Profit maximization in $G/M/1$ queuing system on a set of threshold strategies with two switch points

The problem of maximizing the average profit per time in $G/M/1$ queuing system is considered on a set of stationary access restriction threshold strategies with one “switch point”. The objective function depends on the following measures: service fee, hardware maintenance fee, cost of service delay, fine for unhandled requests, and fine for system idle. The authors have formulated the necessary conditions of existence of finite problem solution on a subset of threshold strategies with fixed distance between the upper and lower thresholds and have got necessary and sufficient conditions for optimality of threshold strategy on this subset. The authors have also developed a method of finding the optimal strategy and algorithm for calculating the parameters of the optimal strategy and the corresponding value of the objective function.