Related papers: Microcanonical and canonical approach to traffic f…
The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of…
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…
Drivers' heterogeneity and the broad range of vehicle characteristics on public roads are primarily responsible for the stochasticity observed in road traffic dynamics. Understanding the behavioural differences in drivers (human or…
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is…
We investigate a traffic model in which cars either move freely with quenched intrinsic velocities or belong to clusters formed behind slower cars. In each cluster, the next-to-leading car is allowed to pass and resume free motion. The…
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…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
Motivated by an analogy with traffic, we simulate two species of particles (`vehicles'), moving stochastically in opposite directions on a two-lane ring road. Each species prefers one lane over the other, controlled by a parameter $0 \leq b…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by…
We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence we have an…
The path integral over Euclidean geometries for the recently suggested density matrix of the Universe is shown to describe a microcanonical ensemble in quantum cosmology. This ensemble corresponds to a uniform (weight one) distribution in…
A two-lane extension of a recently proposed cellular automaton model for traffic flow is discussed. The analysis focuses on the reproduction of the lane usage inversion and the density dependence of the number of lane changes. It is shown…
This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at…
We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flow. We apply this mechanism to several car-following models and…
We study a family of deterministic models for highway traffic flow which generalize cellular automaton rule 184. This family is parametrized by the speed limit $m$ and another parameter $k$ that represents a ``degree of aggressiveness'' in…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…
This paper firstly show that a recent model (Tian et al., Transpn. Res. B 71, 138-157, 2015) is not able to well replicate the evolution concavity in traffic flow, i.e. the standard deviation of vehicles increases in a concave/linear way…
The macroscopic fundamental diagram (MFD) is a large scale description of the traffic in a urban area and relates the average car flow to the average car density. This MFD has been observed empirically in several cities but how its…