Frozen shuffle update for an asymmetric exclusion process with open boundary conditions

TL;DR

This paper introduces a new pedestrian traffic modeling algorithm using a frozen shuffle update for asymmetric exclusion processes with open boundaries, predicting phase transitions and density profiles.

Contribution

The paper presents a novel update algorithm suitable for pedestrian traffic modeling and analytically predicts phase diagrams and density profiles under open boundary conditions.

Findings

Phase diagram with free flow and jammed phases predicted analytically.

Density profiles match Monte Carlo simulations near transition points.

Algorithm effectively models pedestrian dynamics with open boundaries.

Abstract

We introduce a new update algorithm for exclusion processes, more suitable for the modeling of pedestrian traffic. Pedestrians are modeled as hard-core particles hopping on a discrete lattice, and are updated in a fixed order, determined by a phase attached to each pedestrian. While the case of periodic boundary conditions was studied in a companion paper, we consider here the case of open boundary conditions. The full phase diagram is predicted analytically and exhibits a transition between a free flow phase and a jammed phase. The density profile is predicted in the frame of a domain wall theory, and compared to Monte Carlo simulations, in particular in the vicinity of the transition.