  We propose a simple microscopic model for arching phenomena at bottlenecks.
The dynamics of particles in front of a bottleneck is described by a
one-dimensional stochastic cellular automaton on a semicircular geometry. The
model reproduces oscillation phenomena due to formation and collapsing of
arches. It predicts the existence of a critical bottleneck size for continuous
particle flows. The dependence of the jamming probability on the system size is
approximated by the Gompertz function. The analytical results are in good
agreement with simulations.
