resnick, S., Rootzen, H., Stegeman, A.: Is network traffic approximated by stable L\u00e9vy motion or fractional Brownian motion. Ann. Appl. Probab. 12(1), 23\u201368 (2002)","journal-title":"Ann. Appl. Probab."},{"issue":"4","key":"9231_CR8","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1287\/moor.1070.0267","volume":"32","author":"T. Mikosch","year":"2007","unstructured":"Mikosch, T., Samorodnitsky, G.: Scaling limits for cumulative input processes. Math. Oper. Res. 32(4), 890\u2013918 (2007)","journal-title":"Math. Oper. Res."},{"key":"9231_CR9","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.spa.2005.10.003","volume":"116","author":"R. Gaigalas","year":"2006","unstructured":"Gaigalas, R.: A Poisson bridge between fractional Brownian motion and stable L\u00e9vy motion. Stoch. Process. Appl. 116, 447\u2013462 (2006)","journal-title":"Stoch. Process. Appl."},{"issue":"4","key":"9231_CR10","doi-asserted-by":"crossref","first-page":"671","DOI":"10.3150\/bj\/1066223274","volume":"9","author":"R. Gaigalas","year":"2003","unstructured":"Gaigalas, R., Kaj, I.: Convergence of scaled renewal processes and a packet arrival model. Bernoulli 9(4), 671\u2013703 (2003)","journal-title":"Bernoulli"},{"key":"9231_CR11","doi-asserted-by":"crossref","first-page":"2577","DOI":"10.1016\/S0960-0779(00)00218-6","volume":"12","author":"G.J. Jumarie","year":"2001","unstructured":"Jumarie, G.J.: Fractional master equation: non-standard analysis and Liouville\u2013Rieman derivative. Chaos Solitons Fractals 12, 2577\u20132587 (2001)","journal-title":"Chaos Solitons Fractals"},{"key":"9231_CR12","series-title":"SIAM Monographs on Mathematical Modeling and Computation","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718294","volume-title":"Stochastic Modeling in Broadband Communications Systems","author":"I. Kaj","year":"2002","unstructured":"Kaj, I.: Stochastic Modeling in Broadband Communications Systems. SIAM Monographs on Mathematical Modeling and Computation, vol.\u00a08. SIAM, Philadelphia (2002)"},{"key":"9231_CR13","first-page":"199","volume-title":"Fractals in Engineering, New Trends in Theory and Applications","author":"I. Kaj","year":"2005","unstructured":"Kaj, I.: Limiting fractal random processes in heavy-tailed systems. In: Levy-Lehel, J., Lutton, E. (eds.) Fractals in Engineering, New Trends in Theory and Applications, pp.\u00a0199\u2013218. Springer, London (2005)"},{"key":"9231_CR14","series-title":"Progress in Probability","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/978-3-7643-8786-0_19","volume-title":"An Out of Equilibrium\u00a02","author":"I. Kaj","year":"2008","unstructured":"Kaj, I., Taqqu, M.S.: Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach. In: Vares, M.E., Sidoravicius, V. (eds.) An Out of Equilibrium\u00a02. Progress in Probability, vol.\u00a060, pp.\u00a0383\u2013427. Birkh\u00e4user, Basel (2008)"},{"key":"9231_CR15","doi-asserted-by":"crossref","first-page":"23","DOI":"10.2307\/3318631","volume":"6","author":"J.B. L\u00e9vy","year":"2000","unstructured":"L\u00e9vy, J.B., Taqqu, M.S.: Renewal reward processes with heavy-tailed interrenewal times and heavy-tailed rewards. Bernoulli 6, 23\u201344 (2000)","journal-title":"Bernoulli"},{"key":"9231_CR16","first-page":"53","volume":"32","author":"F. Mainardi","year":"2005","unstructured":"Mainardi, F., Gorenflo, R., Scalas, E.: A fractional generalization of the Poisson processes. Vietnam J. Math. 32, 53\u201364 (2005)","journal-title":"Vietnam J. Math."},{"key":"9231_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65809-9","volume-title":"Sums of Independent Random Variables","author":"V.V. Petrov","year":"1975","unstructured":"Petrov, V.V.: Sums of Independent Random Variables. Springer, New York (1975)"},{"key":"9231_CR18","doi-asserted-by":"crossref","first-page":"607","DOI":"10.2307\/3318508","volume":"6","author":"V. Pipiras","year":"2000","unstructured":"Pipiras, V., Taqqu, M.S.: The limit of a renewal-reward process with heavy-tailed rewards is not a linear fractional stable motion. Bernoulli 6, 607\u2013614 (2000)","journal-title":"Bernoulli"},{"key":"9231_CR19","doi-asserted-by":"crossref","first-page":"121","DOI":"10.3150\/bj\/1077544606","volume":"10","author":"V. Pipiras","year":"2004","unstructured":"Pipiras, V., Taqqu, M.S., L\u00e9vy, L.B.: Slow, fast and arbitrary growth conditions for renewal reward processes when the renewals and the rewards are heavy-tailed. Bernoulli 10, 121\u2013163 (2004)","journal-title":"Bernoulli"},{"key":"9231_CR20","series-title":"Springer Series in Operations Research and Financial Engineering","volume-title":"Heavy-Tail Phenomena, Probabilistic and Statistical modeling","author":"S.I. Resnick","year":"2007","unstructured":"Resnick, S.I.: Heavy-Tail Phenomena, Probabilistic and Statistical modeling. Springer Series in Operations Research and Financial Engineering. Springer, New York (2007)"},{"key":"9231_CR21","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1145\/263876.263879","volume":"27","author":"M.S. Taqqu","year":"1997","unstructured":"Taqqu, M.S., Willinger, W., Sherman, R.: Proof of a fundamental result in self-similar traffic modeling. Comput. Commun. Rev. 27, 5\u201323 (1997)","journal-title":"Comput. Commun. Rev."},{"key":"9231_CR22","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0960-0779(02)00579-9","volume":"18","author":"X.-T. Wang","year":"2003","unstructured":"Wang, X.-T., Wen, Z.-X.: Poisson fractional process. Chaos Solitons Fractals 18, 169\u2013177 (2003)","journal-title":"Chaos Solitons Fractals"},{"key":"9231_CR23","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.chaos.2005.05.019","volume":"28","author":"X.-T. Wang","year":"2006","unstructured":"Wang, X.-T., Wen, Z.-X., Zhang, S.-Y.: Fractional Poisson processes (II). Chaos Solitons Fractals 28, 143\u2013147 (2006)","journal-title":"Chaos Solitons Fractals"},{"key":"9231_CR24","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.chaos.2005.09.063","volume":"31","author":"X.-T. Wang","year":"2007","unstructured":"Wang, X.-T., Wen, Z.-X., Fan, S.: Nonhomogeneous fractional Poisson processes. Chaos Solitons Fractals 31, 236\u2013141 (2007)","journal-title":"Chaos Solitons Fractals"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-011-9231-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-011-9231-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-011-9231-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T03:44:41Z","timestamp":1559360681000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-011-9231-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,18]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["9231"],"URL":"https:\/\/doi.org\/10.1007\/s11134-011-9231-4","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,18]]}}}