Microscopic Discontinuities Disrupting Hydrodynamic and Continuum Traffic Flow Models

Abstract

This paper explores short duration disturbances in the traffic stream that are large enough to impact the traffic dynamics and disrupt stationarity when establishing the fundamental diagram, FD, but small enough that they are below the resolution of conventional vehicle detector data and cannot be seen using conventional methods. This empirical research develops the Exclusionary Vehicle Aggregation method (EVA) to extract high fidelity time series data from conventional loop detectors and then extends the method to measure the standard deviation of headways in a given fixed time sample, stdevh. Using loop detector data spanning 18 years and five sites, all of the sites show that samples with low stdevh tend towards a triangular FD while samples with high stdevh tend towards a concave FD that falls inside the triangular FD. The stdevh is also shown to be strongly correlated with the duration of the longest headway within the sample. The presence of a long headway means the state is perceptively different over the sample and thus, the measurement is non-stationary. A review of the earliest FD literature by Greenshields finds strong supporting evidence for these trends. Collectively, the loop detector and historical FD results span over 75 years of empirical traffic data.

Based on the EVA analysis, this work offers the following insights: the shape of equilibrium FD appears to be triangular and that conventional detector data mask critical features needed by hydrodynamic traffic flow models, HdTFM. Because the driver behind a long headway can act independent of their leader, the long headways can correspond to unobserved boundary conditions that generate kinematic waves. If these boundaries were detected many HdTFM could accommodate them, especially multi-class models. But the stochastic nature of the long headways also challenges the predictive abilities of deterministic HdTFM. Perhaps the largest of these challenges is driver agency- the driver behind a long headway can maintain it, resulting in signals propagating downstream or they can close the gap, resulting in signals propagating upstream. Meanwhile, this work provides a test for stationary conditions to help ensure an empirical FD supports the assumptions placed upon it.