A new kind of fundamental diagram with an application to road traffic emission modeling

SUMMARY The main contribution of this paper is to show, on the basis of empirical traffic data, that the distribution of vehicle speeds on a road segment evolves with the occupancy in a simple manner. Under a critical occupancy, the distribution is unimodal, with one peak (the high mode) close to the free‐flow speed. When the occupancy exceeds the critical occupancy, the distribution of speeds becomes bimodal. A second peak (the low mode) appears, at a noticeably lower speed than the high mode. Empirical speed distributions are well fitted when assuming a (appropriately scaled and translated) low “temperature” Maxwell–Boltzmann distribution for the high mode and a high‐temperature distribution for the low mode. The standard fundamental diagram expresses the mean flow speed as a function of occupancy. The model proposed in this paper expresses the distribution of vehicle speeds as a function of the occupancy. We believe this result to be of great importance for both the theory of traffic flow and practical applications. Copyright © 2013 John Wiley & Sons, Ltd.