Approximations for Chat Service Systems Using Many-Server Diffusion Limits

• 成果类型: Article
• 署名作者: Cui, Leon; Tezcan, Tolga
• 署名单位: State University of New York (SUNY) System; Binghamton University, SUNY; University of London; London Business School
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0754
• 发表日期: 2016
• 页码: 775-807
• 关键词: heavy-traffic limits; state-space collapse; halfin

摘要

We study a queueing model of customer service chat systems. A unique feature of these queueing systems is that a single agent can serve multiple customers simultaneously. We prove the convergence of the queueing process to different diffusion processes in a many-server heavy-traffic regime in three different cases. Using this result, we are able to offer approximations for the steady-state performance measures such as the number of customers in the system, the abandonment probability, and the sojourn time of a customer. Our numerical experiments show that proposed approximations are accurate in various cases.