A steady-state analysis of optimal threshold policy with heterogeneous arrivals to the M/G/1 queue

An M/G/1 queue with general server setup time under a control policy is studied. We consider the case when the arrival rate varies according to the serverʹs status: idle, setup and busy states. For this model, the optimal N-value from which the server starts his setup is found by minimizing the total operation cost of the system.