Piecewise linear car-following modeling

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 determine the stationary regimes when they exist. The model is based on a piecewise linear approximation of the fundamental traffic diagram.

Highlight
► Discrete-time microscopic traffic model on a 1-lane road without passing.
► The model extends the linear car-following and the min-plus models.
► We present a variational formulation of the car-dynamics.
► The traffic stability and the stationary regimes are characterized.