The authors have tried to improve the traffic dynamic theory of Professor Pipes and have found the fundamental equation of traffic dynamics for a case in which the velocity of the following vehicle is determined not only by the space between following and lead cars but also by the velocity of the lead car. The safety of the following car with respect to rear end collision when the lead car is in sinusoidal motion is quantified by introducing a safety index. At the same time, the authors describe the stability of the indicial response of the following car, and the stability of the propagation of a sinusoidal disturbance down a line of cars.
In 1970, the Hanshin Expressway Public Corporation started operating an automated traffic control system to maximize the total traffic flowing into its expressway network. The corporation has been improving the system ever since. The system relies on two control methods. The first is to limit the cars coming onto the expressway at each entrance ramp to avoid congestion in any section. The system calculates the maximum allowable inflows by solving a linear programming problem once in every five minutes using data from detectors installed along the expressway and at all ramps. The second method is to give drivers the most recent and accurate traffic information about the expressway and its vicinity, including expected travel times and accidents, through various information channels so that they can decide what routes to take. This system is greatly appreciated by the corporation because it is extremely cost effective and also by drivers, who now consider it an indispensable service.
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