Queueing system with processor sharing and limited memory under control of the AQM mechanism

Consideration was given to the queueing system with processor sharing and limited memory which services random-capacity customers whose lengths depend on their capacities. The system performs the algorithm of active queue management, that is, at the instant of its arrival each customer can be rejected and dropped with a probability depending on the customer capacity and the total capacity of other customers sojourning in the system even if there is a free memory space available. The stationary distribution of the number of customers and the loss probability were determined for the system under consideration.