LWR and shockwave analysis - Failures under a concave fundamental diagram and unexpected induced disturbances

Abstract

This paper undertakes a detailed empirical study of traffic dynamics on a freeway. The results show the traffic dynamics that systematically determine the shape of the fundamental diagram, FD, can also violate the stationarity assumptions of both shockwave analysis and Lighthill, Whitham and Richard's models, thereby inhibiting the applicability of these classical macroscopic traffic flow theories. The outcome is challenging because there is no way to identify the problem using only the macroscopic detector data. The research examines conditions local to vehicle detector stations to establish the FD while the single vehicle passage method is used to analyze the composition of vehicles underlying the aggregate samples. Then, traffic states are correlated between successive stations to measure the actual signal velocities and show they are inconsistent with the classical theories. This analysis also revealed that conditions in one lane can induce signals in another lane. Rather than exhibiting a single signal passing a given point in time and space, the induced and intrinsic signals are superimposed on one another in the given lane. We suspect the subtle dynamics revealed in this research have gone unnoticed because they are far below the resolution of conventional traffic monitoring. The findings could have implications to other traffic flow models that rely on the FD, so care should be taken to assess if a given model is potentially sensitive to the non-stationary dynamics presented herein.The results have a direct impact on practice. Traffic flow theory is a critical input to many aspects of surface transportation, e.g., traffic management, traffic control, network design, vehicle routing, traveler information, and transportation planning all depend on models or simulation software that are based upon traffic flow theory. If the underlying traffic flow theory is flawed it puts the higher level applications at risk. So, the findings in this paper should lead to caution in accepting the predictions from traffic flow models and simulation software when the traffic exhibits a concave FD.