We consider a two-station tandem queue loss model where customers arrive to station 1 according to a Poisson process. A gatekeeper who has complete knowledge of the number of customers at both stations decides to accept or reject each arrival. A costc1is incurred if a customer is rejected, while if an admitted customer finds that station 2 is full at the time of his service completion at station 1, he leaves the system and a costc2is incurred. Assuming exponential service times at both stations, an arbitrary but finite buffer size at station 1 and a buffer size of one at station 2, we show that the optimal admission control policy for minimizing the long-run average cost per unit time has a simple structure. Depending on the value ofc2compared to a threshold valuec*, it is optimal to admit a customer at the time of his arrival either only if the system is empty or as long as there is space at station 1. We also provide the closed-form expression ofc*, which depends on the service rates at both stations, the arrival rate andc1.
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