Frozen shuffle update for an asymmetric exclusion process on a ring

C. Appert-Rolland (1) , J. Cividini (1) , H. J. Hilhorst (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique et Société [physics.soc-ph]

C. Appert-Rolland, J. Cividini, H. J. Hilhorst. Frozen shuffle update for an asymmetric exclusion process on a ring. Journal of Statistical Mechanics: Theory and Experiment, 2011, pp.P07009. ⟨10.1088/1742-5468/2011/07/P07009⟩. ⟨hal-00590468⟩