Analysis and Control of Large-scale Service Systems

大型服务系统分析与控制

• 批准号: 1030589
• 负责人: Jiangang Dai
• 金额: $ 26万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1030589&HistoricalAwards=false
• 关键词: Analysis; Control; Large; scale; Service

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.

本研究项目的目标是深入了解客户呼叫中心和医院等大型服务系统的接近最佳管理。它将通过分析和数字工具，帮助确定资源的数量，以满足某些性能约束，在现实的假设下，对到达时间，服务时间和客户行为。对于一个具有一般服务和耐心时间分布的多服务员排队模型，一个大规模的呼叫中心，（i）PI将建立在传统的和危险率缩放的多服务员繁忙的业务下的测量值扩散限制。(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。(iii)PI将开发一种数值算法来计算扩散极限的平稳分布;该算法的关键是确定一个稳健的参考密度。(iv)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方法来证明扩散极限是必不可少的;它们还建议统计估计零时的耐心时间密度，这是一个关键的系统参数。对于医院运营，PI提出了一种新型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;放电时间被假设为独立同分布（IID），因此服务时间不是IID对于大规模的客户呼叫中心，客户期望要求保持适当的人员配备水平，以便只有一小部分到中等比例的客户放弃系统。对于医院来说，保持一定的服务水平是很重要的;例如，对于从急诊室转到住院病床的病人，只有一小部分床位申请需要等待6小时或更长时间。呼叫中心模型的研究将创造一个尖锐的理解统计分布的作用时，中心是在一个ealistic参数制度，它将提供洞察估计系统参数可靠和有效。医院模型研究有望对床位容量管理和接近最优的出院分布提供关键见解，克服许多挑战，包括（a）到达过程具有周期性到达率，（B）服务时间不是iid，（c）服务器数量很大，（d）由于一般分布假设，没有有限维马尔可夫表示，以及（c）极长的服务时间，与到达率的时间变化相比。