A multi-lane TASEP model for crossing pedestrian traffic flows

Abstract

A one-way 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 ofsize M × M. We consider hard core particles entering each street with an injection probabilityα. On the intersection square the hard core exclusion creates a many-body problem ofstrongly interacting TASEPs and we study the collective dynamics that arises. Weconstruct an efficient algorithm that allows for the simulation of streets of infinitelength, which have sharply defined critical jamming points. The algorithm employsthe ‘frozen shuffle update’, in which the randomly arriving particles have fullydeterministic bulk dynamics. High precision simulations for street widths up toM = 24 show thatwhen α increases, there occur jamming transitions at a sequence ofM critical values . As M grows, the principaltransition point αMM decreases roughly as ∼ (logM)−1 in the range of M values studied. We show that a suitable order parameter is provided by a reflectioncoefficient associated with the particle current in each TASEP.