A short note on the Poisson input queuing system with start-up time and under control-operating policy

The control policy for the M/G/1 queuing system in which the server is started-up when the accumulated number of customers reaches a predetermined value m and serves the system until it is empty. The time required to start up the server follows a general distribution. The mean waiting time of an arbitrary customer for a given value of m is derived and the optimal control policy is presented under a linear cost structure.