Gramian-Based Optimization for the Analysis and Control of Traffic Networks

This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional approaches to control traffic signaling, a simplified framework allows for a more tractable analysis of the network overall dynamics, and enables the design of critical parameters while considering network-wide measures of efficiency. Motivated by the increasing availability of real-time high-resolution traffic data, we cast an optimization problem that formalizes the goal of minimizing the overall network congestion by optimally controlling the durations of green lights at intersections. Our formulation allows us to relate congestion objectives with the problem of optimizing a metric of controllability of an associated dynamical network. We then provide a technique to efficiently solve the optimization by parallelizing the computation among a group of distributed agents. Lastly, we assess the benefits of the proposed modeling and optimization framework through microscopic simulations on typical traffic commute scenarios for the area of Manhattan. The optimization framework proposed in this study is made available online on a Sumo microscopic simulator based interface [1].