An areal continuum model for mixed traffic

TL;DR

This paper introduces a new continuum traffic flow model that accounts for vehicle size heterogeneity in mixed traffic by using vehicle area conservation, providing a more accurate representation of mixed traffic dynamics.

Contribution

It develops an area-based continuum model with conserved variables and demonstrates its applicability through empirical data and a numerical scheme for mixed traffic.

Findings

The model's variables are conserved over time and space.

A bi-variate relationship among area-based variables is established.

The numerical scheme effectively replicates mixed traffic behaviors.

Abstract

A novel continuum model has been developed to address the vehicle size heterogeneity in mixed traffic. By incorporating the principle of vehicle area conservation, a new set of traffic flow variables centered on the concept of vehicle area has been introduced. These variables, namely areal flow and areal density, exhibit the remarkable characteristic of being conserved across time and space and seamlessly related to the traditional space mean speed. Next, the study successfully established a bi-variate relationship among these newly introduced area-based traffic variables based on empirical data from three locations for stream and mode-specific. It is shown that the conventional solution methods for the hyperbolic conservation laws remain applicable to the proposed continuum model. Finally, a multi-class cell transmission model numerical scheme is developed and used to illustrate the performance of the proposed model in replicating the seepage and platoon dispersion behavior in mixed traffic conditions.