The cμ/θ Rule for Many-Server Queues with Abandonment
The cμ/θ Rule for Many-Server Queues with Abandonment
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DOI：
10.1287/opre.1100.0826
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发表时间：
2010-09-01
影响因子：
2.7
通讯作者：
Shimkin, Nahum
中科院分区：
文献类型：
--
作者：
Atar, Rami;Giat, Chanit;Shimkin, Nahum
我们考虑了一个多类服务器和客户放弃的多类排队系统。对于每个客户类别i，每单位时间的保持成本、服务率和放弃率分别由c（i）、mu（i）和theta（i）表示。我们证明了在多服务器流体缩放和过载条件下，服务器调度策略，分配优先级的类，根据他们的索引c（i）mu（i）/theta（i）是渐近最优的总的长期平均持有成本最小化。一个额外的惩罚客户放弃很容易被纳入这个模型，并导致类似的指数规则。
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), mu(i), and theta(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)mu(i)/theta(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.