Stability of Reciprocal-Spacing Type Car Following Models

Ernest A. Unwin and Lucien Duckstein
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Ernest A. Unwin: Systems Engineering Department, University of Arizona, Tucson, Arizona
Lucien Duckstein: Systems Engineering Department, University of Arizona, Tucson, Arizona

Transportation Science, 1967, vol. 1, issue 2, 95-108

Abstract: The problem of studying the stability of the reciprocal-spacing follow-the-leader model of traffic flow is first discussed and an approximate model is proposed. The mathematical functions that are suitable to describe lead-car behavior are examined. The stability of a nonlinear car-following model is then defined rigorously, so that it can be studied in the framework of the Liapounov theory. Previous phase plane results shoiv that the reciprocal-spacing model is barely stable, whereas an asymptotically stable model may describe the dynamics more closely. Using an extension of the Weber Ratio, such a model is derived. A phase plane study of the proposed model is presented together with some numerical results. The results compare favorably with existing data. Results are presented showing the relative behavior of the actual model with time delay and the proposed model, in which a truncated Taylor series has been used to approximate the time delay.

Date: 1967
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