A macroscopic traffic flow model that includes driver sensitivity to the number of free spaces ahead

Abstract

This paper addresses the first-order extension of the Lighthill–Whitham– Richards (LWR) macroscopic traffic flow model. Although previous studies have focused on the fluid aspect of traffic flow, none have addressed the sensitivity of drivers to the number of free spaces within a certain distance ahead of the subject driver. To incorporate driver behavior, we used the number of free spaces ahead of subject drivers and their sensitivity to the number of free spaces within a certain distance ahead. The resulting model is a convection-diffusion model. By computing Einstein's diffusion equation and comparing it with the diffusion coefficient in the extended model, a theoretical relation for the driver's sensitivity was derived. A representation of the numerical results of the LWR model, the convection-diffusion model with a typical diffusion coefficient, and the extended model showed that the proposed model has a lower mean relative error value.

Keywords:

• Traffic flow
• Burger equation
• convection-diffusion equation
• driver sensitivity

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ismael M. Pour  http://orcid.org/0000-0002-4497-2325