First-passage processes in a deterministic one-dimensional cellular automaton model of traffic flow (opens in new tab)

We present analytical results for first-passage processes in a deterministic one-dimensional cellular automaton (CA) model of traffic flow. Starting at time $t=0$ from a random initial state with car density p, at every time step $t\ge 1$ each car moves one step to the right if the cell on its right is empty, and is stopped if it is occupied by another car. The model, which coincides with CA rule 184 in Wolfram's numbering scheme, exhibits a con...