On the asymptotic optimality of the cμ/θ rule under ergodic cost

摘要

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 μ_i, and abandonment occurs at rate θ_i. In a many-server fluid regime, we show that prioritizing the classes in decreasing order of c_iμ_i/θ_i asymptotically minimizes an ergodic holding cost, where c_i denotes the equivalent holding cost per unit time for class i.