Optimal Staffing Policies to Stabilize Performance at Target Levels in Service Networks with Time-Varying Arrivals

这项研究的重点是开发、实施和评估新的有效策略，以设置大规模多服务器排队网络中的适当人员水平，这些网络配备了现实世界服务系统中常见的复杂特征。首先，服务系统的到达率通常随着时间的推移而变化很大，这不是标准排队模型所能考虑的。其次，等待的客户的遗弃会显著改变系统性能，这相当于患者在没有被护理人员看到的情况下离开，或者是呼叫者挂断了呼叫中心的电话。此外，经验数据表明，服务时间和放弃时间都不是指数分布的。最后，服务系统通常表现出复杂的网络结构，例如：(A)已接受服务但仍需要更多服务的客户的重试；以及(B)在多个设施之间的流动，如发生在医院的不同单元之间。尽管有大量的排队论文献，但这些特征的模型复杂性使得精确分析远远超出了现有方法的范围。为了应对这些挑战，本研究将开发具有上述现实特征的大规模排队网络的最优人员配置策略，旨在揭示基本原理，推进运筹学研究方法，设计有效的控制策略以更好地管理服务系统，并寻求将大规模转化为优势而不是劣势的有效近似。如果成功，本研究结果将为更好地设计和管理服务系统提供新的工具，特别是医疗保健系统。为了控制成本，许多医院严重人手不足；当资源(如护士和床位)不可避免地受到限制时，低效的人员配备战略可能会导致过度痛苦、低质量的护理、最终治疗结果的恶化和死亡率的显著增加。这项拟议的研究旨在帮助系统经理做出正确的操作决策；它将有助于回答以下问题：医院应该如何在下周的过程中为医生和护士配备工作人员，以便在治疗前的延误最多为一个小时？有多大比例的患者需要等待超过四个小时？这项研究也与许多其他应用相关，例如，客户联系中心；公共住房当局向低收入租户提供公寓；网络服务器场处理网页请求；以及金融后台处理贷款。教育外展将是这个项目的一个关键组成部分，因为研究人员对本科生和研究生的工程教育都有着深切的承诺。研究人员通过一系列暑期工作坊和夏令营，积极向K-12年级的学生介绍运筹学技术(特别强调排队理论)。这个项目的成果将被整合到调查员新的本科和研究生课程中。

This research is focused on the development, implementation, and evaluation of new and effective policies to set appropriate staffing levels in large-scale multiserver queuing networks that are equipped with complex features typically found in real-world service systems. First, arrival rates in service systems typically vary significantly over time, which is not accounted for by standard queuing models. Second, abandonment by waiting customers, which corresponds to patients leaving without being seen by a care provider, or to callers hanging up in a call center, can significantly alter system performance. In addition, empirical data show that neither service time nor abandonment time is exponentially distributed. Finally, service systems often exhibit complicated network structures, such as the following: (a) retrials by customers who have received service but still need more service; and (b) flows among multiple facilities, as occurring among different units in a hospital. Despite the immense queuing-theory literature, the model complexity of these features makes exact analysis far beyond the scope of existing methodologies. In response to these challenges, this research will develop optimal staffing strategies for large-scale queuing networks with all the above realistic features, aiming at uncovering fundamental principles, advancing operations research methodologies, devising effective control policies for better managing service systems, and seeking effective approximations that turn the large scale into an advantage instead of a disadvantage.If successful, the results of this research will provide new tools to better design and manage service systems, with special emphasis on healthcare systems. To contain costs, many hospitals are significantly understaffed; when resources (such as nurses and beds) are inevitably limited, inefficient staffing strategies can cause excessive suffering, low quality care, degradation of the ultimate treatment outcomes, and significant increases in mortality. The proposed research intends to help system managers make the right operational decisions; it will help answer questions such as: How should a hospital staff the doctors and nurses over the course of the next week so that the delays before treatments are at most one hour? What percentage of patients will have to wait more than four hours? This research is also relevant for many other applications, for example, customer contact centers; public housing authorities providing apartments to low-income tenants; web-server farms processing requests for web pages; and financial back offices processing loans. Education outreach will be a key component of this project, because the investigator shares a deep commitment to engineering education at both the undergraduate and graduate levels. The investigator has been active in introducing operations research techniques (with a special emphasis on queuing theory) to K-12 students through a series of summer workshops and camps. The results of this project will be integrated into the investigator's new undergraduate and graduate courses.