  The Gipps car-following model is a widely used tool for studying and
simulation traffic dynamics. Despite its popularity an often disregarded
property is that under heterogeneous parametrization on the individual vehicles
in the traffic flow, the model may produce collisions. This stands in crude
contrast to the principle, from which the model was derived: drive as fast as
possible while guaranteeing a safe headway in case that the leading vehicle
starts braking hard. Indeed, Gipps proof for the model being collision-free
only holds for ensembles of identical vehicles.
  In this work we examine the circumstances leading to collisions in
heterogeneous ensembles and propose a natural model extension, which conveys
the original models principles to situations, where collisions occur. For these
cases we present analytical and numerical results on the stability of the
equilibrium flow.
