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A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity…
In this paper we present a theoretical analysis of a recently proposed two-dimensional Cellular Automata model for traffic flow in cities with the novel ingredient of turning capability. Numerical simulations of this model show that there…
Many models account for the traffic flow of road users but few take the details of local interactions into consideration and how they could deteriorate into safety-critical situations. Building on the concept of sensorimotor control, we…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
We introduce a traffic flow model that incorporates clustering and passing. We obtain analytically the steady state characteristics of the flow from a Boltzmann-like equation. A single dimensionless parameter, R=c_0v_0t_0 with c_0 the…
We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…
Leveraging the accuracy and consistency of vehicle motion control enabled by the connected and automated vehicle technology, we propose the rhythmic control (RC) scheme that allows vehicles to pass through an intersection in a conflict-free…
A recently introduced scheme for networked conservation laws is analyzed in various experiments. The scheme makes use of a novel relaxation approach that governs the coupling conditions of the network and does not require a solution of the…
This paper gives conditions for the rightmost particle in the $n$th generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a…
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…
Many car-following models of traffic flow admit the possibility of absolute stability, a situation in which uniform traffic flow at any spacing is linearly stable. Near the threshold of absolute stability, these models can often be reduced…
The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are…
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…
In most models of traffic flow, the car density $p$ is the only free parameter in determining the average car velocity $\langle v \rangle$. The critical car density $p_c$, which is defined to be the car density separating the jamming phase…
A key measure of performance and comfort in a road traffic network is the travel time that the users of the network experience to complete their journeys. Travel times on road traffic networks are stochastic, highly variable, and dependent…
The paper examines random dynamical systems related to the classical von Neumann and Gale models of economic growth. Such systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of…
Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize traffic congestion. As the number of traffic sensors is naturally constrained by budgetary requirements, real-time estimation of traffic…
In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the…
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…
We consider the problem of controlling a vehicle to arrive at a fixed destination while minimizing a combination of energy consumption and travel time. Our model includes vehicle speed and accelaration limits, aerodynamic drag, rolling…