| There are a large number of models that can be used to describe traffic flow. Although some were initially theoretically derived, there are many that were constructed with utility alone in mind. The Intelligent Driver Model (IDM) is a microscopic model that can be used to examine traffic behavior on an individual level with emphasis on the relation to an ahead vehicle. One application for this model is that it is easily molded to performing the operations for an Adaptive Cruise Control (ACC) system. Although it is clear that the IDM holds a number of convenient properties, like easily interpreted parameters, there is yet to be any rigorous examining of this model from a mathematical standpoint. This paper will place this model into the form of a vector-valued time-autonomous ODE system and analytically examine it. Additionally, the parameter estimation problem will be formulated. Simulations will demonstrate the model in practice. |
