We consider the problem of admission control to a multiserver finite
buffer queue under partial information. The controller cannot see the
queue but is informed immediately if an admitted customer is lost due to
buffer overflow. Turning away (i.e., blocking) customers is costly and so
is losing an admitted customer. The latter cost is greater than that of
blocking. The controller's objective is to minimize the average cost
of blocking and rejection per incoming customer. Lin and Ross  studied this problem for multiserver loss
systems. We extend their work by allowing a finite buffer and the arrival
process to be of the renewal type. We propose a control policy based on a
novel state aggregation approach that exploits the regenerative structure
of the system, performs well, and gives a lower bound on the optimal cost.
The control policy is inspired by a simulation technique that reduces the
variance of the estimators by not simulating the customer service process.
Numerical experiments show that our bound varies with the load offered to
the system and is typically within 1% and 10% of the optimal cost. Also,
our bound is tight in the important case when the cost of blocking is low
compared to the cost of rejection and the load offered to the system is
high. The quality of the bound degrades with the degree of state
aggregation, but the computational effort is comparatively small.
Moreover, the control policies that we obtain perform better compared to a
heuristic suggested by Lin and Ross. The state aggregation technique
developed in this article can be used more generally to solve problems in
which the objective is to control the time to the end of a cycle and the
quality of the information available to the controller degrades with the
length of the cycle.