Related papers: From Microscopic to Macroscopic Traffic Models

The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random…

We study the application of a recently introduced hierarchical description of traffic flow control by driver-assist vehicles to include lane changing dynamics. Lane-dependent feedback control strategies are implemented at the level of…

Based on simulations with the ``intelligent driver model'', a microscopic traffic model, we explain the recently discovered transition from free over ``synchronized'' traffic to stop-and-go patterns [B. S. Kerner, Phys. Rev. Lett. 81, 3797…

In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are…

In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic on networks. These conditions are based on the consideration of the free space on the respective roads. The macroscopic limit of the kinetic…

We propose a microscopic traffic model where the update velocity is determined by the deceleration capacity and response time. It is found that there is a class of collisions that cannot be distinguished by simply comparing the stop…

The vehicular flow in the urban street canyon is considered. The classical field description is used in the modelling of the vehicular movement and of gaseous mixture in generic urban street canyon. The dynamical variables include vehicular…

The present paper proposes a stochastic model of the traffic flow. This model has a discrete set of states and the continuous time. The model is a generalization of the discrete stochastis model that has been considered in a previous paper…

In heavy traffic with congested roadway the maximum traffic flow also depends on length of cars. This is deduced in a simple derivation suited for classroom demonstration as well as homework. The resulting equation demonstrates a new…

We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…

We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time…

This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…

We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the…

From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized…

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas,…

We propose a macroscopic model in form of a dispersion-transport equation for non-congested flow of the athletes which is coupled to a kinematic-wave model for congested flow. The model takes into account the performance (i.e., free-flow…

Traditional DTA models of large cities suffer from prohibitive computation times and calibration/validation can become major challenges faced by practitioners. The empirical evidence in 2008 in support of the existence of a Macroscopic…

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…

We derive the pressure tensor and the heat flux to accompany the new macroscopic conservation equations that we developed previously in a volume-based kinetic framework for gas flows. This kinetic description allows for expansion or…

We consider traffic flow models at different scales of observation. Starting from the well known hierarchy between microscopic, kinetic and macroscopic scales, we will investigate the propagation of uncertainties through the models using…