{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:23:50Z","timestamp":1759073030105,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T00:00:00Z","timestamp":1613606400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T00:00:00Z","timestamp":1613606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["024.002.003"],"award-info":[{"award-number":["024.002.003"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive drifts, which can be correlated across different queues. The flow of work departing from each server is split deterministically and routed to its neighbors according to a fixed routing matrix, with a fraction of it leaving the network altogether. We study the exponential decay rate of the probability that the steady-state queue length at any given node in the network is above any fixed threshold, also referred to as the \u2018overflow probability\u2019. In particular, we first leverage Schilder\u2019s sample-path large deviations theorem to obtain a general lower bound for the limit of this exponential decay rate, as the number of Gaussian processes goes to infinity. Then, we show that this lower bound is tight under additional technical conditions. Finally, we show that if the input processes to the different queues are nonnegatively correlated, non-short-range dependent fractional Brownian motions, and if the processing rates are large enough, then the asymptotic exponential decay rates of the queues coincide with the ones of isolated queues with appropriate Gaussian inputs.<\/jats:p>","DOI":"10.1007\/s11134-021-09689-9","type":"journal-article","created":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T17:51:38Z","timestamp":1613757098000},"page":"333-371","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Large deviations for acyclic networks of queues with correlated Gaussian inputs"],"prefix":"10.1007","volume":"98","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1320-9893","authenticated-orcid":false,"given":"Martin","family":"Zubeldia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Mandjes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,18]]},"reference":[{"key":"9689_CR1","doi-asserted-by":"crossref","unstructured":"Kilpi, Jorma, Norros, Ilkka: Testing the Gaussian approximation of aggregate traffic. In 2nd ACM SIGCOMM Internet Measurement Workshop, pages 49\u201361, (2002)","DOI":"10.1145\/637201.637207"},{"key":"9689_CR2","unstructured":"Meent, Remco van\u00a0de, Mandjes, Michel, Pras, Aiko: Gaussian traffic everywhere? In 2006 IEEE International Conference on Communications, pages 573\u2013578, (2006)"},{"key":"9689_CR3","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF01245322","volume":"20","author":"D Botvich","year":"1995","unstructured":"Botvich, D., Duffield, N.: Large deviations, the shape of loss curve, and economies of scale in large multiplexers. Queueing Syst. 20, 293\u2013320 (1995)","journal-title":"Queueing Syst."},{"key":"9689_CR4","doi-asserted-by":"publisher","first-page":"886","DOI":"10.2307\/3215366","volume":"33","author":"C Courcoubetis","year":"1996","unstructured":"Courcoubetis, C., Weber, R.: Buffer overflow asymptotics for a buffer handling many traffic sources. J. Appl. Probab. 33, 886\u2013903 (1996)","journal-title":"J. Appl. Probab."},{"key":"9689_CR5","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1002\/ett.4460130303","volume":"13","author":"R Addie","year":"2002","unstructured":"Addie, R., Mannersalo, P., Norros, I.: Most probable paths and performance formulae for buffers with Gaussian input traffic. Eur. Trans. Telecommun. 13, 183\u2013196 (2002)","journal-title":"Eur. Trans. Telecommun."},{"key":"9689_CR6","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1239\/jap\/1059060897","volume":"40","author":"K Debicki","year":"2003","unstructured":"Debicki, K., Mandjes, M.: Exact overflow asymptotics for queues with many Gaussian inputs. J. Appl. Probab. 40, 704\u2013720 (2003)","journal-title":"J. Appl. Probab."},{"key":"9689_CR7","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1214\/105051605000000133","volume":"15","author":"M Mandjes","year":"2005","unstructured":"Mandjes, M., van Uitert, M.: Sample-path large deviations for tandem and priority queues with Gaussian inputs. Ann. Appl. Probab. 15, 1193\u20131226 (2005)","journal-title":"Ann. Appl. Probab."},{"key":"9689_CR8","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1016\/j.comnet.2006.06.006","volume":"51","author":"M Mandjes","year":"2007","unstructured":"Mandjes, M., Mannersalo, P., Norros, I.: Gaussian tandem queues with an application to dimensioning of switch fabrics. Comput. Netw. 51, 781\u2013797 (2007)","journal-title":"Comput. Netw."},{"key":"9689_CR9","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1016\/j.spa.2006.02.003","volume":"116","author":"M Mandjes","year":"2006","unstructured":"Mandjes, M., Mannersalo, P., Norros, I., van Uitert, M.: Large deviations of infinite intersections of events in Gaussian processes. Stoch. Process. Their Appl. 116, 1269\u20131293 (2006)","journal-title":"Stoch. Process. Their Appl."},{"issue":"4","key":"9689_CR10","first-page":"1070","volume":"8","author":"K Ramanan","year":"1998","unstructured":"Ramanan, K.: Large deviation properties of data streams that share a buffer. Ann. Appl. Probab. 8(4), 1070\u20131129 (1998)","journal-title":"Ann. Appl. Probab."},{"issue":"4","key":"9689_CR11","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.1214\/aoap\/1028903373","volume":"8","author":"D Bertsimas","year":"1998","unstructured":"Bertsimas, D., Paschalidis, J.C., Tsitsiklis, J.N.: On the large deviations behavior of acyclic networks of G\/G\/1 queues. Ann. Appl. Probab. 8(4), 1027\u20131069 (1998)","journal-title":"Ann. Appl. Probab."},{"issue":"2\u20133","key":"9689_CR12","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.peva.2004.11.009","volume":"61","author":"M Mandjes","year":"2005","unstructured":"Mandjes, M.: Sample-path large deviations for generalized processor sharing queues with Gaussian inputs. Perform. Eval. 61(2\u20133), 225\u2013256 (2005)","journal-title":"Perform. Eval."},{"key":"9689_CR13","doi-asserted-by":"publisher","DOI":"10.1002\/9780470515099","volume-title":"Large deviations for Gaussian queues: modelling communication networks","author":"M Mandjes","year":"2007","unstructured":"Mandjes, M.: Large deviations for Gaussian queues: modelling communication networks. Wiley, Hoboken (2007)"},{"key":"9689_CR14","doi-asserted-by":"publisher","first-page":"506","DOI":"10.2307\/1427310","volume":"18","author":"A Weiss","year":"1986","unstructured":"Weiss, A.: A new technique for analyzing large traffic systems. Adv. Appl. Probab. 18, 506\u2013532 (1986)","journal-title":"Adv. Appl. Probab."},{"key":"9689_CR15","doi-asserted-by":"crossref","unstructured":"Mannersalo, P., Norros, I.: Approximate formulae for Gaussian priority queues. In: Proceedings of INFOCOM, pp. 991\u20131002 (2001)","DOI":"10.1016\/S1388-3437(01)80186-4"},{"key":"9689_CR16","doi-asserted-by":"crossref","DOI":"10.1214\/lnms\/1215467924","volume-title":"An introduction to continuity, extrema, and related topics for general Gaussian processes","author":"R Adler","year":"1990","unstructured":"Adler, R.: An introduction to continuity, extrema, and related topics for general Gaussian processes. IMS, Hayward (1990)"},{"key":"9689_CR17","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1214\/aop\/1176994985","volume":"7","author":"RR Bahadur","year":"1979","unstructured":"Bahadur, R.R.: Large deviations of the sample mean in general vector spaces. Ann. Probab. 7, 587\u2013621 (1979)","journal-title":"Ann. Probab."},{"issue":"23","key":"9689_CR18","doi-asserted-by":"publisher","first-page":"2415","DOI":"10.1016\/j.spl.2009.08.015","volume":"79","author":"F Lavancier","year":"2009","unstructured":"Lavancier, F., Philippe, A., Surgailis, D.: Covariance function of vector self-similar processes. Stat. Probab. Lett. 79(23), 2415\u20132421 (2009)","journal-title":"Stat. Probab. Lett."},{"key":"9689_CR19","first-page":"65","volume":"28","author":"P-O Amblard","year":"2013","unstructured":"Amblard, P.-O., Coeurjolly, J.-F., Lavancier, F., Philippe, A.: Basic properties of the multivariate fractional Brownian motion. S\u00e9minaries et congres, Soci\u00e9t\u00e9 math\u00e9matique de France 28, 65\u201387 (2013)","journal-title":"S\u00e9minaries et congres, Soci\u00e9t\u00e9 math\u00e9matique de France"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-021-09689-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11134-021-09689-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-021-09689-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T14:26:27Z","timestamp":1697898387000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11134-021-09689-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,18]]},"references-count":19,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["9689"],"URL":"https:\/\/doi.org\/10.1007\/s11134-021-09689-9","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[2021,2,18]]},"assertion":[{"value":"29 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 January 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 January 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}