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Constructing setvalued fundamental diagrams from jamiton solutions in second order traffic models
 Netw. Heterog. Media
"... Abstract. Fundamental diagrams of vehicular traffic flow are generally multivalued in the congested flow regime. We show that such setvalued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic models, such as the classical PayneWhitham model or the ..."
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Abstract. Fundamental diagrams of vehicular traffic flow are generally multivalued in the congested flow regime. We show that such setvalued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic models, such as the classical PayneWhitham model or the inhomogeneous AwRascleZhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multivalued parts in the fundamental diagram correspond precisely to jamitondominated solutions. This study shows that transitions from functionvalued to setvalued parts in a fundamental diagram arise naturally in wellknown second order models. As a particular consequence, these models intrinsically reproduce traffic phases. 1.
A comparison of datafitted first order traffic models and their second order generalizations via trajectory and sensor data
 93RD ANNUAL MEETING OF TRANSPORTATION RESEARCH BOARD, WASHINGTON DC, 2013. PAPER NUMBER 13–4853
, 2013
"... The AwRascleZhang (ARZ) model can be interpreted as a generalization of the first order LighthillWhithamRichards (LWR) model, possessing a family of fundamental diagram curves, rather than a single one. We investigate to which extent this generalization increases the predictive accuracy of the m ..."
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The AwRascleZhang (ARZ) model can be interpreted as a generalization of the first order LighthillWhithamRichards (LWR) model, possessing a family of fundamental diagram curves, rather than a single one. We investigate to which extent this generalization increases the predictive accuracy of the models. To that end, a systematic comparison of two types of datafitted LWR models and their second order ARZ counterparts is conducted, via a version of the threedetector problem test. The parameter functions of the models are constructed using historic fundamental diagram data. The model comparisons are then carried out using timedependent data, of two very different types: vehicle trajectory data, and singleloop sensor data. The study of these PDE models is carried out in a macroscopic sense, i.e., continuous field quantities are constructed from the discrete data, and discretization effects are kept negligibly small.
A variational formulation for higher order macroscopic traffic flow models: numerical investigation
, 2013
"... This paper deals with numerical methods providing semianalytic solutions to a wide classofmacroscopictrafficflow modelsfor piecewiseaffine initial andboundaryconditions. In a very recent paper, a variational principle has been proved for models of the Generic Second Order Modeling (GSOM) family, yi ..."
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This paper deals with numerical methods providing semianalytic solutions to a wide classofmacroscopictrafficflow modelsfor piecewiseaffine initial andboundaryconditions. In a very recent paper, a variational principle has been proved for models of the Generic Second Order Modeling (GSOM) family, yielding an adequate framework for effective numerical methods. Any model of the GSOM family can be recast into its Lagrangian form as a HamiltonJacobi equation (HJ) for which the solution is interpreted as the position of vehicles. This solution can be computed thanks to LaxHopf like formulas and a generalization of the infmorphism property. The efficiency of this computational method is illustrated through a numerical example and finally a discussion about future developments is provided.
Effect of the choice of stagnation density in datafitted first and secondorder traffic models
, 2013
"... Abstract. For a class of datafitted macroscopic traffic models, the influence of the choice of the stagnation density on the model accuracy is investigated. This work builds on an established framework of datafitted firstorder LighthillWhithamRichards (LWR) models and their secondorder AwRasc ..."
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Abstract. For a class of datafitted macroscopic traffic models, the influence of the choice of the stagnation density on the model accuracy is investigated. This work builds on an established framework of datafitted firstorder LighthillWhithamRichards (LWR) models and their secondorder AwRascleZhang (ARZ) generalizations. These models are systematically fitted to historic fundamental diagram data, and then their predictive accuracy is quantified via a version of the threedetector problem test, considering vehicle trajectory data and singleloop sensor data. The key outcome of this study is that with commonly suggested stagnation densities of 120 vehicles/km/lane and above, information travels backwards too slowly. It is then demonstrated that the reduction of the stagnation density to 90–100 vehicles/km/lane addresses this problem and results in a significant improvement of the predictive accuracy of the considered models. 1.