A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

TL;DR

This paper introduces a novel stochastic acceleration-based traffic flow model using a master equation approach, analyzing vehicle interactions and equilibrium velocity distributions to better understand traffic dynamics.

Contribution

It presents a new stochastic jump process model for vehicular acceleration and braking, derived from a Markovian framework, with analysis of equilibrium velocity distributions and fundamental diagrams.

Findings

Velocity distributions in equilibrium are characterized.

Car density affects mean velocity and scattering.

Fundamental diagrams are derived from the model.

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.