Limitations and Improvements of the Intelligent Driver Model (IDM)

This contribution analyzes the widely used and well-known “intelligent driver model” (briefly IDM), which is a second-order car-following model governed by system of ordinary differential equations. Although this was intensively studied in recent years for properly capturing traffic phenomena braking behavior, rigorous study well-posedness has, to our knowledge, never been performed. First, it shown that, specific class initial data, vehicles' velocities become negative or even diverge (-\infty\) finite time, both undesirable properties model. Various modifications IDM are then proposed order avoid such ill-posedness. The theoretical remediation model, rather than post facto ad hoc modification code implementations, allows more sound numerical implementation preservation features. Indeed, inconsistencies ensure dynamics close one original may need inspect clean large input result practically impossible scenarios large-scale simulations. issues might only occur happen frequently when different analyzed especially presence lane changing, on-ramps, other network components, as case most commonly microsimulators. On side, that can be guaranteed straight-forward improvements, those obtained slightly changing acceleration prevent velocity from becoming negative.