The threshold strategy for restricting access in the $M/D/1$ queueing system with penalty function for late service

The paper considers the problem of optimizing the access control on a set of dynamic threshold strategies in an $M/D/1$ system. If the number of concurrent requests in a system is more than the threshold, then the system stops accepting requests. If the number of requests is less or equal to this value, then the system resumes accepting requests. As a target function, the average value of the marginal revenue obtained per time unit in the stationary mode is used. It is assumed that the system receives a fixed fee for each accepted request and pays a fixed penalty for each overdue service of a request. The system does not receive a fee and does not pay a penalty for each rejected request. Estimates of the optimal value of the target function and the optimal threshold value are obtained.