A Cellular Automaton Model for Two-Lane Traffic

We present some long time limit properties of a cellular automaton that models traffic of cars on a (infinite) two-lane road. This model, called TL184, is a natural generalization of the cellular automaton classified as 184 by Wolfram (to be abbreviated by CA184) and studied before as a model for one-lane traffic. TL184 models cars' motions on each lane by particles that interact via the CA184 rules, and cars' lane changes by a possibility for particles to flip from one CA184 to another. We calculate the infinite-time limit of the particle current in TL184, starting from a translation invariant measure, and use this result to show how the possibility of lane changes may enhance the current of cars in TL184 compared to that in a corresponding model of two non-interacting one-lane roads. We provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric, the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution; moreover, the asymptotic car velocities and currents may be different on different lanes. We also show that, for a particular class of initial distributions, the asymptotic car density on a lane may be a non-monotonic function of the initial car density on this lane. Finally, we derive the current-density relation for an extended continuous-time version of TL184 with asymmetric lane-changing rules.