Piecewise linear car-following modeling

Details Piecewise linear car-following modeling Piecewise linear car-following modeling

2011-07-29

arxiv.org/abs/1107.5869v2

Mathematics

Optimization and Control

19 pages, 3 figures

Scientific paper

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.

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