Piecewise linear car-following modeling
For traffic flow researchers, this provides a new theoretical framework for analyzing car-following stability, but the results are incremental as they build on existing models.
The paper extends linear and min-plus car-following models by interpreting discrete-time car dynamics as a stochastic optimal control problem, enabling stability characterization and stationary regime calculation. The model uses a piecewise linear approximation of the fundamental traffic diagram.
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.