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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…
This paper develops output feedback boundary control to mitigate traffic congestion of a unidirectional two-lane freeway segment. The macroscopic traffic dynamics are described by the Aw-Rascle-Zhang (ARZ) model respectively for both the…
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…
We generalize the phase transition model studied in [R. Colombo. Hyperbolic phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002], that describes the evolution of vehicular traffic along a one-lane road. Two…
Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…
Stop-and-go waves in road traffic are complex collective phenomena with significant implications for traffic engineering, safety and the environment. Despite decades of research, understanding and controlling these dynamics remains…
Traffic breakdown, as one of the most puzzling traffic flow phenomena, is characterized by sharply decreasing speed, abruptly increasing density and in particular suddenly plummeting capacity. In order to clarify its root mechanisms and…
Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…
Traffic congestion, a daily frustration for millions and a multi-billion dollar drain on economies, has long resisted deep physical understanding. While simple theoretical models of traffic flow have suggested connections to critical…
Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds…
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…
Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a…
In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…
We numerically elucidate the microscopic mechanisms controlling the relaxation dynamics of a three-dimensional lattice glass model that has static properties compatible with the approach to a random first-order transition. At low…
A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver's perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density relation of this…
For a class of data-fitted macroscopic traffic models, the influence of the choice of the stagnation density on the model accuracy is investigated. This work builds on an established framework of data-fitted first-order…
We develop a control design for stabilization of traffic flow in congested regime, based on an Aw-Rascle-Zhang-type (ARZ-type) Partial Differential Equation (PDE) model, for traffic consisting of both ACC-equipped (Adaptive Cruise…
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 study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some…
This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across…