Thecμ/θRule for Many-Server Queues with Abandonment
Rami Atar, Chanit Giat, Nahum Shimkin
Operations Research · 2010 · Volume 58 · Issue 5
Abstract
We consider a multiclass queueing system with multiple homogeneous servers and customer abandonment. For each customer class i , the holding cost per unit time, the service rate, and the abandonment rate are denoted by c i , μ i , and θ i , respectively. We prove that under a many-server fluid scaling and overload conditions, a server-scheduling policy that assigns priority to classes according to their index c i μ i / θ i is asymptotically optimal for minimizing the overall long-run average holding cost. An additional penalty on customer abandonment is easily incorporated into this model and leads to a similar index rule.
Keywords
multiclass queue, customer abandonment, fluid limits
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