Related papers: Constructing set-valued fundamental diagrams from …
We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic…
We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts,…
We review recent results and present new ones on a deterministic follow-the-leader particle approximation of first and second order models for traffic flow and pedestrian movements. We start by constructing the particle scheme for the first…
In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front…
We study traveling wave solutions of the Kerner--Konh\"auser PDE for traffic flow. By a standard change of variables, the problem is reduced to a dynamical system in the plane with three parameters. In a previous paper (Carrillo, F.A., J.…
In one-dimensional, heterogeneous systems, the whole traffic dynamics depend strongly on the behavior of the leading vehicle. This result holds for a class of vehicular traffic models satisfying the following properties. The interactions…
Efficient traffic monitoring is playing a fundamental role in successfully tackling congestion in transportation networks. Congestion is strongly correlated with two measurable characteristics, the demand and the network density that impact…
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 present a new family of second-order traffic flow models, extending the Aw-Rascle-Zhang (ARZ) model to incorporate nonlocal interactions. Our model includes a specific nonlocal Arrhenius-type look-ahead slowdown factor. We establish both…
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…
The Biham-Middleton-Levine (BML) traffic model, a cellular automaton with east-bound and north-bound cars moving by turns on a square lattice, has been an underpinning model in the study of collective behaviour by cars, pedestrians and even…
We present in this article an algebraic approach to model and simulate road traffic networks. By defining a set of road traffic systems and adequate concatenating operators in that set, we show that large regular road networks can be easily…
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…
Being widely adopted by the transportation and planning practitioners, the fundamental diagram (FD) is the primary tool used to relate the key macroscopic traffic variables of speed, flow, and density. We empirically analyze the relation…
In this paper, we propose a unified procedure for calibration of macroscopic second-order multilane traffic models. The focus is on calibrating the fundamental diagram using the combination stationary detector data and GPS traces. GPS…
This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…
The Nagel-Schreckenberg traffic flow model shows a transition from a free flow regime to a jammed regime for increasing car density. The measurement of the dynamical structure factor offers the chance to observe the evolution of jams…
In this paper we relate dynamics associated to zero-sum games (Fictitious play) to Hamiltonian dynamics. It turns out that the Hamiltonian dynamics which is induced from fictitious play, has properties which are rather different from those…
We construct a sequence of commuting central affine curve flows on $R^n\backslash 0$ invariant under the action of $SL(n,R)$ and prove the following results: (a) The central affine curvatures of a solution of the j-th central affine curve…
We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers'…