A multi-lane TASEP model for crossing pedestrian traffic flows

TL;DR

This paper models crossing pedestrian traffic flows using a multi-lane TASEP framework, revealing jamming transitions at critical injection probabilities and analyzing how these transitions depend on street width.

Contribution

It introduces an efficient simulation algorithm for multi-lane TASEPs with infinite length and characterizes the critical jamming points as street width increases.

Findings

Jamming transitions occur at specific critical injection probabilities.

Critical points decrease roughly as 1/(log M) with increasing street width.

Reflection coefficient serves as an effective order parameter for jamming.

Abstract

A one-way {\em street} of width M is modeled as a set of M parallel one-dimensional TASEPs. The intersection of two perpendicular streets is a square lattice of size M times M. We consider hard core particles entering each street with an injection probability \alpha. On the intersection square the hard core exclusion creates a many-body problem of strongly interacting TASEPs and we study the collective dynamics that arises. We construct an efficient algorithm that allows for the simulation of streets of infinite length, which have sharply defined critical jamming points. The algorithm employs the `frozen shuffle update', in which the randomly arriving particles have fully deterministic bulk dynamics. High precision simulations for street widths up to M=24 show that when \alpha increases, there occur jamming transitions at a sequence of M critical values \alphaM,M < \alphaM,M-1 < ... < \alphaM,1. As M grows, the principal transition point \alphaM,M decreases roughly as \sim 1/(log M) in the range of M values studied. We show that a suitable order parameter is provided by a reflection coefficient associated with the particle current in each TASEP.