Analysis and Control of Large-scale Service Systems

这个研究项目的目标是对大型服务系统（如客户呼叫中心和医院）的近乎最佳管理产生见解。在到达时间、服务时间和客户行为的现实假设下，它将通过分析和数值工具来帮助确定满足某些性能约束的资源数量。对于具有一般服务和耐心时间分布的多服务器队列，模拟大型呼叫中心，(i) PI将在常规和危险率扩展的多服务器大流量下建立测量值扩散限制。（ii）利用这些限制，PI将为大规模系统的服务和耐心时间分布的敏感性提供关键见解。PI将开发一种数值算法来计算扩散极限的平稳分布；该算法的关键在于具有鲁棒的参考密度。PI将建立放弃过程和队列长度过程之间的渐近关系；这些关系对于提供一个模块化的、连续映射的方法来证明扩散极限是必不可少的；他们还提出了零耐心时间密度的统计估计，这是一个关键的系统参数。对于医院操作，PI提出了一种新的多服务器队列模型，其服务时间与患者出院分布密切相关；假定放电时间为独立同分布（IID），因此服务时间不为IID。对于大型客户呼叫中心，客户期望要求保持适当的人员水平，以便只有一小部分到中等比例的客户放弃该系统。对于医院来说，保持一定的服务水平是很重要的；例如，对于从急诊科转到住院部的病人来说，只有一小部分床位要求需要等待6个小时或更长时间。呼叫中心模型的研究将对统计分布的作用有一个清晰的认识，当呼叫中心在一个现实的参数体系中运行时；它将为可靠和有效地估计系统参数提供见解。医院模型研究为床位容量管理和接近最优的出院分配提供了关键见解，克服了许多挑战，包括(a)到达过程具有周期性到达率，(b)服务时间不确定，(c)服务器数量很大，(d)由于一般分布假设而没有有限维马尔可夫表示，以及(c)与到达率的时间变化相比，服务时间非常长。

This objective of this research project is to generate insights into near-optimal management of large-scale service systems such as customer call centers and hospitals. It will over analytical and numerical tools that help determine the amount of resource to meet certain performance constraints, under realistic assumptions on arrival times, service times, and customer behaviors. For a many-server queue with general service and patience time distributions that models a large-scale call center, (i) the PI will establish measure-valued diffusion limits under both the conventional and the hazard-rate scaling many-server heavy traffic. (ii) Using these limits, the PI will provide key insights into the sensitivity of service and patience time distributions for large-scale systems. (iii) The PI will develop a numerical algorithm to compute the stationary distribution of a diffusion limit; the key of the algorithm is to and a robust reference density. (iv) The PI will establish asymptotic relationships between abandonment processes and queue length processes; these relationships are essential to provide a modularized, continuous-mapping approach to proving diffusion limits; they also suggest statistical estimators for the patience time density at zero, a key system parameter. For hospital operations, the PI proposes a novel many-server queue model whose service times are critically linked to a patient discharge distribution; the discharge times are assumed to be independent, identically distributed (IID), and consequently the service times are not IID.For a large-scale customer call center, customer expectation demands that a proper staffng level be maintained so that only a small to moderate fraction of customers abandon the system. For a hospital, it is important to maintain certain service levels; for example, for patients who are transferred from the emergency department to inpatient beds, only a small fraction of bed-requests have to wait six hours or longer. The call center model research will create a sharp understanding on the role of statistical distributions when the center is operating in a ealistic parameter regime; it will provide insights into estimating system parameters reliably and efficiently. The hospital model research promises key insights into bed-capacity management and near-optimal discharge distribution, overcoming many challenges including (a) the arrival process has a periodic arrival rate, (b) the service times are not iid, (c) the number of servers is large, (d) there is no finite-dimensional Markovian representation due to general distributional assumptions, and (c) extremely long service times, compared with the time-variations of the arrival rate.