Intersection of two TASEP traffic lanes with frozen shuffle update

TL;DR

This paper analyzes two intersecting TASEP lanes with frozen shuffle update, revealing phase diagrams with free flow and jammed states, supported by analytical solutions and Monte Carlo simulations.

Contribution

It introduces an analytical framework for phase behavior in intersecting TASEP lanes with frozen shuffle update, extending understanding of traffic flow models.

Findings

Each lane can be in free flow or jammed state.

Phase diagram has four regions with boundaries depending on entry and exit probabilities.

Analytical predictions match Monte Carlo simulation results.

Abstract

Motivated by interest in pedestrian traffic we study two lanes (one-dimensional lattices) of length $L$ that intersect at a single site. Each lane is modeled by a TASEP (Totally Asymmetric Exclusion Process). The particles enter and leave lane $\sigma$ (where $\sigma=1,2$) with probabilities $\alpha_\sigma$ and $\beta_\sigma$, respectively. We employ the `frozen shuffle' update introduced in earlier work [C. Appert-Rolland et al, J. Stat. Mech. (2011) P07009], in which the particle positions are updated in a fixed random order. We find analytically that each lane may be in a `free flow' or in a `jammed' state. Hence the phase diagram in the domain $0\leq\alpha_1,\alpha_2\leq 1$ consists of four regions with boundaries depending on $\beta_1$ and $\beta_2$. The regions meet in a single point on the diagonal of the domain. Our analytical predictions for the phase boundaries as well as for the currents and densities in each phase are confirmed by Monte Carlo simulations.