Asymmetric exclusion processes with shuffled dynamics

TL;DR

This paper investigates the ASEP with shuffled dynamics, revealing its unique non-product steady state and providing approximate formulas for its steady state distribution and flow characteristics.

Contribution

It introduces and analyzes the ASEP with shuffled update, a novel stochastic dynamic update, and derives approximate steady state and flow formulas.

Findings

ASEP with shuffled dynamics lacks a product measure steady state.

Exact results obtained for deterministic motion (p=1).

Approximate formulas match simulation data well.

Abstract

The asymmetric simple exclusion process (ASEP) with periodic boundary conditions is investigated for shuffled dynamics. In this type of update, in each discrete timestep the particles are updated in a random sequence. Such an update is important for several applications, e.g. for certain models of pedestrian flow in two dimensions. For the ASEP with shuffled dynamics and a related truncated process exact results are obtained for deterministic motion (p=1). Since the shuffled dynamics is intrinsically stochastic, also this case is nontrivial. For the case of stochastic motion (0<p<1) it is shown that, in contrast to all other updates studied previously, the ASEP with shuffled update does not have a product measure steady state. Approximative formulas for the steady state distribution and fundamental diagram are derived that are in very good agreement with simulation data.