A macroscopic model to reproduce self-organization at bottlenecks

9 pages, 27 ref.We propose a model for self-organized traffic flow at bottlenecks that consists of a scalar conservation law with a nonlocal constraint on the flux. The constraint is a function of an organization marker which evolves through an ODE depending on the upstream traffic density and its variations. We prove well-posedness for the problem, construct and analyze a finite volume scheme, perform numerical simulations and discuss the model and related perspectives

A quantum vocal theory of sound

Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study of human voice, considered as a probe to investigate the world of sounds. We present a theoretical framework that is based on observables of vocal production, and on some measurement apparati that can be used both for analysis and synthesis. In analogy to the description of spin states of a particle, the quantum-mechanical formalism is used to describe the relations between the fundamental states associated with phonetic labels such as phonation, turbulence, and supraglottal myoelastic vibrations. The intermingling of these states, and their temporal evolution, can still be interpreted in the Fourier/Gabor plane, and effective extractors can be implemented. The bases for a quantum vocal theory of sound, with implications in sound analysis and design, are presented

Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic

In the context of road traffic modeling we consider a scalar hyperbolic conservation law with the flux (fundamental diagram) which is discontinuous at x = 0, featuring variable velocity limitation. The flow maximization criterion for selection of a unique admissible weak solution is generally admitted in the literature, however justification for its use can be traced back to the irrelevant vanishing viscosity approximation. We seek to assess the use of this criterion on the basis of modeling proper to the traffic context. We start from a first order microscopic follow-the-leader (FTL) model deduced from basic interaction rules between cars. We run numerical simulations of FTL model with large number of agents on truncated Riemann data, and observe convergence to the flow-maximizing Riemann solver. As an obstacle towards rigorous convergence analysis, we point out the lack of order-preservation of the FTL semigroup

First-Order Macroscopic Traffic Models

Macroscopic traffic models describe the traffic behaviour at a high level of aggregation, i.e. the traffic dynamics is expressed through aggregate variables, such as traffic density, mean speed and flow. Macroscopic models rely on the analogy between the flow of vehicles and the flow of fluids or gases and are based on a limited number of equations that are relatively easy to handle. This chapter is devoted to describe a very relevant class of macroscopic models, i.e. first-order traffic flow models, which capture the dynamics of only one aggregate variable, namely, the traffic density. A very important first-order macroscopic model is the Lighthill\u2013Whitham\u2013Richards model, developed in the 50s, but still of interest nowadays both for theoretical analysis and practical applications. It is a continuous model, which describes the dynamics of the macroscopic variables through partial differential equations. The most famous discretised version of the Lighthill\u2013Whitham\u2013Richards model is the so-called Cell Transmission Model, developed in the 90s and very widespread in the communities of mathematicians and traffic engineers

Sliding Modes Control in vehicle longitudinal dynamics control

Sliding Mode Control is a nonlinear control methodology based on the use of a discontinuous control input which forces the controlled system to switch from one continuous structure to another, evolving as a variable structure system. This structure variation makes the system state reach in a finite time a pre-specified subspace of the system state space where the desired dynamical properties are assigned to the controlled system. In the past years, an extensive literature has been devoted to the developments of Sliding Mode Control theory. This kind of methodology offers a number of benefits, the major of which is its robustness versus a significant class of uncertainties and disturbances. Yet, it presents a crucial drawback, the so-called chattering phenomenon, which may disrupt or damage the actuators and induce unacceptable vibrations throughout the controlled system, limiting the practical applicability of the methodology, especially in case of mechanical or electromechanical plants. This drawback has been better studied recently. Theoretical developments, oriented to increase the order of the sliding mode, thus producing efficient Second Order and Higher Order Sliding Mode Control algorithms, may be useful to attenuate the drawbacks caused by the use of a discontinuous control. Then, Sliding Mode Control can be profitably used to efficiently solve automotive control and observation problems, as testified by several recent publications and research projects. The aim of this chapter is to provide an overview of available examples of application of sliding mode control to the automotive field, focusing on recent developments at the University of Pavia

Emerging freeway traffic control strategies

Classical freeway traffic control approaches can be conveniently revisited in the light of the new technologies which have revolutionised data collection, data processing, communications and computing. In this chapter, the emerging freeway traffic control paradigms are illustrated, without claiming to be exhaustive, as the emerging control concepts are constantly evolving together with the new technologies on which they are based. The scenarios that unfold on the horizon are incredibly dense with potentialities and opportunities. Traffic data acquisition can be performed supplementing fixed sensors with probe vehicles. The overall traffic flow, even in case of mixed traffic consisting of conventional vehicles and intelligent vehicles, can be influenced by acting in a coordinated way at the level of the single intelligent vehicle. Large amounts of data can be collected, also exploiting unconventional data sources like social networks, making of paramount importance the development of traffic-oriented big data technologies, as well as efficient data mining techniques, in order to distinguish between useful and non-useful data and suitably process them. Privacy-preserving data sharing, cybersecurity, fault-tolerance and resilience concepts also play an important role in this new and challenging scenario