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arXiv · 1107.5166

Intersection of two TASEP traffic lanes with frozen shuffle update

C. Appert-Rolland·J. Cividini·H. J. Hilhorst
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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 $σ$ (where $σ=1,2$) with probabilities $α_σ$ and $β_σ$, 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 $0\leqα_1,α_2\leq 1$ consists of four regions with boundaries depending on $β_1$ and $β_2$. 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.

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C. Appert-Rolland, J. Cividini, H. J. Hilhorst. 2011-07-26. Intersection of two TASEP traffic lanes with frozen shuffle update. https://doi.org/10.1088/1742-5468%2F2011%2F10%2Fp10014

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