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A Contribution to Theory of Traffic Flow

Authors: L. A. Pipes; C. K. Wojcik;

A Contribution to Theory of Traffic Flow

Abstract

<div class="htmlview paragraph">This paper presents an analysis of a car following model of general form: ẍ<sub>n + 1</sub> = A (ẋ<sub>n</sub> -ẋ<sub>n + 1</sub>)/(x<sub>n</sub> - x<sub>n + 1</sub>)<sup>m</sup>, where A and m are constants, x<sub>n + 1</sub> is the position of the following car, x<sub>n</sub> the position of the followed car, ẋ<sub>n + 1</sub> and ẋ<sub>n</sub> the corresponding velocities, and ẍ<sub>n + 1</sub> the acceleration of the following car. Several specific values of m are considered and their correlation with various traffic flow diagrams is established. Traffic flow in which all drivers, in line of vehicles, maintain a certain minimum safe distance is represented by the case, m = 0. The case, m = l, is shown to lead to a velocity-concentration curve due to Greenberg. The case, m = 2, is correlated with the rate of change of the visual perceptual angle of the follower and is shown to lead to Greenshields' velocity-concentration curve. Finally, the implications of the case when → ∞ are explored.</div>

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Top 10%
Average
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