Admission control of an M/M/1 queue with multiple deterioration states

Properly controlled arrival process via accepting or rejecting arrivals can effectively reduce system congestion level. This paper finds the optimal admission control policy of an M/M/1 queue which is susceptible to a cumulative shock failure process. Assuming that the server is minimally repaired when it fails and can be preventively maintained at the end of each busy period, the optimal admission policy of this unreliable queue is proved to be of control-limit-type and the optimal admission control limit is such that the controller rejects more arrival when the state of the server deteriorates more.