Queuing Systems with Dependencies: Theory and Applications

顾客流模型是研究服务业顾客流的重要方法。 医院中的患者流和对大规模呼叫中心的呼叫提供了系统的示例，其中队列中的等待时间和服务时间可能表现出在现有模型中通常不考虑的复杂依赖结构。 这个项目将提供基本的新的理论理解，以及有效的计算方法，为排队系统的服务需求可能会表现出某些类型的依赖与排队等候时间。 该项目将专门为重症监护服务系统寻求更好的模式和政策，例如，在医院急诊科，病人的健康在等待服务时可能会严重恶化。 这项研究将支持研究生在开发新的定量技能，并使用这些来解决具有挑战性的业务problems.The依赖的服务时间的延迟队列（内源性依赖）或耐心分布（外源性依赖）引起大量的经验和数学上的困难，由于事实上，队列过程不承认（有限维）马尔可夫表示。即使是有限的近似无限维马尔可夫（测量值）表示需要新的技术，因为现有的技术在很大程度上依赖于独立于其他原始分布的服务时间。该项目将开发严格的新工具来克服这些困难。特别是，新的随机过程近似和限制技术将被采用，以提供有效的近似的复杂的湍流动力学，并反过来，优化操作。为了促进项目模型在实践中的实施，也将解决经验上的挑战，以使模型适当地适应现实世界的系统。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Queuing models provide important methods for studying customer flow in many service industries. Patient flow in hospitals and calls to large-scale call centers provide examples of systems where waiting time in queue and service time may exhibit a complicated dependance structure not typically accounted for in existing models. This project will provide fundamental new theoretical understanding as well as efficient computational approaches for queueing systems where service requirements may exhibit certain types of dependance with waiting times in the queue. The project will specifically seek better models and policies for critical care service systems, for example, in hospital emergency departments where patient health can deteriorate significantly while waiting for service. This research will support graduate students in developing new quantitative skills and to use these to solve challenging operational problems.The dependence of the service times on the delay in queue (endogenous dependence) or the patience distribution (exogenous dependence) gives rise to substantial empirical and mathematical difficulties due to the fact that the queue processes do not admit a (finite-dimensional) Markov representation. Even limiting approximations for infinite-dimensional Markov (measure-valued) representations require new techniques, because existing techniques rely heavily on the service times being independent of other primitive distributions. This project will develop rigorous new tools to overcome these difficulties. In particular, novel stochastic-process approximations and limiting techniques will be employed in order to provide effective approximations for the complex queueing dynamics, and in turn, to optimize operations. To facilitate the implementation of the project's models in practice, the empirical challenges will be addressed as well, in order to appropriately fit the models to real-world systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.