Traffic dispersion and its mapping to one-sided ballistic deposition

We study the dispersion of vehicles induced by a noise on a single-lane highway under the open boundary. We present the time headway model (continuous-in time and integer-in space model) taking into account velocity fluctuation, where vehicles are updated sequentially. The characteristics of traffic dispersion are clarified. It is found that the vehicular traffic exhibits the scaling property. The traffic dispersion is compared with the one-sided ballistic deposition. The traffic model exhibits the same scaling behavior as the one-sided ballistic deposition model of random update. When vehicle i and arrival time ti(n) at position n correspond, respectively, to position (site) i and height h(i,n) at time n in the deposition model, the traffic model is mapped to the one-sided ballistic deposition model.