  The collective motion of self-driven particles shows interesting novel
phenomena such as swarming and the emergence of patterns. We have recently
proposed a model for counterflowing particles that captures this idea and
exhibits clogging transitions. This model is based on a generalization of the
Fermi-Dirac statistics wherein the maximal occupation of a cell is used. Here
we present a detailed study comparing synchronous and asynchronous stochastic
dynamics within this model. We show that an asynchronous updating scheme
supports the mobile-clogging transition and eliminates some mobility anomalies
that are present in synchronous Monte Carlo simulations. Moreover, we show that
this transition is dependent upon its initial conditions. Although the Gini
coefficient was originally used to model wealth inequalities, we show that it
is also efficient for studying the mobile-clogging transition. Finally, we
compare our stochastic simulation with direct numerical integration of partial
differential equations used to describe this model.
