Related papers: An Extended AW-Rascle Model with Source Terms and …
Daganzo's criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277-286 (1995)] and Aw and Rascle's proposal how to overcome them [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916-938 (2000)] have…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
In this paper, we describe a relation between a microscopic traffic cellular automaton (TCA) model (i.e., the stochastic TCA model of Nagel and Schreckenberg) and the macroscopic first-order hydrodynamic model of Lighthill, Whitham, and…
The one-dimensional Aw-Rascle (AR) system has become a cornerstone of macroscopic models for single-lane vehicular traffic. A possible generalization of this model to a multi-dimensional setting is the so-called dissipative AR model, which…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have…
Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…
This paper presents a mesoscopic traffic flow model that explicitly describes the spatio-temporal evolution of the probability distributions of vehicle trajectories. The dynamics are represented by a sequence of factor graphs, which enable…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
This paper develops boundary observer for estimation of congested freeway traffic states based on Aw-Rascle-Zhang(ARZ) partial differential equations (PDE) model. Traffic state estimation refers to acquisition of traffic state information…
We present new numerical schemes to integrate stochastic partial differential equations which describe the spatio-temporal dynamics of reaction-diffusion (RD) problems under the effect of internal fluctuations. The schemes conserve the…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…
In today's urban landscape, traffic congestion poses a critical challenge, especially during outlier scenarios. These outliers can indicate abrupt traffic peaks, drops, or irregular trends, often arising from factors such as accidents,…
The paper provides conditions that guarantee existence and uniqueness of classical solutions for a non-local conservation law on a ring-road with possible nudging (or "look behind") terms. The obtained conditions are novel, as they are not…
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…
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
We investigate the effect of quenched disorder in the Nagel-Schreckenberg model of traffic flow. Spatial inhomogenities, i.e. lattice sites where the braking probability is enlarged, are considered as well as particle disorder, i.e. cars of…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…