Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models
Benjamin Seibold - Temple University, Department of Mathematics, 1805 North Broad Street Philadelphia, PA 19122, United States (email)
Abstract: Fundamental diagrams of vehicular traffic flow are generally multi-valued in the congested flow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic 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 traffic phases.
Keywords: Second order, traffic model, Payne-Whitham, Aw-Rascle-Zhang, jamiton, traveling wave, fundamental diagram, sensor data, effective flow rate.
Received: April 2012; Revised: June 2013; Available Online: October 2013.
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