Related papers: A sharp critical threshold for a traffic flow mode…
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…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
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…
A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg-Landau energy…
We propose and study a one-dimensional $2\times 2$ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different…
Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models,…
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…
Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and…
This paper establishes a sharp, expanded wave-breaking criterion for a class of nonlinear nonlocal Whitham-type equations, significantly generalizing the classical threshold introduced by Seliger. While the system of inequalities governing…
We study deterministic discrete time exclusion type spatially heterogeneous particle processes in continuum. A typical example of this sort is a traffic flow model with obstacles: traffic lights, speed bumps, spatially varying local…
In this note, we propose a case study of freeway traffic flow modeled as a hybrid system. We describe two general classes of networks that model flow along a freeway with merging onramps. The admission rate of traffic flow from each onramp…
We provide a model to understand how adverse weather conditions modify traffic flow dynamic. We first prove that the microscopic Free Flow Speed of the vehicles is changed and then provide a rule to model this change. For this, we consider…
We present a preliminary study of a new phenomena associated with the Euler-Poisson equations -- the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…
Safety validation for Level 4 autonomous vehicles (AVs) is currently bottlenecked by the inability to scale the detection of rare, high-risk long-tail scenarios using traditional rule-based heuristics. We present Deep-Flow, an unsupervised…
The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…
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…
Our aim in this paper is to establish a theoretical fundamental diagram for a multi-class traffic flow from a gas-kinetic-like traffic model. We start with a multi-class generalization of the Prigogine-Herman-Boltzmann equation to construct…
Traffic prediction is a fundamental task in many real applications, which aims to predict the future traffic volume in any region of a city. In essence, traffic volume in a region is the aggregation of traffic flows from/to the region.…
Traffic control is at the core of research in transportation engineering because it is one of the best practices for reducing traffic congestion. It has been shown in recent years that the traffic control problem involving…