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This contribution analyzes the widely used and well-known "intelligent drivermodel (briefly IDM), which is a second order car-following model governed by asystem of ordinary differential equations. Although this model was intensivelystudied in recent years for properly capturing traffic phenomena and driverbraking behavior, a rigorous study of the well-posedness has, to our knowledge,never been performed. First it is shown that, for a specific class of initialdata, the vehicles' velocities become negative or even diverge to $-\infty$ infinite time, both undesirable properties for a car-following model. Variousmodifications of the IDM are then proposed in order to avoid suchill-posedness. The theoretical remediation of the model, rather than post factoby ad-hoc modification of code implementations, allows a more sound numericalimplementation and preservation of the model features. Indeed, to avoidinconsistencies and ensure dynamics close to the one of the original model, onemay need to inspect and clean large input data, which may result in practicallyimpossible scenarios for large-scale simulations. Although well-posednessissues occur only for specific initial data, this may happen frequently whendifferent traffic scenarios are analyzed, and especially in presence oflane-changing, on ramps and other network components as it is the case for mostcommonly used micro-simulators. On the other side, it is shown thatwell-posedness can be guaranteed by straight-forward improvements, such asthose obtained by slightly changing the acceleration to prevent the velocityfrom becoming negative.

Limitations and Improvements of the Intelligent Driver Model (IDM)