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Description
This volume presents a coherent and high-quality collection of contributions addressing key challenges in traffic modeling and control. The chapters showcase a blend of theoretical rigor and practical relevance, with diverse methodologies ranging from PDE control to game theory and data-driven modeling. One chapter presents a retrospective on PDE backstepping techniques for stabilizing stop-and-go waves, extending from single-lane models to more complex multi-lane and multi-class systems. Another introduces a second-order time-to-collision metric that accounts for non-static acceleration and turning, improving predictive accuracy in safety analysis. The CGARZ model simplifies second-order traffic dynamics by collapsing free-flow regimes while preserving detail in congestion, striking a balance between realism and tractability. A multi-population mean field game framework is proposed to model the interaction between human-driven and autonomous vehicles, with a detailed stability analysis that sheds light on the benefits of CAV integration. Another contribution develops a multi-lane model where autonomous vehicles act as mobile bottlenecks, coupling macroscopic flow dynamics with controlled microscopic agents. The volume also includes a rigorous analysis of the Hughes model for pedestrian flow with affine cost functions, exploring uniqueness and sensitivity with respect to both initial data and model parameters.
A Collapsed Generalized Aw-Rascle-Zhang Model and Its Model Accuracy.- Second-Order Time to Collision With Non-Static Acceleration.- On stability of one-dimensional Hughes dynamics with affine costs.- Traffic Control by Backstepping: a Retrospective.- MACROSCOPIC MANIFESTATIONS OF TRAFFIC WAVES IN MICROSCOPIC MODELS.- A multi-scale multi-lane model for traffic regulation via autonomous vehicles.- Ramp metering control for mixed-autonomy traffic.- Multi-population Mean Field Game for Mixed Traffic Flow Consisting of Human-Driven and Connected and Autonomous Vehicles.
Maria Teresa Chiri is Assistant Professor in the Department of Mathematics and Statistics at Queen s University in Kingston, Ontario, Canada. Her research lies at the intersection of partial differential equations, control theory, and applied analysis, with a focus on conservation laws, traffic flow models with autonomous vehicles, and optimal control problems arising in math biology.
Benedetto Piccoli is University Professor and the Joseph and Loretta Lopez Chair Professor of Mathematics at Rutgers University - Camden. He also served as Vice Chancellor for Research and is currently chair of the Department of Mathematical Sciences. His research interests span various areas of applied mathematics, including control theory, traffic flow on networks, crowd dynamics, math finance and application to autonomous driving, population health and bio-medical systems. He is author of more than 350 research papers and 7 books and is the founding editor of Networks and Heterogeneous Media. Piccoli is the 2009 Fubini Prize recipient, Plenary speaker at ICIAM 2011, 2012 inaugural Fellow of American Mathematical Society, 2024 SIAM W.T. and Idalia Reid Prize recipient, and 2024 IEEE ITS Institutional Lead Award recipient for the CIRCLES consortium. He spent the 2023-24 AY visiting the Institute for Advanced Study in Princeton.
