About the problem of profit maximization in $G/M/1$ queuing systems with threshold control of the queue

The problem of maximizing the average profit per time in $G/M/1$ queuing systems is considered on the set of stationary access restriction threshold strategies with one “switch point”. Profit is defined as the following measures: service fee; hardware maintenance fee; fine for service delay; fine for unhandled requests; and fine for system idle. The authors formulated the necessary and sufficient conditions for optimality of the finite threshold value. The authors developed a method of sequential descent to the optimal threshold. The authors proposed an algorithm for calculating the optimal threshold value and the corresponding value of the objective function.