Customer Abandonment in Many-Server Queues

• 成果类型: Article
• 署名作者: Dai, J. G.; He, Shuangchi
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1100.0443
• 发表日期: 2010
• 页码: 347-362
• 关键词: impatient customers

摘要

We study G/G/n + GI queues in which customer patience times are independent, identically distributed following a general distribution. When a customer's waiting time in queue exceeds his patience time, the customer abandons the system without service. For the performance of such a system, we focus on the abandonment process and the queue length process. We prove that under some conditions, a deterministic relationship between the two stochastic processes holds asymptotically under the diffusion scaling when the number of servers n goes to infinity. These conditions include a minor assumption on the arrival processes that can be time-nonhomogeneous and a key assumption that the sequence of diffusion-scaled queue length processes, indexed by n, is stochastically bounded. We also establish a comparison result that allows one to verify the stochastic boundedness by studying a corresponding sequence of systems without customer abandonment.