Related papers: Linearized Theory of Traffic Flow
This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…
This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…
To gain essential understandings of traffic flow, four theorems are derived to establish the kinematics of the basic unit of traffic flow, namely two consecutive vehicles. The first is to determine the two critical distances of the vehicle…
In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental…
Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal…
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…
The scientific field of traffic engineering encompasses a rich set of mathematical techniques, as well as researchers with entirely different backgrounds. This paper provides an overview of what is currently the state-of-the-art with…
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…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity…
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…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers,…
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…
We describe traffic flows in one lane roadways using kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the…
By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…
We present a macroscopic traffic flow model that extends existing fluid-like models by an additional term containing the second derivative of the safe velocity. Two qualitatively different shapes of the safe velocity are explored: a…
We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…