Macroscopic fluid-like models and their discretizations such as the Cell Transmission Model (CTM) have proven successful in modeling traffic flows in large-scale transportation networks. In general, these models employ discontinuous dynamics or nonlinear terms to describe phenomena like shock waves and phantom jams. Given the complexity of these models, it is not surprising that the dynamical properties of these models are not yet well characterized, especially in congested regimes. Furthermore, control policies using these models are often designed for free flow regimes. Yet, practical transportation networks often operate in states where at least one of the constituent roads are congested. In this context, this dissertation addresses two open problems concerning the analysis and distributed control of transportation networks, modeled by variants of the CTM, operating in congested regimes.
This dissertation is divided into two parts. In the first part, we study the dynamical properties of a transportation network that is modeled using the Cell Transmission Model (CTM), when driver behavior at intersections is governed by a first-in-first-out (FIFO) policy. While properties such as the existence and stability of steady states of the resulting dynamical system in the free flow regime have recently been identified for some classes of network topologies, the analysis of the dynamical behavior of this system in congested regimes remains an open problem. To address this problem, we propose a novel analysis and design framework, in which we prove the dynamical equivalence between the CTM and a class of autocatalytic chemical reaction networks (CRNs). We then exploit structural results and entropy-like Lyapunov functions from chemical reaction network theory to provide simple analytical conditions for the existence and local stability of steady states in congested regimes, based on the connectedness of the network topology, and network parameters like the velocities, turning ratios and exogenous inflows. We demonstrate how the structural results arising from this framework can be applied in network planning studies to mitigate congestion by redesigning existing transportation networks, contribute to sensor and actuator placement, and inform control strategies like ramp metering.
In the second part, we consider the problem of designing fast local control policies to mitigate traffic congestion arising from large disturbances in the traffic flow, such as accidents and peak-hour demand surges, before they develop into propagating traffic jams or shock waves. While typical control policies designed using free flow traffic models are robust to small disturbances, the design of control strategies for networks operating under large disturbances largely remains an open problem. Using the CTM with a non-FIFO relaxation for driver behavior at intersections, we address this problem by proposing a distributed synthesis framework to locally compute distributed control policies that limit the spatial propagation of congestion to small areas. We demonstrate the application of this framework in locally synthesizing traffic light sequences for urban networks, as well as ramp queue controllers and speed limits for freeway networks with connected and autonomous vehicles, to mitigate congestion caused by large disturbances like accidents and peak-hour demand surges.