Performance Analysis of a Queue with Congestion-Based Staffing Policy

• 成果类型: Article
• 署名作者: Zhang, Zhe George
• 署名单位: Western Washington University; Simon Fraser University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1080.0914
• 发表日期: 2009
• 页码: 240-251
• 关键词: congestion-based staffing; matrix-geometric solution; regeneration cycle; fluid limits approximation; Markovian queues; (e; n; N) policy; border-crossing station

摘要

This paper analyzes a waiting line system that is motivated by the operations of border-crossing stations between the United States and Canada. There are two main conflicting goals in such a system: high security level, which often leads to a longer line; and good customer service, which requires a shorter line. Thus, unlike other queueing systems, maintaining the average queue length within a certain range is the primary objective. This is achieved using a staffing policy, called congestion-based staffing, or CBS, where the number of servers (inspection booths) is adjusted according to the queue length during a planning period. We first present an exact benchmark model of Markovian type based on the matrix-geometric solution. For practical CBS policies, we develop a set of closed-form formulas for the major performance measures based on regenerative cycle analysis and fluid limit approximation. Numerical examples show that these approximation formulas are simple, accurate, and robust for practitioners to use in designing CBS policies.