  The paper studies a single-server queueing system with autonomous service and
$\ell$ priority classes. Arrival and departure processes are governed by marked
point processes. There are $\ell$ buffers corresponding to priority classes,
and upon arrival a unit of the $k$th priority class occupies a place in the
$k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total
$k$th buffer content. The values $N^{(k)}$ are assumed to be large, and
queueing systems both with finite and infinite buffers are studied. In the case
of a system with finite buffers, the values $N^{(k)}$ characterize buffer
capacities.
  The paper discusses a circle of problems related to optimization of
performance measures associated with overflowing the quota of buffer contents
in particular buffers models. Our approach to this problem is new, and the
presentation of our results is simple and clear for real applications.
