Optimization of Two-Phase Queuing System and Its Application to the Control of Data Transmission between Two Robotic Agents

A tandem queuing system that contains two single-channel stations with finite buffers and allows blocking of the first server is considered. The first station receives nonstationary Poisson packet flow that is processed at a controlled rate. In the case of the queue overflow in the first system, the input packet is lost. The second station does not allow overflow due to control of the acceptance probability (a decrease in such a probability leads to slowing of packet sending from the first station). The queuing system is described with the aid of the controlled Markov process. The optimal control problem is considered over a finite time horizon using the criterion of minimum average losses under the constraints on the total service time and energy consumption of the first station. Optimization algorithms are proposed for synthesis of the control law for nonstationary data flow in two-agent robotic system.