{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T04:14:32Z","timestamp":1680495272908},"reference-count":28,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[2014,5]]},"abstract":" Bandwidth-sharing networks as considered by Roberts and Massouli\u00e9 [28] (Roberts JW, Massouli\u00e9 L (1998) Bandwidth sharing and admission control for elastic traffic. Proc. ITC Specialist Seminar, Yokohama, Japan) provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers. Under mild assumptions, it has been established that a wide family of so-called \u03b1-fair bandwidth-sharing strategies achieve stability in such networks provided that no individual link is overloaded. <\/jats:p> In the present paper we focus on bandwidth-sharing networks where the load on one or several of the links exceeds the capacity. To characterize the overload behavior, we examine the fluid limit, which emerges when the flow dynamics are scaled in both space and time. We derive a functional equation characterizing the fluid limit, and show that any strictly positive solution must be unique, which in particular implies the convergence of the scaled number of flows to the fluid limit for nonzero initial states when the load is sufficiently high. For the case of a zero initial state and a zero-degree homogeneous rate allocation function, we show that there exists a linear solution to the fluid-limit equation, and obtain a fixed-point equation for the corresponding asymptotic growth rates. It is proved that a fixed-point solution is also a solution to a related strictly concave optimization problem, and hence exists and is unique. In addition, we establish uniqueness of fluid-model solutions for monotone rate-preserving networks (in particular tree networks). <\/jats:p>","DOI":"10.1287\/moor.2013.0618","type":"journal-article","created":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T05:30:11Z","timestamp":1380605411000},"page":"533-560","source":"Crossref","is-referenced-by-count":4,"title":["Fluid Limits for Bandwidth-Sharing Networks in Overload"],"prefix":"10.1287","volume":"39","author":[{"given":"Sem","family":"Borst","sequence":"first","affiliation":[{"name":"Alcatel-Lucent Bell Labs, Murray Hill, New Jersey 07974; and Centrum Wiskunde & Informatica, 1090 GB Amsterdam, The Netherlands; and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"}]},{"given":"Regina","family":"Egorova","sequence":"additional","affiliation":[{"name":"Centrum Wiskunde & Informatica, 1090 GB Amsterdam, The Netherlands; and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"}]},{"given":"Bert","family":"Zwart","sequence":"additional","affiliation":[{"name":"Centrum Wiskunde & Informatica, 1090 GB Amsterdam, The Netherlands; and VU University, Faculty of Sciences, 1081 HV Amsterdam, The Netherlands; and Georgia Institute of Technology, H. Milton Stewart School of Industrial and Systems Engineering, Atlanta, Georgia 30332"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1109\/INFCOM.2004.1356984"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01225324"},{"key":"B3","volume-title":"Nonlinear Programming: Theory and Algorithms","author":"Bazaraa MS","year":"1993"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1145\/378420.378438"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024094807532"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1023\/B:QUES.0000032802.41986.c6"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1145\/378420.378845"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1394-9"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005066"},{"key":"B11","volume-title":"Presentation at the 13th INFORMS Applied Probability Conf.","author":"Bramson M","year":"2005"},{"key":"B12","volume-title":"Proc. Allerton 2006 Conf.","author":"Chiang M","year":"2006"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1109\/INFCOM.1999.751468"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1109\/90.909020"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2007.06.024"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-011-0351-8"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1031863171"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1214\/074921708000000417"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1214\/08-AAP541"},{"key":"B20","volume-title":"Presentation at the 30th Conf. Math. Oper. Res.","author":"Jean-Marie A","year":"2005"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1007\/BF01158692"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1214\/105051604000000224"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1109\/9.106156"},{"key":"B24","doi-asserted-by":"publisher","DOI":"10.1214\/105051606000000907"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1109\/INFCOM.1999.752159"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.1109\/90.879343"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1050.0181"},{"key":"B28","volume-title":"Proc. ITC Specialist Seminar","author":"Roberts JW","year":"1998"}],"container-title":["Mathematics of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubsonline.informs.org\/doi\/pdf\/10.1287\/moor.2013.0618","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T19:48:51Z","timestamp":1680464931000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubsonline.informs.org\/doi\/10.1287\/moor.2013.0618"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["10.1287\/moor.2013.0618"],"URL":"https:\/\/doi.org\/10.1287\/moor.2013.0618","relation":{},"ISSN":["0364-765X","1526-5471"],"issn-type":[{"value":"0364-765X","type":"print"},{"value":"1526-5471","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5]]}}}