In the context of road traffic modeling we consider a scalar hyperbolic conservation law with the flux (fundamental diagram) which is discontinuous at x=0, featuring variable velocity limitation. The flow maximization criterion for selection of a unique admissible weak solution is generally admitted in the literature, however justification for its use can be traced back to the irrelevant vanishing viscosity approximation. We seek to assess the use of this criterion on the basis of modeling proper to the traffic context. We start from a first order microscopic follow-the-leader (FTL) model deduced from basic interaction rules between cars. We run numerical simulations of FTL model with large number of agents on truncated Riemann data, and observe convergence to the flow-maximizing Riemann solver. As an obstacle towards rigorous convergence analysis, we point out the lack of order-preservation of the FTL semigroup.

Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic

Rosini M. D.
Ultimo
2020

Abstract

In the context of road traffic modeling we consider a scalar hyperbolic conservation law with the flux (fundamental diagram) which is discontinuous at x=0, featuring variable velocity limitation. The flow maximization criterion for selection of a unique admissible weak solution is generally admitted in the literature, however justification for its use can be traced back to the irrelevant vanishing viscosity approximation. We seek to assess the use of this criterion on the basis of modeling proper to the traffic context. We start from a first order microscopic follow-the-leader (FTL) model deduced from basic interaction rules between cars. We run numerical simulations of FTL model with large number of agents on truncated Riemann data, and observe convergence to the flow-maximizing Riemann solver. As an obstacle towards rigorous convergence analysis, we point out the lack of order-preservation of the FTL semigroup.
2020
978-3-030-46078-5
978-3-030-46079-2
Conservation laws, Discontinuous flux, First order follow-the-leader model, Follow-the-leader semigroup, Order-preservation, Point constraint on the flux, Riemann solvers, Traffic flow
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2427495
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