Automatic fitting procedure for the fundamental diagram

Abstract

The fundamental diagram of a road, including free flow capacity and queue discharge rate, is very important for traffic engineering purposes. In the real word, most traffic measurements come from stationary loop detectors. This paper proposes a method to fit Wu’s fundamental diagram to loop detector data. Wu’s fundamental diagram is characterised by five parameters, being the free flow speed, wave speed, free flow capacity, queue discharge rate and jam density. The fits appear to be not very sensitive to the right value for the wave speed or the free flow speed. The proposed method therefore entails fixing these two parameters. The method consists of two steps. We first use a triangular fundamental diagram to separate the congested branch from the free flow branch. Then, the remaining three parameters of Wu’s fundamental diagram are fitted on each of the branches using a least square fit. This method is shown to be robust for cases tested in real life, and hence very noisy, data.