Vehicular Traffic Flow Model Research Articles

A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

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.

Numerical Investigation of a Mesoscopic Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

In this paper, a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a modified direct simulation Monte Carlo method (DSMC) well known in nonequilibrium gas kinetic. The velocity and acceleration distribution functions in stochastic equilibrium, mean velocity, traffic density, accelerated noise (ACN), velocity scattering and correlations between some of these variables and their car density dependences are discussed.

The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model

In this paper a direct simulation Monte Carlo (DSMC) method is applied to a spatial homogeneous mesoscopic vehicular traffic flow model, based on a Boltzmann-like master equation. In contrast to gas kinetics, where in a collision a velocity jump change occurs, the interaction now changes the acceleration value of the following car in a leading car pair. There are no conservation laws in a single interaction. Therefore the Bird simulation scheme seems not to be the right choice for the approximation of the interaction integral. It is shown that a Nanbu like scheme is natural for this process. To avoid the typical double loop computational effort of the Nanbu scheme, a sampling algorithm developed by Babovsky is applied. Several car interaction profiles are examined and their resulting stochastic equilibrium solutions are discussed. First, simple interaction profiles are used to compare the simulation results with analytic calculated velocity distributions showing excellent agreement. Second, a realistic distance threshold interaction profile is applied to the simulation and the results are shown to be in qualitative agreement with measured traffic flow data. The simulation procedure seems to be applicable to study the influence of different interaction profiles to the macroscopic vehicular traffic flow quantities in stochastic equilibrium.

Boundary value steady solutions of a class of hydrodynamic models for vehicular traffic flow

This paper deals with the solution of a boundary value problem related to a steady nonuniform description of a class of traffic flow models. The models are obtained by the closure of the mass conservation equation with a phenomenological relation linking the local mass velocity to the local density. The analysis is addressed to define the proper framework toward the identification of the parameter characterizing the model. The last part of the paper develops a critical analysis also addressed to the design of new traffic flow models.

Formal Asymptotic Models of Vehicular Traffic. Model Closures

Formal closed models for vehicular traffic flow are obtained based on the novel equilibrium solution of the Prigogine--Herman equation. To that effect, Hilbert and Chapman--Enskog asymptotic series expansions are employed, obtaining the Euler and Navier--Stokes equivalent equations for traffic flow.

A numeric investigation of a vehicular traffic flow model based on a stochastic acceleration process

In this paper a new acceleration oriented mesoscopic vehicular traffic flow model based on a Boltzmann equation ansatz together with its numerical solving method is discussed. A direct simulation Monte Carlo method is adopted from gas dynamics to solve the model equation for a spatial homogeneous traffic flow and different driver interaction profiles. For a simple academic interaction case the numerical solution is found to be in very good agreement with the analytical calculated result. For a more applied interaction profile the numerical results are in good qualitative conformance to measurements or other traffic flow theories.

Driver memory, traffic viscosity and a viscous vehicular traffic flow model

This paper studies the linkage between microscopic car-following and macroscopic fluid-like behavior of traffic flow. We find that driver memory in car-following leads to viscous effects in continuum traffic flow dynamics. This linkage is further exploited to develop a second-order continuum model with viscosity. Further, we show that this viscous model contains practically every well-known continuum model as a special case (e.g., the Lighthill–Whitham–Richards model and the Payne–Whitham model), has a stable wave structure of first- and second-order waves, and controls the extent of non-anisotropic and diffusive influences through a dimensionless parameter called anisotropic factor.