Evidence of Non-Equilibrium Critical Phenomena in a Simple Model of Traffic

We present a novel approach to understand vehicular traffic jams by studying a simple model, Elementary Cellular Automaton Rule 184 (ECA 184). Using key traffic observables, such as the total delay and relaxation time, as well as microscopic measures like delays and lifetimes of individual jams, we show how these quantities can fully characterize the system's behavior, revealing features analogous to those of a continuous phase transition. We exploit specific properties of ECA 184 to develop an efficient algorithm for calculating these observables numerically and introduce an auxiliary quantity, termed ''elementary jams'', which allows us to determine these observables. We discuss the implications of our results, highlighting connections to a potential field-theoretic description of traffic and suggest future application of these methods to more complex models. Supporting code can be found on: https://github.com/Aryaman-Jha/ECA_184_Critical