Optimal Admission Control for Tandem
Queues with Loss
Bo Zhang and Hayriye Ayhan
H. Milton Stewart School of Industrial and Systems Engineering
Georgia Institute of Technology, Atlanta, GA 30332-0205, U.S.A
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 c1.