Title

Some Macroscopic Laws of Urban Traffic Dynamics: Analysis, Physical Evidence and Control Applications

Abstract

It is shown that under some conditions some properties of a road link — such as its capacity and its fundamental diagram — scale up when several links are joined together to form a regular structure (e.g., a ring). Of particular interest is the existence of both, a macroscopic fundamental diagram (MFD) relating a network’s space-mean flows, densities and speeds, and a relationship linking the space-mean flows and the number of trips completed.


By following imaginary moving observers that track vehicles we develop simple formulae for the mean flow at any given mean density. These formulae turn out to be the exact MFD for translationally symmetric arterials and rotationally symmetric rings with either signalized or unsignalized intersections. For less regular networks, the result is only an approximation. The formulae depend on the total length and surface area of the network; the average footprint of a vehicle; the distance between intersections; the speed limit; the saturation flow rate; and the method of intersection control. Simulations of San Francisco (USA) and a real-life experiment in Yokohama (Japan) confirm the results. An optimal control scheme that uses the MFD to improve urban mobility will be presented and illustrated with an interactive web-based game.