Related papers: A sharp critical threshold for a traffic flow mode…
We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold conditions that distinguish the initial data into a trichotomy:…
In this work, we study a Lighthill-Whitham-Richard (LWR) type traffic flow model with a non-local flux. We identify a threshold condition for shock formation for traffic flow models with Arrhenius look-ahead-behind (i.e., nudging) dynamics…
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…
Motivated by the traffic flow model with Arrhenius look-ahead relaxation dynamics introduced in [A. Sopasakis and M.A. Katsoulakis, SIAM J. Appl. Math., 66 (2006), p. 921--944], this paper proposes a traffic flow model with look ahead…
We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters.…
Dynamic arrest is a general phenomenon across a wide range of dynamic systems, but the universality of dynamic arrest phenomena remains unclear. We relate the emergence of traffic jams in a simple traffic flow model to the dynamic slow down…
This paper presents a new class of one-dimensional (1D) traffic models with look-ahead rules that take into account of two effects: nonlocal slow-down effect and right-skewed non-concave asymmetry in the fundamental diagram. The proposed 1D…
We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars…
The macroscopic traffic flow model is widely used for traffic control and management. To incorporate drivers' anticipative behaviors and to remove impractical speed discontinuity inherent in the classic Lighthill-Whitham-Richards (LWR)…
We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model…
We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit for all ranges of traffic data. Moreover, the…
In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called…
We consider a quasilinear system of hyperbolic equations that describes plane one-dimensional non-relativistic oscillations of electrons in a cold plasma with allowance for electron-ion collisions. Accounting for collisions leads to the…
The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…
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 present a traffic flow model consisting of a gluing between the Lighthill-Whitham and Richards macroscopic model with a first order microscopic follow the leader model. The basic analytical properties of this model are investigated.…
We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a finite speed and the model involves a space-time nonlocal…
A simple model of the driven motion of interacting particles in a two dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state…
We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…
This paper examines the optimal velocity follow-the-leader dynamics, a microscopic traffic model, and explores different aspects of the dynamical model, with particular emphasis on collision analysis. More precisely, we present a rigorous…