Systems of conservation laws with discontinuous fluxes and applications to traffic

In this paper we study 2 × 2 systems of partial differential equations with discontinuous fluxes arising in vehicular traffic modeling. The main goal is to introduce an appropriate notion of solution. To this aim we consider physically reasonable microscopic follow-the-leader models. Macroscopic Riemann solvers are then obtained as many particle limits

Statistical Physics of Vehicular Traffic and Some Related Systems

In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include

Micro-Macro limit of a non-local generalized Aw-Rascle type model

International audienceWe introduce a Follow-the-Leader approximation of a non-local generalized Aw-Rascle-Zhang (GARZ) model for traffic flow. We prove the convergence to weak solutions of the corresponding macroscopic equations deriving $L ∞$ and BV estimates. We also provide numerical simulations illustrating the micro-macro convergence and we investigate numerically the non-local to local limit for both the microscopic and macroscopic models

Strategic and Tactical Guidance for the Connected and Autonomous Vehicle Future

Autonomous vehicle (AV) and Connected vehicle (CV) technologies are rapidly maturing and the timeline for their wider deployment is currently uncertain. These technologies are expected to have a number of significant societal benefits: traffic safety, improved mobility, improved road efficiency, reduced cost of congestion, reduced energy use, and reduced fuel emissions. State and local transportation agencies need to understand what this means for them and what they need to do now and in the next few years to prepare for the AV/CV future. In this context, the objectives of this research are as follows: Synthesize the existing state of practice and how other state agencies are addressing the pending transition to AV/CV environment Estimate the impacts of AV/CV environment within the context of (a) traffic operations—impact of headway distribution and traffic signal coordination; (b) traffic control devices; (c) roadway safety in terms of intersection crashes Provide a strategic roadmap for INDOT in preparing for and responding to potential issues This research is divided into two parts. The first part is a synthesis study of existing state of practice in the AV/CV context by conducting an extensive literature review and interviews with other transportation agencies. Based on this, we develop a roadmap for INDOT and similar agencies clearly delineating how they should invest in AV/CV technologies in the short, medium, and long term. The second part assesses the impacts of AV/CVs on mobility and safety via modeling in microsimulation software Vissim

Nonlinear Hyperbolic Problems: modeling, analysis, and numerics

The workshop gathered together leading international experts, as well as most promising young researchers, working on the modelling, the mathematical analysis, and the numerical methods for nonlinear hyperbolic partial differential equations (PDEs). The meeting focussed on addressing outstanding issues and identifying promising new directions in all three fields, i.e. modelling, analysis, and numerical discretization. Key questions settled around the lack of well-posedness theories for multidimensional systems of conservation laws and the use of hyperbolic modelling beyond the classical topic of gas dynamics. A focal point in numerics has been the discretization of random evolutions and uncertainty quantification. Equally important, new multi-scale methods and schemes for asymptotic regimes have been considered

Discrete kinetic and stochastic game theory for vehicular traffic: Modeling and mathematical problems

n this thesis we are concerned with the mathematical modeling of vehicular traffic atthe kinetic scale. In more detail, starting from the general structures proposed by Arlottiet al. and by Bellomo, we develop a discrete kinetic framework in which thevelocity of the vehicles is not regarded as a continuous variable but can take a finite number of values only. Discrete kinetic models have historically been conceived in connection with the celebrated Boltzmann equation, primarily as mathematical tools to reduce the analytical complexity of the latter (see e.g., Bellomo and Gatignol, Gatignol): The Boltzmann’s integro-differential equation is converted into a set of partial differential equations in time and space, which share with the former some good mathematical properties being at the same time easier to deal with. In the present context, however, the discretization of the velocity plays a specific role in modeling the system rather than being simply a mathematical simplification, because it allows one to relax the continuum hypothesis for the velocity variable and to include, at least partially, the strongly granular nature of the flow of cars in the kinetic theory of vehicular traffic. The discrete velocity framework also gives rise to an interesting structure of the interaction terms of the kinetic equations, which are inspired by the stochastic game theory