
doi: 10.4271/680171
<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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