On the asymptotic optimality of the c mu/theta rule under ergodic cost
We consider an overloaded multi-server multi-class queueing model where customers may abandon while waiting to be served. For class i, service is provided at rate mu (i) , and abandonment occurs at rate theta (i) . In a many-server fluid regime, we show that prioritizing the classes in decreasing order of c (i) mu (i) /theta (i) asymptotically minimizes an ergodic holding cost, where c (i) denotes the equivalent holding cost per unit time for class i.
asymptotic optimality ergodic cost multi-class queues queues with abandonment fluid limits