  The Intelligent Driver Model is studied and several drawbacks with respect to
driving simulators are defined. We present two modifications of the IDM. The
first one gives any predefined distance to the leading vehicle in a steady
state. The second modification is a combination of the first one and the
optimal velocity model. It takes into account drivers reaction time explicitly
and is described by delay differential equation. This model always results in
realistic vehicles accelerations what allows simulating real traffic
collisions. Necessary and sufficient conditions are obtained, that guarantee a
non-oscillating solution near the equilibrium for the vehicle platoon. We
suggest the calibrating framework based on a numerical solution of the
constrained optimization problem. Nonlinear constraints are generated by the
numerical integration scheme. The suggested procedure incorporates the local
stability conditions obtained and takes into account vehicle dynamics, drivers
behavior and weather conditions.
