Macroscopic traffic models from microscopic car-following models

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of a conservation equation and a momentum equation, and the latter contains a relaxation term, an anticipation term, and a diffusion term. Properties of the resulting macroscopic model are compared with those of the optimal velocity model through numerical simulations, and reasonable agreement is found although there are deviations in the quantitative level. The derivation is also extended to general car-following models.Comment: 12 pages, 4 figures; to appear in Phys. Rev.

Solitons and kinks in a general car-following model

We study a car-following model of traffic flow which assumes only that a car's acceleration depends on its own speed, the headway ahead of it, and the rate of change of headway, with only minimal assumptions about the functional form of that dependence. The velocity of uniform steady flow is found implicitly from the acceleration function, and its linear stability criterion can be expressed simply in terms of it. Crucially, unlike in previously analyzed car-following models, the threshold of absolute stability does not generally coincide with an inflection point in the steady velocity function. The Burgers and KdV equations can be derived under the usual assumptions, but the mKdV equation arises only when absolute stability does coincide with an inflection point. Otherwise, the KdV equation applies near absolute stability, while near the inflection point one obtains the mKdV equation plus an extra, quadratic term. Corrections to the KdV equation "select" a single member of the one-parameter set of soliton solutions. In previous models this has always marked the threshold of a finite- amplitude instability of steady flow, but here it can alternatively be a stable, small-amplitude jam. That is, there can be a forward bifurcation from steady flow. The new, augmented mKdV equation which holds near an inflection point admits a continuous family of kink solutions, like the mKdV equation, and we derive the selection criterion arising from the corrections to this equation.Comment: 25 page

An extended car following approach using agent based model on evacuation system of micro traffic

We proposed an extended car-following approach on evacuation system of micro traffic. It is based on the agent model. Parameter which is owned by the agent is the velocity. We added one driving behavior in the car-following a smart driver. Characteristics of smart driver he has a concern for the distance between his vehicle with the vehicle in front of him so that he will change the speed based on aforementioned conditions. Smart driver is determined randomly, and he can become an agent. In the simulation, we observed the evacuation time toward the smart driver and the mean speed respectively based on the number of agents. Keyword: car-following, micro traffic, smart driver, agent based model, evacuation tim