Traffic Flow Models with Noise

Driver behavior differs among drivers and over time, and this variability is not typically captured by macroscopic PDE models. Three models accounting for these effects are proposed. The first are equilibrium and non-equilibrium models augmented by a stochastic behavior equation. These models make use of a fundamental diagram \( V(\rho , z) \) that depends on both traffic density and on the behavior parameter \( z \) . In addition, a non-equilibrium model is proposed, in which the noise is introduced directly into the velocity field. The resulting stochastic models adhere to accepted principles for traffic modeling and are capable of reproducing a richer set of traffic flow phenomena. Most notably, they illustrate that small perturbations may grow into large coherent wave structures including the formation of jams and emergence of stop-and-go flow patterns.