Efficient parameter estimation in a macroscopic traffic flow model by discrete mollification

Abstract

Our concern is the numerical identification of traffic flow parameters in a macroscopic one-dimensional model whose governing equation is strongly degenerate parabolic. The unknown parameters determine the flux and the diffusion terms. The parameters are estimated by repeatedly solving the corresponding direct problem under variation of the parameter values, starting from an initial guess, with the aim of minimizing the distance between a time-dependent observation and the corresponding numerical solution. The direct problem is solved by a modification of a well-known monotone finite difference scheme obtained by discretizing the nonlinear diffusive term by a formula that involves a discrete mollification operator. The mollified scheme occupies a larger stencil but converges under a less restrictive Courant-Friedrichs-Lewy (CFL) condition, which allows one to employ a larger time step. The ability of the proposed procedure for the identification of traffic flow parameters is illustrated by a numerical experiment.

Keywords:

• traffic flow
• inverse problem
• degenerate parabolic equation
• parameter estimation
• discrete mollification

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

CDA and CEM acknowledge support by Universidad Nacional de Colombia through the project Mathematics and Computation, Hermes code 20305. RB acknowledges support by Conicyt Anillo project ACT 1118 (ANANUM), Fondecyt project 1130154, BASAL project CMM at Universidad de Chile, and Centro de Investigación en Ingeniería Matemática (CI²MA), Universidad de Concepción and Red Doctoral REDOC.CTA, project UCO 1202 at U. de Concepción.