Mathematical Models of Traffic Flow at a Signalized Intersection
Analysis of PDEs
2026-04-29 v1
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.
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Cite
@article{arxiv.2604.25484,
title = {Mathematical Models of Traffic Flow at a Signalized Intersection},
author = {Akbota Senkebayeva},
journal= {arXiv preprint arXiv:2604.25484},
year = {2026}
}
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4 pages