Search results for "Scalar conservation law"

showing 2 items of 2 documents

Representation of capacity drop at a road merge via point constraints in a first order traffic model

2018

We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by c…

Mathematical optimizationTraffic model010103 numerical & computational mathematics01 natural sciencesScalar conservation law; LWR model; traffic flow on networks; point constraint on the flux; finite volumes schemesNOfinite volumes schemes[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]point constraint on the flux0101 mathematics[MATH]Mathematics [math]Scalar conservation lawMathematicsLWR modelNumerical AnalysisApplied MathematicsFirst order010101 applied mathematicsFinite volumes schemes; LWR model; Point constraint on the flux; Scalar conservation law; Traffic flow on networksComputational MathematicsModeling and Simulationtraffic flow on networksOutflowfinite volumes schemeMerge (version control)Analysis
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Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux

2016

We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exits in the context of pedestrians traffic and reduction of lanes on a road under construction in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (" panic ") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence …

Crowd dynamicsMathematical optimizationFixed point argumentsDiscretizationGeneral MathematicsScalar (mathematics)Crowd dynamics; Finite volume approximation; Nonlocal point constraint; Scalar conservation law; Vehicular traffics; Well-posedness; Mathematics (all); Applied Mathematics01 natural sciencesMSC : 35L65 90B20 65M12 76M12NONonlocal point constraintCrowdsData acquisitionMathematics (all)[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]DoorsUniqueness[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsScalar conservation lawMathematicsConservation lawVehicular trafficsFinite volume methodApplied Mathematics010102 general mathematics[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]010101 applied mathematicsWell-posednessFinite volume schemeFinite volume approximationConvergence of approximations[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]Journal de Mathématiques Pures et Appliquées
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