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The two problems are formulated, and we discuss the mutual equivalence between the problems, the existence and uniqueness of solutions, and the relation between the formulations with path and link flow patterns. We show that a link-traffic loop-free property holds within each class for both individually and overall optimal routing for a wide range of networks, and we show the condition that characterizes the category of networks for which the property holds.<\/jats:p>","DOI":"10.1155\/2011\/645954","type":"journal-article","created":{"date-parts":[[2011,7,6]],"date-time":"2011-07-06T17:40:51Z","timestamp":1309974051000},"page":"1-21","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Routing for Multiclass Networks"],"prefix":"10.1155","volume":"2011","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1912-6709","authenticated-orcid":true,"given":"Hisao","family":"Kameda","sequence":"first","affiliation":[{"name":"Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba Science City, Ibaraki 305-8573, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Li","sequence":"additional","affiliation":[{"name":"Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba Science City, Ibaraki 305-8573, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eitan","family":"Altman","sequence":"additional","affiliation":[{"name":"INRIA, BP93, 06902 Sophia Antipolis Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1994","key":"18"},{"key":"22","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1680\/ipeds.1952.11259","volume":"1","year":"1952","journal-title":"Proceedings of the Institution of Civil Engineers"},{"year":"1992","key":"2"},{"key":"7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1002\/net.3230030202","volume":"3","year":"1973","journal-title":"Networks"},{"issue":"1","key":"8","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1109\/TCOM.1977.1093711","volume":"25","year":"1977","journal-title":"IEEE Transactions on Communications"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/0-8176-4429-6_20"},{"issue":"2","key":"3","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1109\/90.588114","volume":"5","year":"1997","journal-title":"IEEE\/ACM Transactions on Networking"},{"issue":"5","key":"17","first-page":"614","volume":"1","year":"1993","journal-title":"IEEE\/ACM Transactions on Networking"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2005.05.009"},{"issue":"4","key":"4","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1287\/trsc.5.4.366","volume":"5","year":"1971","journal-title":"Transportation Science"},{"key":"5","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1287\/trsc.6.1.73","volume":"6","year":"1972","journal-title":"Transportation Science"},{"issue":"2","key":"6","first-page":"91","volume":"73b","year":"1969","journal-title":"Journal of Research of the National Bureau of Standards"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1109\/9.880619"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1145\/567112.567113"},{"year":"1991","key":"16"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1006\/game.1996.0044"},{"year":"1970","key":"19"},{"year":"1971","key":"10"},{"volume":"102","year":"1986","key":"11"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/12.660168"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1145\/3149.3156"}],"container-title":["Advances in Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/645954.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/645954.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/645954.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,19]],"date-time":"2017-06-19T22:53:23Z","timestamp":1497912803000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aor\/2011\/645954\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":21,"alternative-id":["645954","645954"],"URL":"https:\/\/doi.org\/10.1155\/2011\/645954","relation":{},"ISSN":["1687-9147","1687-9155"],"issn-type":[{"type":"print","value":"1687-9147"},{"type":"electronic","value":"1687-9155"}],"subject":[],"published":{"date-parts":[[2011]]}}}