Delay of vehicle motion in traffic dynamics

We demonstrate that in the Optimal Velocity Model (OVM) delay times of vehi cles coming from the dynamical equation of motion of OVM explain the order of delay times observed in actual traffic flows without introducing explici t delay times. This implies that the explicit delay time is not important i n contrast to the traditional car following models, in which the explicit d elay time was thought to be essential to explain realistic traffic flow. Ef fective delay times in various cases are estimated: the case of a leader ve hicle and its follower, a queue of vehicles controlled by traffic lights an d the many-vehicle case of highway traffic flow. The remarkable result is t hat in most of the situation for which we can make a reasonable definition of an effective delay time, the obtained delay time is of order one second. This agrees with the observed data very well.