Control of connected Markov chains. Application to congestion avoidance in the Internet

The article considers the optimal control for the system of finite number of controlled connected Markov chains (CMC). Such models come from queuing systems with many service lines and/or from the control of resources of multiple connected dams. The state of such CMC is represented as a tensor of the depth d; where d is the number of controlled chains. This tensor form is much more convenient for derivation of the dynamic programming equation. We give a tensor form for the control problems arising in the router control which is aimed to the congestion avoidance with the aid of two telecommunication lines having different properties and cost of services.