Steady-state traffic flow on a ring road with up- and down- slopes

TL;DR

This paper analyzes steady-state traffic flow on a ring road with slopes using a semi-discrete model, revealing conditions for stability and the potential for stop-and-go waves, enhancing understanding of real inhomogeneous traffic dynamics.

Contribution

It introduces a method to determine unique steady-state solutions on a ring road with slopes and analyzes their stability using semi-discrete and continuum models.

Findings

Steady-state solutions are uniquely determined and stable under certain conditions.

Instability in equilibrium states can lead to stop-and-go traffic waves.

The model provides physically significant insights into inhomogeneous road traffic flow.

Abstract

This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely determined for a given total number of vehicles on the ring road. The solution is exact and always stable with respect to the first-order continuum model, whereas it is a good approximation with respect to the semi-discrete model provided that the involved equilibrium constant states are linearly stable. In an otherwise case, the instability of one or more equilibria could trigger stop-and-go waves propagating in certain road sections or throughout the ring road. The indicated results are reasonable and thus physically significant for a better understanding of real traffic flow on an inhomogeneous road.