Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing

• 成果类型: Article
• 署名作者: Huang, Junfei; Mandelbaum, Avishai; Zhang, Hanqin; Zhang, Jiheng
• 署名单位: Chinese University of Hong Kong; Technion Israel Institute of Technology; National University of Singapore; Hong Kong University of Science & Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1619
• 发表日期: 2017
• 页码: 1380-1397
• 关键词: many-server queues; fluid models; impatient customers; call center; ABANDONMENT; PERSPECTIVE; diffusion; systems; IMPACT; LIMITS

摘要

Data has revealed a noticeable Impact of delay-time-related information on phone-customers; for example and somewhat surprisingly, delay announcements can abruptly increase the likelihood to abandon (hang up). Our starting point is that the latter phenomena can be used to support the control of queue lengths and delays. We do so by timing the announcements appropriately and determining the staffing levels accordingly. To this end, we model a service system as an overloaded GI/M/s+GI queue, in which we seek to minimize the number of servers, s, subject to quality-of-service constraints (e.g., fraction abandoning), while accounting for the instantaneous (hence discontinuous) impact of an announcement on the distribution (hazard rate) of customer patience. For tractability, our analysis is asymptotic as s increases indefinitely, and it is naturally efficiency-driven (namely the servers are highly busy, and hence essentially all customers are delayed in queue prior to service). This requires one to go beyond existing theory, which turns out to be too crude for our needs (e.g., it requires a continuous hazard rate of impatience and hence cannot be applied). We thus develop a refined process and steady-state models, and use them to solve our minimization problem and more. The value and accuracy of our models are demonstrated via extensive numerical experiments.