A new framework for solving dynamic scheduling games

Optimum scheduling is a key objective in many communications systems where different users have to share a common resource. Typically, centralized implementations are capable of guaranteeing certain fairness. In our approach, we follow a different path modeling the scheduling process as a dynamic infinite horizon discrete-time game. This formulation allows us to include any kind of dynamics and distributed implementations. Despite, these games are very difficult to solve, we are able to show that they are in fact dynamic potential games equivalent to a non-stationary multivariate optimum control problem. The dynamic control problem is solved via an augmented Bellman equation including time as an extra state.