Intelligent Cruise Control Systems and Traffic Flow Stability

In analogy to the ow of uids, it is expected that the aggregate density and the velocity of vehicles in a section of a freeway adequately describe the tra c ow dynamics. The conservation of mass equation together with the aggregation of the vehicle following dynamics of controlled vehicles describes the evolution of the tra c density and the aggregate speed of a tra c ow. There are two kinds of stability associated with tra c ow problems string stability (or car-following stability) and tra c ow stability. We make a clear distinction between tra c ow stability and string stability, and such a distinction has not been recognized in the literature, thus far. String stability is stability with respect to intervehicular spacing; intuitively, it ensures the knowledge of the position and velocity of every vehicle in the tra c, within reasonable bounds of error, from the knowledge of the position and velocity of a vehicle in the tra c. String stability is analyzed without adding vehicles to or removing vehicles from the tra c. On the other hand, tra c ow stability deals with the evolution of tra c velocity and density in response to the addition and/or removal of vehicles from the ow. Tra c ow stability can be guaranteed only if the velocity and density solutions of the coupled set of equations is stable, i.e., only if stability with respect to automatic vehicle following and stability with respect to density evolution is guaranteed. Therefore, the ow stability and critical capacity of any section of a highway is dependent not only on the vehicle following control laws and the information used in their synthesis, but also on the spacing policy employed by the control system. Such a dependence has practical consequences in the choice of a spacing policy for adaptive cruise control laws and on the stability of the tra c ow consisting of vehicles equipped with adaptive cruise control features on the existing and future highways. This critical dependence is the subject of investigation in this paper. This problem is analyzed in two steps: The rst step is to understand the e ect of spacing policy employed by the Intelligent Cruise Control (ICC) systems on tra c ow stability. The second step is to understand how the dynamics of ICC system a ects tra c ow stability. Using such an analysis, it is shown that cruise control systems that employ a constant time headway policy lead to unacceptable characteristics for the tra c ows.