General phase transition models for vehicular traffic with point constraints on the flow

TL;DR

This paper extends a traffic flow phase transition model to include point constraints on flow, analyzing how traffic evolves between free and congested states with localized flow restrictions.

Contribution

It introduces a generalized phase transition model incorporating point flow constraints and studies the resulting Riemann problems for traffic evolution.

Findings

Model successfully captures traffic behavior with flow constraints.

Analysis of Riemann problems under point constraints.

Provides a framework for traffic management with localized restrictions.

Abstract

We generalize the phase transition model studied in [R. Colombo. Hyperbolic phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002], that describes the evolution of vehicular traffic along a one-lane road. Two different phases are taken into account, according to whether the traffic is low or heavy. The model is given by a scalar conservation law in the \emph{free-flow} phase and by a system of two conservation laws in the \emph{congested} phase. In particular, we study the resulting Riemann problems in the case a local point constraint on the flux of the solutions is enforced.