A cellular automaton model for two-lane traffic

We present some long time limit properties of a cellular automaton that mod els traffic of cars on a (infinite) two-lane road. This model, called TL184 , is a natural generalization of the cellular automaton classified as 184 b y Wolfram (to be abbreviated by CA184) and studied before as a model for on e-lane traffic. TL184 models cars' motions on each lane by particles that i nteract via the CA184 rules. and cars' lane changes by a possibility for pa rticles to flip from one CA184 to another. We calculate the infinite-time l imit of the particle current in TL184, starting from a translation invarian t 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 correspondin g model of two non-interacting one-lane roads. We provide examples which de monstrate that even though the rules that regulate lane changes are complet ely symmetric, the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution; moreover, the a symptotic car velocities and currents may be different on different lanes. We also show that, for a particular class of initial distributions. the asy mptotic car density on a lane may be a non-monotonic function of the initia l car density on this lane. Finally, we derive the current-density relation for an extended continuous-time version of TL 184 with asymmetric lane-cha nging rules.