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.