Scale-Dependent Observability of Emergent Dynamics: Application to Traffic Flow with Connected Vehicles

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Global emergent patterns are observed in several large-scale complex systems, such as transportation networks, power grids, and financial markets. Gaining understanding of these dynamically evolving behavioral patterns is very important to solve problems associated with such systems. For example, in transportation networks, these emergent patterns usually dictate congestion dynamics and are poised to undergo a transformative change with the introduction of connected vehicles that can communicate with each other. Consequently, our ability to observe such patterns plays a critical role in effectively managing the transition to a smarter transportation network as well as in improving system performance and reducing congestion costs. This research seeks to answer questions about the appropriate scale at which these patterns may be best observed. Additionally, this work also seeks to assess the effect of varying penetration rates of connected vehicles on the ability to observe emergent patterns in traffic. This work has a great potential to significantly improve our ability to monitor, predict and control the occurrence of emergent congestion events. In the case of traffic flow applications, this study could help reduce worldwide congestion costs that are estimated to be in several hundreds of billions of US dollars annually. The techniques developed during this study will enhance our fundamental knowledge about how to observe the emergent behavior and use this knowledge to analyze and solve the problems associated with several other complex systems. The project also has highly innovative educational plan of creating visually appealing and lucid graphics material to engage undergraduate and graduate students, as well as the general public.The primary objective of this research project is to create a rigorous methodology to determine the spatial scale and model order required to observe and predict emergent phenomena in complex systems. In a narrower context of traffic flow, the project seeks to establish the modeling requirements for observing emergent congestion events on a multi-lane highway, and predicting such behavior with better accuracy than current prediction models. The approach will modify existing Krylov subspace-based model order reduction techniques by explicitly incorporating spatial scales into the process. More importantly, the novel contribution of this work will be the control-theoretic formulation of the renormalization group theory borrowed from the field of statistical mechanics to gain an understanding of how the observability of emergent dynamics depends on spatial scale. The research will include the study of spatial dependence of observability in complex systems in a control-theoretic setting. This work will also contribute to the study of how penetration rate (i.e., the distribution of a sensor network in a complex system) impacts the observability of emergent behavior in complex traffic flow dynamics.