The location of two ring roads and the control of traffic speed which together minimises radial travel in a town

Abstract

In a simple theoretical model, we seek the location of two ring roads which minimises the total radial travel in a circular town of unit radius. We assume that drivers choose least time paths and that the speed of vehicles is controlled so as to minimise radial travel. We show that, whatever the distribution of origins and destinations, if an internal ring road minimises the total radial travel then the radial traffic flow just inside the ring equals the radial traffic flow just outside the ring. We show that if origins and destinations are uniformly and independently distributed over that part of the radials within the town, and a circumferential ring road already exists, then the optimum radius of a single inner ring road is √2 − 1.