Related papers: A sharp critical threshold for a traffic flow mode…
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…
The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted…
In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of…
The totally asymmetric exclusion process (TASEP) with periodic boundaries is considered as traffic flow model. The large-L approximation of the stationary state is used for the derivation of the time-headway distribution (an important…
In recent works, we have proposed a stochastic cellular automaton model of traffic flow connecting two exactly solvable stochastic processes, i.e., the Asymmetric Simple Exclusion Process and the Zero Range Process, with an additional…
The objective of this paper is to initiate a qualitative analysis of dynamic flow in traffic networks by using the competitive equilibrium model of multiple market systems. A network is modeled as a dynamic graph where routes (edges) are…
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…
We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with…
The utilization of traffic conflict indicators is crucial for assessing traffic safety, especially when the crash data is unavailable. To identify traffic conflicts based on traffic flow characteristics across various traffic states, we…
Traffic safety at intersections is studied quantitatively using methods from Statistical Mechanics on the basis of simple microscopic traffic flow models. In order to determine a relationship between traffic flow and the number of crashes,…
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…
We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the…
We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a…
Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…
This paper studies the problem of traffic flow forecasting, which aims to predict future traffic conditions on the basis of road networks and traffic conditions in the past. The problem is typically solved by modeling complex…
Very little is yet known regarding the Willmore flow of surfaces with Dirichlet boundary conditions. We consider surfaces with a rotational symmetry as initial data and prove a global existence and convergence result for solutions of the…
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…
We study some anisotropic heterogeneous nonlinear integral equations arising in epidemiology. We focus on the case where the heterogeneities are spatially periodic. In the first part of the paper, we show that the equations we consider…
A nucleation model for the breakdown phenomenon in freeway free traffic flow at an on-ramp bottleneck is presented. This model, which can explain empirical results on the breakdown phenomenon, is based on assumptions of three-phase traffic…
Traffic congestion is one of the most notable problems arising in worldwide urban areas, importantly compromising human mobility and air quality. Current technologies to sense real-time data about cities, and its open distribution for…