  A multi-species generalization of the Asymmetric Simple Exclusion Process
(ASEP) has been considered in the presence of a single impurity on a ring. The
model describes particles hopping in one direction with stochastic dynamics and
hard core exclusion condition. The ordinary particles hop forward with their
characteristic hopping rates and fast particles can overtake slow ones with a
relative rate. The impurity, which is the slowest particle in the ensemble of
particles on the ring, hops in the same direction of the ordinary particles
with its intrinsic hopping rate and can be overtaken by ordinary particles with
a rate which is not necessarily a relative rate. We will show that the phase
diagram of the model can be obtained exactly. It turns out that the phase
structure of the model depends on the density distribution function of the
ordinary particles on the ring so that it can have either four phases or only
one. The mean speed of impurity and also the total current of the ordinary
particles are explicitly calculated in each phase. Using Monte Carlo
simulation, the density profile of the ordinary particles is also obtained. The
simulation data confirm all of the analytical calculations.
