Optimal control of M/M/1 queueing system with constant retrial rate and non-reliable removable server

The paper is concerned with the optimal control with respect to N-policy of the M/M/1 queue with constant retrial rate and non-reliable removable server. According to the N-policy, the server can start service only when the number of customers in the system reaches level N (N ¿ 1). We perform a steady-state analysis of the corresponding continuous-time Markov chain and calculate optimal threshold level to minimize the long-run average losses given cost structure.