As for M/G/1 queueing system, we use various control policies, with which we can optimize the system. Up to now the most widely adopted policies are N-Policy, T-Policy, D-Policy, and so on. The existing researches are largely concerned to find an optimal operation condition or to optimize the system under single policy in M/G/1 system. There are, however, few literatures dealing with multiple control policies at once to enhance the flexibility of the model. In this study, we consider M/G/1 system adopting N-Policy and T-Policy simultaneously. If one of two conditions is satisfied, then, the server starts the service. We call this Min(N,T)-Policy. We find the probability distribution of the number of customers and mean waiting time in steady state and derive a cost function. Next, we seek the $N^*$, optimal threshold under various N values. Finally, we reveal the characteristics of cost function.