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 The following excerpt is taken from Chapter 2 (pp. 17-20) of the Transportation Research Board Special Report on Traffic Flow Theory, published on the website http://www.tfhrc.gov/its/tft/tft.htm. Speed-Flow Model The problem for traffic flow theory is that these curves are empirically derived. There is not really any theory that would explain these particular shapes, except perhaps for Edie et al. (1980), who propose qualitative flow regimes that relate well to these curves. The task that lies ahead for traffic flow theorists is to develop a consistent set of equations that can replicate this reality. . . . It is instructive to review the history of depictions of speed-flow curves in light of this current understanding. Probably the seminal work on this topic was the paper by Greenshields in 1935, in which he derived the following parabolic equation for the speed-flow curve on the basis of a linear speed-density relationship together with the equation, flow = speed * density:
where uf is the free-flow speed, and kj is the jam density. . . . In short, Greenshields’ model dominated the field for over 50 years, despite at least three problems. The most fundamental is that Greenshields did not work with freeway data. Yet his result for a single lane of traffic was adopted directly for freeway conditions. (This of course was not his doing.) The second problem is that by current standards of research the method of analysis of the data, with overlapping groups and averaging prior to curve-fitting, would not be acceptable. The third problem is that despite the fact that most people have used a model that was based on holiday traffic, current work focuses on regular commuters who are familiar with the road, to better ascertain what a road is capable of carrying. . . . Speed-flow models are now recognized to be important for freeway management strategies, and will be of fundamental importance for ITS implementation of alternate routing; hence there is currently considerably more work on this topic than on the remaining two bivariate topics. . . . Hence, it is sensible to turn to discussion of speed-concentration models, and to deal with any other speed-flow models as a consequence of speed-concentration work, which is the way they were developed.
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