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Multi-Server Queues with Time-Varying Arrival Rates

具有时变到达率的多服务器队列

基本信息

批准号：
1066372
负责人：
Ward Whitt
金额：
$ 32.5万
依托单位：
Columbia University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2011
资助国家：
美国
起止时间：
2011-07-01 至 2014-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1066372&HistoricalAwards=false
关键词：
Multi Server Queues Time Varying

项目摘要

The research objective of this project is to develop methods to describe and control the level of congestion (e.g., customer waiting times and queue lengths)in multi-server stochastic queueing models with time-varying arrival rates. The models will also include the important features of customer abandonment, non-exponential service and patience distributions, and network structure. The research will focus on models in which the system alternates between periods of overloading and underloading, as seen when the sta±ng levels cannot be adjusted flexibly in response to rapidly changing arrival rates. This research focuses on approximating deterministic time-varying fluid models, yielding approximations for the time-dependent mean values of queue lengths and waiting times as a function of the model parameters and the initial conditions. Then the research will consider refined Gaussian approximations for the full probability distributions. The approximations will be substantiated by simulation experiments and stochastic process limits.If successful, the results of this research will provide the basis for new methods and tools to design and manage large-scale service systems, such as healthcare systems and customer contact centers, for which there is a recognized need for new methods to improve capacity planning and operational control. The models are also relevant for many other applications, e.g., web server farms processing web-page requests, public housing authorities providing apartments to low-income tenants and financial back offices processing loan applications. Successful results can contribute to better ways to select capacity levels in design decisions and better ways to select staffing levels and to route and schedule customers in operational decisions. Nonstandard methods for treating time-varying arrivals are especially important when service times are relatively long, as in healthcare.

该项目的研究目标是开发描述和控制拥塞水平的方法（例如，顾客等待时间和排队长度）的多服务台随机排队模型的时变到达率。这些模型还将包括客户放弃，非指数服务和耐心分布，以及网络结构的重要特征。研究将集中于系统在超载和欠载期间交替的模型，如不能灵活调整sting水平以响应快速变化的到达率时所见。本研究的重点是近似确定性的时变流体模型，产生近似的时间依赖的平均值的队列长度和等待时间作为模型参数和初始条件的函数。然后，研究将考虑全概率分布的精细高斯近似。如果成功的话，本研究的结果将提供新的方法和工具的基础上设计和管理大规模的服务系统，如医疗系统和客户联络中心，有一个公认的需要新的方法来提高容量规划和运营控制。这些模型也适用于许多其他应用，例如，处理网页请求的网络服务器群、向低收入租户提供公寓的公共住房当局以及处理贷款申请的金融后台办公室。成功的结果有助于在设计决策中更好地选择能力水平，以及在运营决策中更好地选择人员配备水平和安排客户路线。当服务时间相对较长时，如在医疗保健中，处理时变到达的非标准方法尤其重要。