  We consider the exclusion process on segments of the integers in a
site-dependent random environment. We assume to be in the ballistic regime in
which a single particle has positive linear speed. Our goal is to study the
mixing time of the exclusion process when the number of particles is linear in
the size of the segment. We investigate the order of the mixing time depending
on the support of the environment distribution. In particular, we prove for
nestling environments that the order of the mixing time is different than in
the case of a single particle.
