Jam Occupancy and Other Lingering Problems with Empirical Fundamental Relationships

This paper explores several commonly overlooked factors affecting empirical fundamental relationships that are commonly used to relate the traffic state parameters: speed, flow, and concentration. Most of these factors are conceptually simple, but collectively they result in unexpectedly large, nonlinear distortions of the empirical traffic state measurements. In some cases the impacts are known but are underappreciated, for example, passenger car equivalents and measurement errors arising from sampling artifacts. In other cases the impacts have not been recognized in the literature; for example, jam occupancy should be about 80%. The paper also discusses often-overlooked effects of an inhomogeneous vehicle fleet and nonstationary traffic, both of which can add considerable noise to empirical measurements of the traffic state. As a result of these distortions, on a freeway more than half the physical distance along the queued regime of the fundamental relationship in the flow density plane (and flow occupancy plane) results from speeds below 10 mph. This outcome inadvertently gives greater weight to the low-speed measurements because they are spread over a large physical region of the plane, while the higher-speed measurements are compressed into a narrow sliver. However, as the paper illustrates, the low-speed samples are subject to the largest measurement errors, are the least likely to come from stationary conditions, and often violate the assumptions used to measure the traffic state. Aggregated low-speed data from conventional vehicle detectors should be discounted or possibly discarded when an empirical fundamental relationship is constructed.