Multi-Server Queues with Time-Varying Arrival Rates

本课题的研究目标是开发一种方法来描述和控制具有时变到达率的多服务台随机排队模型中的拥塞程度(如顾客等待时间和排队长度)。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。研究的重点将放在系统在超载和欠载期间交替的模型上，如无法灵活地调整STAn？ng水平以应对快速变化的到达率。本研究的重点是逼近确定性时变流体模型，得到排队长度和等待时间的随时间变化的平均值作为模型参数和初始条件的函数的近似值。然后，研究将考虑全概率分布的精化高斯近似。如果成功，这项研究的结果将为设计和管理大型服务系统提供新的方法和工具的基础，例如医疗保健系统和客户联系中心，对于这些系统，人们认识到需要新的方法来改进容量规划和运营控制。这些模型还适用于许多其他应用程序，例如处理网页请求的Web服务器场、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产能水平，在运营决策中更好地选择人员配备水平以及安排客户路线和日程。当服务时间相对较长时，治疗随时间变化的抵达的非标准方法尤其重要，例如在医疗保健领域。

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.