Queuing transitions in the asymmetric simple exclusion process

Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling properties. Below the transition, the traffic jam is macroscopic in the sense that the length of the queue scales linearly with system size. Above the transition, only a power-law shaped queue remains. Its density profile scales as $\delta \rho\sim x^{-\nu}$ with $\nu={1/3}$, and $x$ is the distance from the obstacle. We construct a heuristic argument, indicating that the exponent $\nu={1/3}$ is universal and independent of the dynamic exponent of the underlying…