A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

Abstract

A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity, and acceleration with an additional vehicular chaos assumption and is derived via a Markovian ansatz for car pairs. This equation is analyzed using simple driver interaction models in the spatial homogeneous case. Velocity distributions in stochastic equilibrium, together with the car density dependence of their moments, i.e., mean velocity and scattering and the fundamental diagram are presented.

Keywords:

• Vehicular traffic flow model
• Kinetic modeling
• Direct simulation Monte Carlo method
• Action point interaction profile