Congestion control as a stochastic control problem with action delays

We consider the design of explicit rate-based congestion control for high-speed communication networks and show that this can be formulated as a stochastic control problem where the controls of different users enter the system dynamics with different delays. We discuss the existence, derivation and the structure of the optimal controller, as well as of suboptimal controllers of the certainty-equivalent type — a terminology that is precisely defined in the paper for the specific context of the congestion control problem considered. We consider, in particular, two certainty-equivalent controllers which are easy to implement, and show that they are stabilizing, i.e., they lead to bounded infinite-horizon average cost, and stable queue dynamics. Further, these controllers perform well in simulations.