Analysis and optimization of a controlled model for a closed queueing network

We consider a closed network consisting of two queuing systems: the main system simulates a packet transmission queue over an unreliable communication channel, and the auxiliary multiserver system contains lost packets for resending. The service rate in the main system is controllable and is supposed to be optimized with the aim of minimizing the time of successful transmission, taking into account the cost of using network resources. We obtain optimality conditions in two cases: 1) in the model based on fluid approximation in the presence of heavy load; 2) in the steady state using stationary strategies.