The cμ/θ rule

We consider a multi-class queueing system with customer abandonment. For class i, the holding cost per unit time, the service rate and the abandonment rate are denoted by ci, μi and θi, respectively. Our results show that under a manyserver fluid scaling and heavy traffic conditions, a routing policy that assigns non-preemptive priority to classes according to their index ciμi/θi, is asymptotically optimal for minimizing the overall long run average holding cost.