From Microscopic to Macroscopic Traffic Flow: A Queuing Theoretic Approach

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Emerging capabilities in driverless cars and inter-vehicle communication are outpacing the analysis and design capabilities of traditional simulation-based modeling tools. This project will focus on methods linking vehicle-scale characteristics to system-level performance metrics. For example, features such as autonomous car-following and lane-changing will be related to macroscopic traffic properties such as peak capacity and average travel times. Systematic analysis and design of urban traffic systems may save lives, prevent injuries, ease traffic congestion, and improve the environment. More generally, the project will create a rigorous statistical mechanics theory applicable to other multi-particle/agent systems, such as crowd motion and formations of mobile robots. The research will be tightly integrated with the education component through software projects in the graduate and undergraduate courses developed by the PI. Existing programs at the University of Southern California will be utilized to integrate inclusive teaching practices into educational activities in order to address retention of women, underrepresented and minority students. This project seeks to overcome the shortcomings of existing analytical and simulation-based traffic models. Available analytical techniques either apply only to closed systems, i.e., to a fixed number of vehicles whose motion is possibly coordinated by a leader, or they assume that the flow dynamics are quasi-static. Simulation-based methodologies are not suitable for developing fundamental insights. This project will address these shortcomings through two novel research thrusts. The first thrust is formulation of a rigorous horizontal traffic queuing theory under various car following and lane-changing models. The distinguishing feature of this theory is the ability to capture microscopic congestion effects, in contrast to the limited resolution inherent in approaches that use point queue models. The analysis begins by identifying fundamental relationships between throughput and average travel times associated with traffic flow for specified parameters of the underlying road infrastructure, communication network between the vehicles, and mechanical constraints of individual vehicles. The second research thrust is use of the fluid limit to derive macroscopic traffic flow models for a given set of microscopic interaction rules. A key tool here is the notion of measure-valued state descriptors, taken from the processor sharing queue literature, which provides a unified setting for the analysis of traffic systems with time-varying dimension in a common state space.