Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
effective flow rate
Permanent link to this recordhttp://hdl.handle.net/20.500.12613/5944
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AbstractFundamental diagrams of vehicular traiic ow are generally multivalued in the congested ow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traiic models, such as the classical Payne-Whitham model or the inhomogeneous Aw-Rascle-Zhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multi-valued parts in the fundamental diagram correspond precisely to jamiton-dominated solutions. This study shows that transitions from function-valued to set-valued parts in a fundamental diagram arise naturally in well-known second order models. As a particular consequence, these models intrinsically reproduce traiic phases. © American Institute of Mathematical Sciences.
Citation to related workAmerican Institute of Mathematical Sciences (AIMS)
Has partNetworks and Heterogeneous Media
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