A Characteristic Particle Method for Traffic Flow Simulations on Highway Networks
A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method particleclaw, which solves scalar one dimensional hyperbolic conservation laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.
KeywordsParticle Characteristic Particleclaw Shock Traffic flow Network
Y. Farjoun was partially financed by the Spanish Ministry of Science and Innovation under grant FIS2008-04921-C02-01. The authors would like to acknowledge support by the National Science Foundation. B. Seibold was supported through grant DMS–1007899. In addition, B. Seibold wishes to acknowledge partial support by the National Science Foundation through grants DMS–0813648 and DMS–1115278. Y. Farjoun wishes to acknowledge partial support through grant DMS–0703937. In addition, Farjoun thanks Luis Bonilla at the UC3M and Rodolfo R. Rosales at MIT for providing a framework under which this work was done.
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