{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T14:51:29Z","timestamp":1786978289743,"version":"3.56.0"},"reference-count":20,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":8075,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1984,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>New characterizations of optimal state\u2010dependent routing strategies are obtained for the continuous traffic network model proposed by Segall for linear cost with unity weighting at each node and for constant inputs. The concept of flow relaxation is introduced and is used t o transform the optimal routing problem into an initial flow optimization problem with convex cost and linear constraints. Three algorithms are given for open\u2010loop computation of the optimal initial flow. The first is a simple iterative algorithm based on gradient descent with bending and it is well suited for decentralized computation. The second algorithm reduces the problem t o a series of max\u2010flow problems and it computes the exact optimal initial flow in O(lN14) compu\u2010 tations, where IN1 is the number of nodes in the network. The third algorithm is based on a search for successive bottlenecks in the network.<\/jats:p>","DOI":"10.1002\/net.3230140308","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T14:47:29Z","timestamp":1178894849000},"page":"457-487","source":"Crossref","is-referenced-by-count":60,"title":["Optimal dynamic routing in communication networks with continuous traffic"],"prefix":"10.1002","volume":"14","author":[{"given":"Bruce","family":"Hajek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard G.","family":"Ogier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.7.4.501"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0320018"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400875184"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1964-11178-2"},{"key":"e_1_2_1_6_2","article-title":"An optimal control approach to dynamic routing in communication networks, Part II: A maximal flow approach","author":"Jodorkovsky M.","journal-title":"IEEE Trans. Automatic Control."},{"key":"e_1_2_1_7_2","series-title":"EE Publ. 358","volume-title":"A maximal flow approach to dynamic routing in communication networks","author":"Jodorkovsky M.","year":"1979"},{"key":"e_1_2_1_8_2","volume-title":"An Introduction to Applied Optimal Control","author":"Knowles G.","year":"1981"},{"key":"e_1_2_1_9_2","volume-title":"Introduction to Linear and Nonlinear Programming","author":"Luenberger D. G.","year":"1973"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(78)90016-9"},{"key":"e_1_2_1_11_2","first-page":"315","article-title":"Anti\u2010zig\u2010zagging by bending","volume":"15","author":"McCormick G. P.","year":"1969","journal-title":"Management Sci. (Theory)"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"F. H.Moss The application of optimal control theory to dynamic routing in communication networks. Ph.D. Thesis Massachusetts Institute of Technology (Elect. Syst. Lab. Rept. ESL\u2010R\u2010721) (1977).","DOI":"10.21236\/ADA041241"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1982.1102915"},{"key":"e_1_2_1_14_2","series-title":"EE Publs. 312 and 319","volume-title":"An optimal control approach to dynamic routing in data communication networks","author":"Moss F. H.","year":"1977"},{"key":"e_1_2_1_15_2","first-page":"565","volume-title":"Proceedings, 1983 Conference on Information Sciences and Systems","author":"Ogier R. G.","year":"1983"},{"key":"e_1_2_1_16_2","volume-title":"Combinatorial Optimization\u2010Algorithms and Complexity","author":"Papadimitriou C. H.","year":"1982"},{"key":"e_1_2_1_17_2","volume-title":"Real and Complex Analysis","author":"Rudin W.","year":"1974"},{"key":"e_1_2_1_18_2","volume-title":"Functional Analysis","author":"Rudin W.","year":"1973"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1977.1093715"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1979.1094274"},{"key":"e_1_2_1_21_2","unstructured":"S.ShatsandA.Segall Open\u2010loop solutions for the dynamic routing problem. Report LIDS\u2010R\u2010922 Laboratory for Information and Decision Systems Massachusetts Institute of Technology (1980)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230140308","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230140308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T16:57:22Z","timestamp":1697734642000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230140308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,9]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1984,9]]}},"alternative-id":["10.1002\/net.3230140308"],"URL":"https:\/\/doi.org\/10.1002\/net.3230140308","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,9]]}}}