Frozen shuffle update for an asymmetric exclusion process on a ring

TL;DR

This paper introduces a new pedestrian traffic model on a ring using a fixed update order, analyzing phase transitions from free flow to jammed flow through analytical and simulation methods.

Contribution

It proposes a novel update rule for TASEP with fixed pedestrian order and provides analytical predictions for phase transition behavior and finite size effects.

Findings

Identified a critical density for phase transition from free flow to jammed flow.

Derived the current-density diagram analytically for the infinite system.

Determined the scaling function for finite size rounding at the transition.

Abstract

We introduce a new rule of motion for a totally asymmetric exclusion process (TASEP) representing pedestrian traffic on a lattice. Its characteristic feature is that the positions of the pedestrians, modeled as hard-core particles, are updated in a fixed predefined order, determined by a phase attached to each of them. We investigate this model analytically and by Monte Carlo simulation on a one-dimensional lattice with periodic boundary conditions. At a critical value of the particle density a transition occurs from a phase with `free flow' to one with `jammed flow'. We are able to analytically predict the current-density diagram for the infinite system and to find the scaling function that describes the finite size rounding at the transition point.