Advancing Traffic Flow Theory Using Empirical Microscopic Data
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Advancing Traffic Flow Theory Using Empirical Microscopic Data

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    As reviewed in Section 1.1, much of traffic flow theory depends a fundamental relationship (FR) between flow, density, and space mean speed; either explicitly, e.g., hydrodynamic models such as LWR (Lighthill and Whitham, 1955, and Richards, 1956) or implicitly, e.g., car following models (Chandler et al., 1958; Gazis et al., 1961). While conventional theory has proven to be a good first-order approximation, there are numerous unreasonable assumptions that are often employed (e.g., "near stationary traffic" and "homogeneous vehicles") that limit the applicability of many theories. Most conventional FR curves are fit to a cloud of the coarsely aggregated data and as a result, the fit is poor, requiring prior assumptions of the curve shape before fitting. Typically, many other curve shapes could easily fit the point cloud just as well if the assumptions were changed (see, e.g., Drake et al., 1967 for an early work that remains typical of contemporary, conventional efforts). The scattered cloud of empirical data points has commonly been accepted as unavoidable; yet Coifman (2014a) found evidence that much of the scatter could be attributed to large, underappreciated sampling errors arising from the conventional, fixed time aggregation process. In response to these challenges, Coifman (2014b) developed a new data-driven approach for aggregating the individual vehicle measurements from dual loop detectors that leads to a very clean FR derived from empirical data. The start of Section 2 summarizes the details of this new method. For now it is sufficient to note that the approach accommodates inhomogeneous vehicles, does not require "near stationary" traffic, and it does not require any preconceived curve to be fit to the data. Coifman (2014b) only contemplated flow-occupancy relationships. As discussed in the latter portion of Section 2, the current work extends the methodology to macroscopic flow-density and microscopic speed-spacing relationships derived entirely from empirical loop detector data, yielding relationships that have historically been difficult to measure. The key distinction of this advance is how vehicle length is accounted for. Section 3 then applies the new methodology to three large data sets. The advances provide a new level of accuracy to calibrate macroscopic hydrodynamic models and microscopic car following models using commonly deployed dual loop detectors. These advances in turn should advance traffic flow theory. A key finding of this work is the fact that many of the critical parameters (e.g., the slope of the congested regime) turn out to depend on vehicle length. These relationships are obscured in conventionally aggregated data because vehicles of different lengths are arbitrarily grouped together based on arrival order. Then the report closes in Section 4 with a discussion and conclusions.
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