  For a multiclass G/G/1 queue with finite buffers, admission and scheduling
control, and holding and rejection costs, we construct a policy that is
asymptotically optimal in the heavy traffic limit. The policy is specified in
terms of a single parameter which constitutes the free boundary point from the
Harrison-Taksar free boundary problem, but otherwise depends "explicitly" on
the problem data. The c mu priority rule is also used by the policy, but in a
way that is novel, and, in particular, different than that used in problems
with infinite buffers. We also address an analogous problem where buffer
constraints are replaced by throughput time constraints.
