  Effects of large value assigned to the maximal car velocity on the
fundamental diagrams in the Nagel-Schreckenberg model are studied by extended
simulations. The function relating the flow in the congested traffic phase with
the car density and deceleration probability is found numerically. Properties
of the region of critical changes, so-called jamming transition parameters, are
described in details. The basic model, modified by the assumption that for each
car an individual velocity limit is assigned, is investigated in the aim to
find the best supplementary rule allowing the jammed traffic to move with
velocity larger than the slowest driving vehicle.
