Asymptotically Optimal Controls for Time-Inhomogeneous Networks

A framework is introduced for the identification of controls for single-class timevarying queueing networks that are asymptotically optimal in the so-called uniform acceleration regime. A related, but simpler, first-order (or fluid) control problem is first formulated and, for a class of performance measures that satisfy a certain continuity property, it is then shown that any policy that is optimal for the fluid control problem is asymptotically optimal for the original network problem. Examples of performance measures with this property are presented, and simulations implementing proposed asymptotically optimal policies are presented. The use of directional derivatives of the reflection map for solving fluid optimal control problems is also illustrated. This work serves to complement a large body of literature on asymptotically optimal controls for time-homogeneous networks.