Optimal Routing in Output-Queued Flexible Server Systems

We consider a queueing system with multi-type customers and non-homogeneous flexible servers, in the heavy traffic asymptotic regime and under a complete resource pooling (CRP) condition. For the input-queued (IQ) version of such a system (with customers being queued at the system "entrance", one queue per each type), it was shown in [12] that a simple parsimonious Gcmu scheduling rule is optimal in that it asymptotically minimizes the system customer workload and some strictly convex queueing costs. In this paper we consider a different - output-queued (OQ) - version of the model, where each arriving customer must be assigned to one of the servers immediately upon arrival.