Optimal control of queue in the $\mathrm{M\vert G}\vert1\vert\infty$ system with possibility of customer admission restriction

Consideration was given to optimization of the queue control strategy in the $\mathrm{M\vert G}\vert1\vert\infty$ queuing system where decision about continuing or stopping admission of customers is made at the service completion instants of each customer in compliance with the distribution on the set of decisions depending on the number of customers remaining in the system. The mean specific income in the stationary mode was used as the efficiency criterion, and the set of permissible strategies coincided with the set of homogeneous randomized Markov strategies. It was proved that if there exists an optimal strategy, then it is degenerate and threshold with one point of control switching, that is, if the number of customers in the system exceeds a certain level, then admission of customers must be stopped or, otherwise, it must be continued.