Piecewise linear car-following modeling

TL;DR

This paper introduces a piecewise linear car-following model that extends existing traffic models using a stochastic optimal control framework, enabling stability analysis and stationary regime computation.

Contribution

It develops a novel piecewise linear traffic model based on a variational formulation, connecting traffic dynamics with stochastic control theory.

Findings

Model characterizes stability of traffic flow.

Allows calculation of stationary traffic regimes.

Extends linear and min-plus traffic models.

Abstract

We present a traffic model that extends the linear car-following model as well as the min-plus traffic model (a model based on the min-plus algebra). A discrete-time car-dynamics describing the traffic on a 1-lane road without passing is interpreted as a dynamic programming equation of a stochastic optimal control problem of a Markov chain. This variational formulation permits to characterize the stability of the car-dynamics and to calculte the stationary regimes when they exist. The model is based on a piecewise linear approximation of the fundamental traffic diagram.