  The asymmetric simple exclusion process (ASEP) with periodic boundary
conditions is investigated for shuffled dynamics. In this type of update, in
each discrete timestep the particles are updated in a random sequence. Such an
update is important for several applications, e.g. for certain models of
pedestrian flow in two dimensions. For the ASEP with shuffled dynamics and a
related truncated process exact results are obtained for deterministic motion
(p=1). Since the shuffled dynamics is intrinsically stochastic, also this case
is nontrivial. For the case of stochastic motion (0<p<1) it is shown that, in
contrast to all other updates studied previously, the ASEP with shuffled update
does not have a product measure steady state. Approximative formulas for the
steady state distribution and fundamental diagram are derived that are in very
good agreement with simulation data.
