Stable Phase-Plane and Car-Following Behavior as Applied to a Macroscopic Phenomenon

An attempt is made to furnish plausible explanations for some observed traffic-flow phenomena, based on known behavior of a pair of cars in a car-following situation, A fundamental psychophysical approach is applied deterministically in assessing actual driver performance.

Observation of driver behavior in the traffic stream indicates that there are trajectories which loop clockwise in the phase (spacing/relative speed) plane. Based on these observations, and on a car-following equation appropriate for a two-regime (free-flow and congested-flow) phenomenon, an approximate limit cycle in the phase plane (switch-type behavior) is derived. The enveloping curves to these limit cycles may represent actual relatively close spacing conditions. It is realized that the intersection point of an approximate enveloping curve and a threshold curve for detecting relative speed at a given spacing has an important property, and may be associated with the critical spacing which represents transition between the congested-flow and free-flow regimes.