  We reinterpret and generalize conjectures of Lam and Williams as statements
about the stationary distribution of a multispecies exclusion process on the
ring. The central objects in our study are the multiline queues of Ferrari and
Martin. We make some progress on some of the conjectures in different
directions. First, we prove their conjectures in two special cases by
generalizing the rates of the Ferrari-Martin transitions. Secondly, we define a
new process on multiline queues, which have a certain minimality property. This
gives another proof for one of the special cases; namely arbitrary jump rates
for three species.
