A varied form of the Nagel-Schreckenberg model

By making slight changes of the Nagel-Schreckenberg model, we propose a varied model for a realistic description of the traffic flow on single-lane highways. While the NaSch model falls to cover the "takeover", this realistic situation gets a good description in our model. Moreover, from the fundamental diagrams achieved in our model, we can divide the forms of traffic flow into five different modes, which are obviously observed in their corresponding time-space diagrams. We also make a comparison of the results of a simple kind of mean-field approximation and the cellular automaton approach.