In this paper, two different kinds of (N, T )-policies for an M/M/m queueing system are studied. The system operates only intermittently and is shut down when no customers are present any more. A fixed setup cost of K > 0 is incurred each time the system is reopened. Also, a holding cost of h > 0 per unit time is incurred for each customer present. The two (N, T )policies studied for this queueing system with cost structures are as follows: (1) The system is reactivated as soon as N customers are present or the waiting time of the leading customer reaches a predefined time T , and (2) the system is reactivated as soon as N customers are present or the time units after the end of the last busy period reaches a predefined time T . The equations satisfied by the optimal policy (N * , T * ) for minimizing the long-run average cost per unit time in both cases are obtained. Particularly, we obtain the explicit optimal joint policy (N * , T * ) and optimal objective value for the case of a single server, the explicit optimal policy N * and optimal objective value for the case of multiple servers when only predefined customers number N is measured, and the explicit optimal policy T * and optimal objective value for the case of multiple servers when only predefined time units T is measured, respectively. These results partly extend (1) the classic N or T policy to a more practical (N, T )-policy and (2) the conclusions obtained for single server system to a system consisting of m (m โฅ 1) servers.