A Modified Car-Following Model

Abstract

This paper is written in the hopes that an equation will evolve which will help predict and explain the phenomena of car-following. In order for this equation to be applied to traffic data, the road being investigated should be single-laned, afford following cars very little chance of passing, and be of fairly high density. As will be shown in the results later, densities of less than thirty vehicles per mile lead to very large mean squared errors for speed and volume. These first three conditions may not exactly be true of the road being analyzed, but they should be adhered to as closely as possible. Although there are quite a few models already in existence, they are all related to each other by the idea of reaction time. At this point, a resume of Perception, lntellection, Emotion, and Volition Theory is in order. P.I.E.V. Theory as far as we are concerned, is an explanation and dissection of how long a driver would take to respond to the lead car. He must first perceive the stimulus, after which he will absorb it and start to think or intellect about how he should respond to it. At this point, his emotions become involved and then he physically reacts to the stimulus with a corresponding acceleration or deceleration. The last step of physically reacting to the stimulus is called volition. The whole process takes an individual three to five seconds. In a broad sense, the response is the driver’s ability to accelerate or decelerate; the stimulus is the gap and speed differences between the lead and following cars; and the degree to which he reacts to the stimulus can be termed sensitivity. The sensitivity of a driver is measured in car-following models by a sensitivity coefficient. In this particular paper, it is called the “c” factor. This factor is dependent on the gap between the two cars and also on the relative velocities associated with the cars. Because we are considering the steady-state conditions of the vehicles and not the transient effects, the time lag factor is neglected in the following results.