Traffic dispersion induced by noise in off-lattice model

We study the dispersion of vehicles induced by speed fluctuation on a single-lane highway under open boundary. We extend the cellular automaton model on one-dimensional lattice to the real-variable model on off-lattice (continuous-in space model) in order to take into account the fluctuation of vehicular speed. Vehicles extend over the highway when moving forward. The characteristics of traffic dispersion are derived. It is shown that vehicular traffic exhibits scaling property. When a vehicle accelerates for following the vehicle ahead, vehicles move forming a cluster without dispersion. The relationship between the width of vehicular cluster and acceleration rate is clarified.