An analytical approximation for the macropscopic fundamental diagram of urban traffic

This paper shows that a macroscopic fundamental diagram (MFD) relating flow and average density must exist on any street with blocks of diverse widths and lengths, but no turns, even if all or some of the intersections are controlled by arbitrarily timed traffic signals. The timing patterns are assumed to be fixed in time. Exact expressions in terms of a shortest path recipe are given, both, for the street’s capacity and its MFD. Approximate formulas that require little data are also given. Conditions under which the results can be approximately extended to networks encompassing large city neighborhoods are discussed. The MFD’s produced with this method for the central business districts of San Francisco (California) and Yokohama (Japan) are compared with those obtained experimentally in earlier publications.