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