Characterising scattering features in flow-density plots using a stochastic platoon model

The scattering features of points in flow-density plot remain as an attractive topic in the last several decades. Some previous studies either assumed that the points of congested traffic flows were completely random or that the implicit rules of hidden distribution were difficult to describe. Although the scattering features are influenced by various factors (e. g. lane-changing manoeuvers, merging behaviours and driver heterogeneity), we believe that they are mainly dominated by the microscopic headway/spacing distributions. In this paper, we relax the assumption of deterministic headway/spacing in Newell's simplified car-following model and allow random headways/spacings in a homogeneous platoon (vehicles run closely at the same velocity). Further extending the conventional deterministic reciprocal relationship between flow rate and headway, we find that the reciprocal of average headway of a homogeneous platoon and the corresponding flow rate should follow the same distribution. Based on these two extensions, we can link the conditional distributions of average headway in a homogeneous platoon and the conditional distributions of flow rate, all with respect to velocity. When the aggregation time interval is small enough (e. g. 30 s), tests on Performance Measurement System (PeMS) data reveal that the seemingly disorderly scattering points in the macroscopic flow-density plot follow the estimated flow rate distributions from Next Generation Simulation vehicular trajectories. While if the aggregation time interval increases (e. g. to 5 min), the measured vehicles probably pass the loop detectors at different velocities and form heterogeneous platoons. It becomes difficult to find a definite distribution model that can fit average headway/spacing for heterogeneous platoons. However, most points in flow-velocity plot still locate within a certain 2D region, whose boundaries can be obtained from the homogeneous platoon model. Finally, tests on PeMS data verify the estimated boundaries.