Agent-based modelling and simulation of urban evacuation: relative effectiveness of simultaneous and staged evacuation strategies

We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic jams with a power law distribution \(P(t) \sim t^{-3/2}\) of lifetimes, \(t\). On varying the vehicle density in a closed system, this critical state separates lamellar and jammed regimes, and exhibits \(1/f\) noise in the power spectrum. Using random walk arguments, in conjunction with a cascade equation, we develop a phenomenological theory that predicts the critical exponents for this transition and explains the self-organizing behavior. These predictions are consistent with all of our numerical results.