Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems

• 成果类型: Article
• 署名作者: Gurvich, Itay; Whitt, Ward
• 署名单位: Columbia University; Columbia University
• 刊物名称: M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT
• ISSN/ISSBN: 1523-4614
• DOI: 10.1287/msom.1070.0211
• 发表日期: 2009
• 页码: 237-253
• 关键词: Queues; many-server queues; heavy-traffic limits for queues; Service Systems; cost minimization in many-server queues; skill-based routing; generalized-c mu rule; queue-and-idleness-ratio control

摘要

In a recent paper we introduced the queue-and-idleness ratio (QIR) family of routing rules for many-server service systems with multiple customer classes and server pools. A newly available server serves the customer from the head of the queue of the class (from among those the server is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. Under fairly general conditions, QIR produces an important state-space collapse as the total arrival rate and the numbers of servers increase in a coordinated way. That state-space collapse was previously used to delicately balance service levels for the different customer classes. In this sequel, we show that a special version of QIR stochastically minimizes convex holding costs in a finite-horizon setting when the service rates are restricted to be pool dependent. Under additional regularity conditions, the special version of QIR reduces to a simple policy: linear costs produce a priority-type rule, in which the least-cost customers are given low priority. Strictly convex costs (plus other regularity conditions) produce a many-server analogue of the generalized-c mu (Gc mu) rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.