Fitting Time-Varying Queueing Models to Service System Data: Accounting for Dependence in the Arrival and Service Processes

该奖项的研究目标是开发方法，将时变非马尔可夫多服务器排队模型与来自医疗保健系统和客户联络中心的数据拟合，以便模型可用于分析和改善性能;例如，设置人员配备水平。需要复杂的模型，因为：到达率通常随时间变化显着;经常有客户放弃，这显着改变性能;服务时间和客户耐心时间通常不是指数分布;最后，服务系统往往需要表示为一个网络的队列。将特别注意在到达和服务过程以及非指数分布和随时间变化的到达率的依赖性所造成的随机变化。这种依赖性可能是由网络结构引起的，包括当第一个队列拥塞时从一个队列溢出到另一个队列，如在医院的不同病房中发生的。已经发现溢出过程中的依赖性（“突发性”）对电信网络中的性能有很大影响。估计将指导许多服务器的高流量限制，揭示关键的部分特征的模型需要分析和提高performance.If成功的，这项研究的结果将提供新的方法和工具，以适应随机模型服务系统数据的基础。这些模型将为设计和管理大型服务系统（如医疗保健系统和客户联络中心）的新方法和工具提供基础，这些系统需要新方法来改善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。

The research objective of this award is to develop methods to fit time-varying non-Markovian multi-server queueing models to data from healthcare systems and customer contact centers, so that the models can be used to analyze and improve the performance; e.g., to set staffing levels. Complex models are needed because: the arrival rates typically vary significantly over time; there is often customer abandonment, which significantly alters performance; service times and customer patience times are usually not exponentially distributed; finally, service systems often need to be represented as a network of queues. Special attention will be given to stochastic variability caused by dependence in the arrival and service processes as well as non-exponential distributions and the time-varying arrival rates. Such dependence can be caused by network structure, including overflows from one queue to another when the first is congested, as occurs in the different wards of a hospital. The dependence ("burstiness") in overflow processes has been found to have a big impact upon performance in telecommunication networks. Estimation will be guided by many-server heavy-traffic limits, revealing key partial characterizations of the model needed to analyze and improve the performance.If successful, the results of this research will provide the basis for new methods and tools to fit stochastic models to service system data. These models 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.