Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition

TL;DR

This paper investigates the stability of uniform flow in the optimal velocity model for traffic and granular flow under open boundary conditions, revealing stable regions, oscillatory solutions, and their relation to real traffic phenomena.

Contribution

It identifies conditions under which uniform flow remains stable or becomes oscillatory, providing new insights into flow stability and oscillations in traffic and granular systems.

Findings

Stable uniform flow exists even in linearly unstable regions.

Oscillatory solutions are present in unstable regions, with periods unrelated to car spacing.

Oscillatory behavior resembles synchronized traffic flow observed in real-world scenarios.

Abstract

We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter region where the uniform solution is stable against a localized perturbation. We also found an oscillatory solution in the linearly unstable region and its period is not commensurate with the periodicity of the car index space. The oscillatory solution has some features in common with the synchronized flow observed in real traffic.