{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:33:30Z","timestamp":1787236410307,"version":"build-2736575974"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>We propose a new model in the analysis of car traffic flow phenomena which in particular refers to a bus route, namely, a closed path embedded in the urban network of roads. The model consists in a scalar balance law for the (macroscopic) density of cars, with source terms representing incoming and outgoing roads (with respect to the bus route), and a coupled system of ODEs describing the dynamics of (microscopic) buses along the route. The coupling takes into account both the buses as moving bottlenecks in the car flow and the effect of the car flow on the buses' ODEs as microscopic vehicles. The resulting fully coupled micro--macro model promises to give an appropriate description for the car flow as well as for the buses. Finally, we study the model numerically.<\/jats:p>","DOI":"10.1137\/130906350","type":"journal-article","created":{"date-parts":[[2013,9,19]],"date-time":"2013-09-19T11:34:55Z","timestamp":1379590495000},"page":"925-942","source":"Crossref","is-referenced-by-count":13,"title":["Vehicular Traffic Flow Dynamics on a Bus Route"],"prefix":"10.1137","volume":"11","author":[{"given":"Ingenuin","family":"Gasser","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Corrado","family":"Lattanzio","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amelio","family":"Maurizi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,9,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.51.1035"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2011.11.001"},{"key":"atypb3","unstructured":"G. Bretti, E. Cristiani, C. Lattanzio, A. Maurizi, and B. Piccoli,\n                      A Coupled PDE-ODE Tracking Algorithm for Moving Bottlenecks in Traffic Flow\n                      , preprint, CNR-IAC, Rome, Italy; Universita\u0300 degli Studi dell'Aquila, L'Aquila, Italy; Department of Mathematics, Rutgers University, New Brunswick, NJ, 2012."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/070697768"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2007.07.021"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1134"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"C. M. Dafermos,\n                      Hyperbolic Conservation Laws in Continuum Physics\n                      , 3rd ed., Grundlehren Math. Wiss. 325, Springer-Verlag, Berlin, 2010.","DOI":"10.1007\/978-3-642-04048-1_10"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2009.04.002"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2004.02.003"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2010.06.005"},{"key":"atypb11","unstructured":"N. Fisher,\n                      Ein verkehrsflussmodell fu\u0308r einen kreisverkehr\n                      , Master's thesis, University of Hamburg, Hamburg, Germany, 2008."},{"key":"atypb12","unstructured":"M. Garavello and B. Piccoli,\n                      Traffic Flow on Networks\n                      , AIMS Ser. Appl. Math. 1, AIMS, Springfield, MO, 2006."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.07.008"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2010.0118"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.26.3.223"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1287\/opre.9.4.545"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(02)00622-2"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.trc.2008.10.003"},{"key":"atypb19","unstructured":"C. Lattanzio, A. Maurizi, and B. Piccoli,\n                      Modeling and simulation of vehicular traffic flow with moving bottlenecks\n                      , in IMACS Series in Computational and Applied Mathematics 15, Elsevier, New York, 2010."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/090767224"},{"key":"atypb21","unstructured":"J. A. Laval and C. F. Daganzo,\n                      A hybrid model of traffic flow: Impacts of roadway geometry on capacity\n                      , in TRB 2003 Annual Meeting CD-ROM, Washington, DC, 2003."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2005.04.003"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.3141\/1644-08"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.3141\/1883-01"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1955.0089"},{"key":"atypb26","first-page":"2203","volume":"55","author":"Mahnke R.","year":"1997","journal-title":"Phys. Rev. E"},{"key":"atypb27","first-page":"441","author":"Mun\u0342oz J. C.","year":"2002","journal-title":"New York"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1016\/S0191-2615(98)00007-1"},{"key":"atypb29","unstructured":"I. Prigogine and R. Herman,\n                      Kinetic Theory of Vehicular Traffic\n                      , Elsevier, New York, 1971."},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1287\/opre.4.1.42"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/080731451"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130906350","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:24:41Z","timestamp":1787232281000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130906350"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1137\/130906350"],"URL":"https:\/\/doi.org\/10.1137\/130906350","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}