Multiclass Multilane Traffic Models And Integrated Optimal Control Strategies For Freeways

This monograph provides an extended overview of modelling and control approaches for freeway traffic systems, moving from the early methods to the most recent scientific results and field implementations. The concepts of green traffic systems and smart mobility are addressed in the book, since a modern freeway traffic management system should be designed to be sustainable. Future perspectives on freeway traffic control are also analysed and discussed with reference to the most recent technological advancements The most widespread modelling and control techniques for freeway traffic systems are treated with mathematical rigour, but also discussed with reference to their performance assessment and to the expected impact of their practical usage in real traffic systems. In order to make the book accessible to readers of different backgrounds, some fundamental aspects of traffic theory as well as some basic control concepts, useful for better understanding the addressed topics, are provided in the book. This monograph can be used as a textbook for courses on transport engineering, traffic management and control. It is also addressed to experts working in traffic monitoring and control areas and to researchers, technicians and practitioners of both transportation and control engineering. The authors’ systematic vision of traffic modelling and control methods developed over decades makes the book a valuable survey resource for freeway traffic managers, freeway stakeholders and transportation public authorities with professional interests in freeway traffic systems. Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Congestion has been a longstanding problem in urban transportation systems. It is the root of system deterioration in mobility, safety and sustainability, manifested as travel delay and travel uncertainty, crashes, air pollution, etc. A strong science into the understanding, modeling, computation and control of congestion dynamics in complex, uncertain and intelligent traffic systems is thus at the core of incorporating emerging technologies and devising sound and effective traffic management strategies.This dissertation aims at addressing the shortcomings of classical macroscopic traffic flow models in dealing with the boundary measurements and control. Due to construction, the traditional hydrodynamics based traffic modeling approaches are usually incapable or extremely tedious in incorporating trajectory-level details in either modeling or control. This constitutes the main hurdle for integrating sound physics with empirical observations in traffic systems estimation and control, especially when mobile or other non-regular sensing techniques are involved.In this dissertation, I develop a novel variational theory based traffic flow modeling framework and provide detailed discussions on its implications for traffic systems estimation, computation and control problems. The new modeling approach explores and consolidates the linkage between hyperbolic conservation equations associated with the kinematic wave theory and Hamilton-Jacobi equations associated with the optimal control theory. In a broader context, this linkage represents the translation between PDE (partial differential equation) and ODE (ordinary differential equation) problems. Though mathematically equivalent, the latter perspective allows us to tackle the moving observations more easily because of relaxed assumptions on boundary geometry. In addition, the analytical and numerical difficulties associated with solving traffic flow models are suppressed, thanks to the variational principle pertaining to the latter formulation. Major results presented in this dissertation include the following. First, I derive the variational formulations for multi-class and non-equilibrium traffic flow models respectively, through exploiting the isomorphic relation between a conservation law problem with its auxiliary optimal control problem. In the derivations, the relation of kinematic wave and solution to the optimal control problem are analyzed in detail. Based on the new formulations, simplified solution schemes are proposed. These solution schemes are flexible with the setting of computational grids and boundary conditions. Analysis of their error bounds are given. Then I look into the calibration of Hamiltonian, i.e. fundamental diagram, in multi-lane freeway setting. An automated adaptive calibrator is constructed using the mixed integer programming (MIP) technique and tested using I-80 freeway data. At last, I presented a decentralized urban signalized traffic network control scheme, motivated by the queuing properties implied in the variational principle.

This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level. The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on traffic instabilities and model calibration/validation present these topics in a novel and systematic way. Finally, the theoretical framework is shown at work in selected applications such as traffic-state and travel-time estimation, intelligent transportation systems, traffic operations management, and a detailed physics-based model for fuel consumption and emissions.