Queue-and-Idleness-Ratio Controls in Many-Server Service Systems

• 成果类型: Article
• 署名作者: Gurvich, Itay; Whitt, Ward
• 署名单位: Northwestern University; Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1080.0366
• 发表日期: 2009
• 页码: 363-396
• 关键词: heavy-traffic limits; scheduling flexible servers; convex delay costs; approximations; optimality; networks; centers

摘要

Motivated by call centers, we study large-scale service systems with multiple customer classes and multiple agent pools, each with many agents. We propose a family of routing rules called queue-and-idleness-ratio (QIR) rules. A newly available agent next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified state-dependent proportion of the total queue length. An arriving customer is routed to the agent pool whose idleness most exceeds a specified state-dependent proportion of the total idleness. We identify regularity conditions on the network structure and system parameters under which QIR produces an important state-space collapse (SSC) result in the quality-and-efficiency-driven (QED) many-server heavy-traffic limiting regime. The SSC result is applied here to prove stochastic-process limits and in subsequent papers to solve important staffing and control problems for large-scale service systems.