Admission control with incomplete information of a queueing system

We consider a multiple-server loss model where customers arrive at a gatekeeper according to a Poisson process. A cost c is incurred if a new arrival is blocked from entering the system by the gatekeeper, while a larger cost K is incurred if an admitted customer finds all servers busy and therefore has to leave the system. The key assumption is that the gatekeeper is informed when an admitted customer finds all servers busy, but is not informed when served customers depart. Assuming an exponential service distribution, we show that, in the case of a single server. a threshold-type policy that blocks for a certain amount of time after a new arrival is admitted is optimal. When there are multiple servers, we propose two types of heuristic policies. We analytically compute the best policy of the first type, and use simulation to estimate that of the other.