The cμ/θ Rule for Many-Server Queues with Abandonment

• 成果类型: Article
• 署名作者: Atar, Rami; Giat, Chanit; Shimkin, Nahum
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1100.0826
• 发表日期: 2010
• 页码: 1427-1439
• 关键词: Asymptotic Optimality; call center; mu-rule; approximations; COSTS

摘要

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.