Optimal admission control for tandem queues with loss

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 cost c1 is 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 cost c2 is 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 of c2 compared to a threshold value c, 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 of c, which depends on the service rates at both stations, the arrival rate and c 1. © 2012 IEEE.