Traffic Theory

This work describes a type of distributed feedback control algorithm that acts on a vertical queueing network where flow dynamics may greatly outpace the rate of feedback and actuation. The modeled network has a known, finite set of feasible actuations for the binary controllers located at each network node. It also has known expected demands, split ratios, and maximum service rates. Previous work proposed the application of a max pressure controller to maximize throughput on such a network without the need for centralized computation of a control policy. Here we extend the max pressure...

This paper presents a new approach which links the solution to the Burgers tracking problem to the concept of capture basin used in viability theory. This link enables the proof of the existence and uniqueness of the solution of the Burgers tracking problem. The Burgers tracking problem is linked to the Frankowska solutions of the Burgers equation. These results are easily extended to any first order hyperbolic partial differential equation (PDE) written in conservation law form, which is illustrated with the famous Lighthit-Whitham-Richards (LWR) PDE, known in highway traffic theory. The...

An Eulerian network model for air traffic flow in the National Airspace System is developed and used to design flow control schemes which could be used by Air Traffic Controllers to optimize traffic flow. The model relies on a modified version of the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE), which contains a velocity control term inside the divergence operator. This PDE can be related to aircraft count, which is a key metric in air traffic control. An analytical solution to the LWR PDE is constructed for a benchmark problem, to assess the gridsize required to...