Mathematical Models of Traffic Flow at a Signalized Intersection

TL;DR

This paper develops two mathematical models for traffic flow at signalized intersections, capturing different traffic light states through hyperbolic and parabolic systems.

Contribution

It introduces novel first-order hyperbolic and mixed hyperbolic-parabolic models for traffic flow at intersections under different signal conditions.

Findings

Flow density and velocity are derived from initial-boundary value problems.

Models differentiate between permissive and prohibitive traffic light states.

Provides a mathematical framework for analyzing traffic dynamics at intersections.

Abstract

This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by solving an initial-boundary value problem for a first-order hyperbolic system. When the signal is prohibitive, the same quantities are governed by a mixed system comprising a second-order parabolic equation for the velocity and a first-order equation for the density.