Determining the Breakpoints of Fundamental Diagrams

Abstract

The breakpoints of fundamental diagrams (FDs) are an important foundation for estimating capacity, identifying traffic conditions, and determining the phase regime of multi-regime FDs. Unfortunately, to our best knowledge, there has been little research on determining breakpoints in a scientific way. This paper applies a Gaussian mixture model (GMM) to describe multi-component traffic conditions, and introduces the GMMs of traffic flow parameters (speed and occupancy). In order to avoid the possible singularities or degeneracies of typical maximum likelihood (ML) estimation, maximum a posteriori (MAP) estimation is introduced for the parameter estimation. The minimum cumulative probability method is then proposed for the determination of critical parameters at breakpoints. Nine datasets collected from the Caltrans Performance Measurement System (PeMS) are used for the estimation and validation of the proposed methods. The results show that the proposed methods can effectively divide up traffic conditions and determine breakpoints. Meanwhile, the effects of mixture weight and vehicle type on breakpoints are investigated and the proposed methods show stable performance in the determination of breakpoints under different conditions. The estimated critical occupancies and speeds are also applied for capacity estimation and calibration of the triangular FD model and three-regime speed-occupancy relationship.