{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:28:56Z","timestamp":1766269736765,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,9,10]],"date-time":"2015-09-10T00:00:00Z","timestamp":1441843200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Telecommun Syst"],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1007\/s11235-015-0086-6","type":"journal-article","created":{"date-parts":[[2015,9,10]],"date-time":"2015-09-10T09:04:15Z","timestamp":1441875855000},"page":"461-479","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A packet-switched network with On\/Off sources and a fair bandwidth sharing policy: state space collapse and heavy-traffic"],"prefix":"10.1007","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1208-9236","authenticated-orcid":false,"given":"Rosario","family":"Delgado","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,9,10]]},"reference":[{"key":"86_CR1","volume-title":"Convergence of probability measures","author":"P Billingsley","year":"1968","unstructured":"Billingsley, P. (1968). Convergence of probability measures. New York: Wiley."},{"key":"86_CR2","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1145\/384268.378438","volume":"29","author":"T Bonald","year":"2001","unstructured":"Bonald, T., & Massouli\u00e9, L. (2001). Impact of fairness on internet performance. ACM Sigmatrics Performance Evaluation Review, 29, 82\u201391.","journal-title":"ACM Sigmatrics Performance Evaluation Review"},{"issue":"1","key":"86_CR3","first-page":"3","volume":"40","author":"JG Dai","year":"1995","unstructured":"Dai, J. G., & Williams, R. J. (1995). Existence and uniqueness of semimartingale reflecting Brownian motions in convex polytopes. Theory of Probability and Its Applications, 40(1), 3\u201353.","journal-title":"Theory of Probability and Its Applications"},{"key":"86_CR4","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/90.909020","volume":"9","author":"G Veciana De","year":"2001","unstructured":"De Veciana, G., Lee, T. J., & Konstantopoulos, T. (2001). Stability and performance analysis of networks supporting elastic services. IEEE\/ACM Transactions on Networking, 9, 2\u201314.","journal-title":"IEEE\/ACM Transactions on Networking"},{"key":"86_CR5","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1023\/B:QUES.0000021144.61749.aa","volume":"46","author":"K Debicki","year":"2004","unstructured":"Debicki, K., & Mandjes, M. (2004). Traffic with an fBm limit: Convergence of the stationary workload process. Queueing Systems, 46, 113\u2013127.","journal-title":"Queueing Systems"},{"key":"86_CR6","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.spa.2006.07.001","volume":"117","author":"R Delgado","year":"2007","unstructured":"Delgado, R. (2007). A reflected fBm limit for fluid models with ON\/OFF sources under heavy traffic. Stochastic Processes and Their Applications, 117, 188\u2013201.","journal-title":"Stochastic Processes and Their Applications"},{"key":"86_CR7","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s11134-008-9080-y","volume":"59","author":"R Delgado","year":"2008","unstructured":"Delgado, R. (2008). State space collapse for asymptotically critical multi-class fluid networks. Queueing Systems, 59, 157\u2013184.","journal-title":"Queueing Systems"},{"issue":"1","key":"86_CR8","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s11134-012-9320-z","volume":"74","author":"R Delgado","year":"2013","unstructured":"Delgado, R. (2013). Heavy-traffic limit for a feed-forward fluid model with heterogeneous heavy-tailed On\/Off sources. Queueing Systems, 74(1), 41\u201363.","journal-title":"Queueing Systems"},{"key":"86_CR9","first-page":"31","volume":"35","author":"P Dupuis","year":"1991","unstructured":"Dupuis, P., & Ishii, H. (1991). On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics, 35, 31\u201362.","journal-title":"Stochastics"},{"key":"86_CR10","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s004400050269","volume":"115","author":"P Dupuis","year":"1999","unstructured":"Dupuis, P., & Ramanan, K. (1999). Convex duality and the Skorokhod problem I. Probability Theory and Related Fields, 115, 153\u2013195.","journal-title":"Probability Theory and Related Fields"},{"key":"86_CR11","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s004400050270","volume":"115","author":"P Dupuis","year":"1999","unstructured":"Dupuis, P., & Ramanan, K. (1999). Convex duality and the Skorokhod problem II. Probability Theory and Related Fields, 115, 197\u2013236.","journal-title":"Probability Theory and Related Fields"},{"key":"86_CR12","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316658","volume-title":"Markov processes: Characterization and convergence","author":"SN Ethier","year":"1986","unstructured":"Ethier, S. N., & Kurtz, T. G. (1986). Markov processes: Characterization and convergence. New York: Wiley."},{"issue":"4","key":"86_CR13","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1109\/TNET.2011.2173553","volume":"20","author":"K Jagannathan","year":"2012","unstructured":"Jagannathan, K., Markakis, M., Modiano, E., & Tsitsiklis, J. N. (2012). Queue-length asymptotics for generalized max-weight scheduling in the presence of heavy-tailed traffic. IEEE\/ACM Transactions on Networking, 20(4), 1096\u20131111.","journal-title":"IEEE\/ACM Transactions on Networking"},{"issue":"5","key":"86_CR14","doi-asserted-by":"crossref","first-page":"1719","DOI":"10.1214\/08-AAP591","volume":"19","author":"WN Kang","year":"2009","unstructured":"Kang, W. N., Kelly, F. P., Lee, N. H., & Williams, R. J. (2009). State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy. The Annals of Applied Probability, 19(5), 1719\u20131780.","journal-title":"The Annals of Applied Probability"},{"key":"86_CR15","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1214\/105051606000000899","volume":"17","author":"WN Kang","year":"2007","unstructured":"Kang, W. N., & Williams, R. J. (2007). An invariance principle for semimartingale reflecting Brownian motions in domains with piecewise smooth boundaries. The Annals of Applied Probability, 17, 741\u2013779.","journal-title":"The Annals of Applied Probability"},{"key":"86_CR16","doi-asserted-by":"crossref","unstructured":"Kelly, F. P., & Williams, R. J. (2004). Fluid model for a network operating under a fair bandwidth-sharing policy. The Annals of Applied Probability, 14(3), 1055\u20131083.","DOI":"10.1214\/105051604000000224"},{"key":"86_CR17","first-page":"257","volume":"117","author":"T Konstantopoulos","year":"1996","unstructured":"Konstantopoulos, T., & Lin, S. J. (1996). Fractional Brownian approximations of stochastic networks. Stochastic Networks, Stability and Rare Events, Lecture Notes in Statistics, 117, 257\u2013274.","journal-title":"Stochastic Networks, Stability and Rare Events, Lecture Notes in Statistics"},{"issue":"1","key":"86_CR18","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/TNET.2013.2246869","volume":"22","author":"MG Markakis","year":"2014","unstructured":"Markakis, M. G., Modiano, E., & Tsitsiklis, J. N. (2014). Max-weight sheduling in queueing networks with heavy-tailed traffic. IEEE\/ACM Transactions on networking, 22(1), 257\u2013270.","journal-title":"IEEE\/ACM Transactions on networking"},{"key":"86_CR19","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1023\/A:1019138827659","volume":"15","author":"L Massouli\u00e9","year":"2000","unstructured":"Massouli\u00e9, L., & Roberts, J. (2000). Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems, 15, 185\u2013201.","journal-title":"Telecommunication Systems"},{"key":"86_CR20","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/90.879343","volume":"8","author":"J Mo","year":"2000","unstructured":"Mo, J., & Walrand, J. (2000). Fair end-to-end window-based congestion control. IEEE\/ACM Transactions on Networking, 8, 556\u2013567.","journal-title":"IEEE\/ACM Transactions on Networking"},{"key":"86_CR21","doi-asserted-by":"crossref","unstructured":"Perry, O., & Whitt, W. (2013). A fluid limit for an overloaded X model via a stochastic averaging principle. Mathematics of Operations Research, 38(2), 294\u2013349.","DOI":"10.1287\/moor.1120.0572"},{"key":"86_CR22","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s11134-013-9363-9","volume":"76","author":"O Perry","year":"2014","unstructured":"Perry, O., & Whitt, W. (2014). Diffusion approximation for an overloaded X model via a stochastic averaging principle. Queueing System, 76, 347\u2013401.","journal-title":"Queueing System"},{"key":"86_CR23","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1287\/moor.16.1.90","volume":"16","author":"WP Peterson","year":"1991","unstructured":"Peterson, W. P. (1991). Diffusion approximations for networks of queues with multiple customers types. Mathematics of Operations Research, 16, 90\u2013118.","journal-title":"Mathematics of Operations Research"},{"key":"86_CR24","first-page":"209","volume-title":"Proceedings of the international seminar on modeling and performance evaluation methodology, Lecture notes in control and information sciences","author":"MI Reiman","year":"1984","unstructured":"Reiman, M. I. (1984). Some diffusion approximations with state space collapse. In F. Baccelli & G. Fayolle (Eds.), Proceedings of the international seminar on modeling and performance evaluation methodology, Lecture notes in control and information sciences (pp. 209\u2013240). New York: Springer."},{"issue":"1","key":"86_CR25","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1214\/11-AAP759","volume":"22","author":"D Shah","year":"2012","unstructured":"Shah, D., & Wischik, D. (2012). Switched networks with maximum weight police: Fluid approximation and multiplicative state space collapse. The Annals of Applied Probability, 22(1), 70\u2013127.","journal-title":"The Annals of Applied Probability"},{"key":"86_CR26","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1145\/263876.263879","volume":"27","author":"MS Taqqu","year":"1997","unstructured":"Taqqu, M. S., Willinger, W., & Sherman, R. (1997). Proof of a fundamental result in self-similar traffic modeling. Computer Communication Review, 27, 5\u201323.","journal-title":"Computer Communication Review"},{"key":"86_CR27","doi-asserted-by":"crossref","first-page":"1936","DOI":"10.1109\/9.182479","volume":"37","author":"L Tassiulas","year":"1992","unstructured":"Tassiulas, L., & Ephremides, A. (1992). Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Transactions on Automatic Control, 37, 1936\u20131948.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"86_CR28","doi-asserted-by":"crossref","first-page":"74","DOI":"10.2307\/3211839","volume":"8","author":"W Whitt","year":"1971","unstructured":"Whitt, W. (1971). Weak convergence theorems for priority queues: Preemptive resume discipline. Journal of Applied Probability, 8, 74\u201394.","journal-title":"Journal of Applied Probability"},{"key":"86_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/b97479","volume-title":"Stochastic-process limits: An introduction to stochastic-process limits and their applications to queues. Springer series in operations research","author":"W Whitt","year":"2002","unstructured":"Whitt, W. (2002). Stochastic-process limits: An introduction to stochastic-process limits and their applications to queues. Springer series in operations research. New York: Springer."},{"key":"86_CR30","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1019108819713","volume":"30","author":"RJ Williams","year":"1998","unstructured":"Williams, R. J. (1998). Diffusion approximations for open multi-class queueing networks: Sufficient conditions involving state space collapse. Queueing Systems, 30, 27\u201388.","journal-title":"Queueing Systems"}],"container-title":["Telecommunication Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11235-015-0086-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11235-015-0086-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11235-015-0086-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,30]],"date-time":"2019-08-30T05:40:39Z","timestamp":1567143639000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11235-015-0086-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,10]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["86"],"URL":"https:\/\/doi.org\/10.1007\/s11235-015-0086-6","relation":{},"ISSN":["1018-4864","1572-9451"],"issn-type":[{"type":"print","value":"1018-4864"},{"type":"electronic","value":"1572-9451"}],"subject":[],"published":{"date-parts":[[2015,9,10]]}}}