Taking into account the startup behaviour of following vehicles in the waiting\narea of urban traffic signal, we propose an extended Nagel-Schreckenberg\nmodel for single-lane traffic flow, in which the dynamic behavior of each vehicle\ndepends on not only its own headway but also the headway of the immediately\npreceding one. The numerical simulation of the present model reproduces\nsome complicated nonlinear phenomena observed in real traffic\nsuch as free flow, ghostly blockage, synchronized flow and so on. For specific\nparameter combinations the flow-density relation of this model shows two\nmeta-stable branches near the transition density from free flow to wide moving\ntraffic jam. Finally, the analytical results of the model under some specific\nparameters are given by using the mean field theory.
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