Discrete-Review Control of Service Processing Networks with Applications to Patient Flow Management in Emergency Departments

随机排队网络通常用于服务系统（如医院、联络中心和共享单车系统）的建模和分析，其控制一直是过去广泛研究的主题。文献主要关注连续时间控制，即控制器可以在任何时间点与系统交互。然而，在许多服务设置中，系统管理器只能以离散的、可能很长的时间间隔与系统交互。也就是说，尽管相关的信息是可用的，但在下次评审时间开始之前，控制者不能行使控制。对离散时间或离散审查策略的控制限制通常从根本上改变了最优控制策略的结构，使相应的连续时间策略（如果已知）变得不切实际，并且难以解释其见解。然而，尽管应用和潜在的好处，排队网络的离散审查控制在文献中仍未被探索。提出的研究计划旨在首先对施加离散审查限制对动态控制策略性能的影响提供基本见解，其次，为复杂排队网络的控制开发实用有效的离散审查策略。特别是，我将考虑两个重要的操作决策，即动态容量分配和容量规划，并研究排队模型，这主要是由急诊科（EDs）患者流管理应用程序驱动的。通过与两家大型医疗保健提供商（安大略省密西沙加的Tritium Health Partners （THP）和纽约州纽约的New York Presbyterian （NYP）医院）的合作，并使用他们的数据，该计划将包括校准模型，评估拟议政策的绩效，并努力在实践中实施。这个研究项目的一个重要特点是，它强调实际的政策，并依赖于基于现实世界数据的模型。因此，如果成功，研究结果将有助于减少加拿大急诊科的等待时间，在那里过度拥挤越来越令人担忧。此外，尽管所提出的模型主要是由患者流程管理的应用程序驱动的，但它们捕获了各种服务系统中存在的动态和特征。因此，预计本项目中开发的方法和见解将是有用的，并导致对其他服务系统的进一步研究，这些系统由于人为影响或与系统交互的高成本而无法实现连续时间控制。

Control of stochastic queueing networks which are often used in modeling and analysis of service systems (e.g., hospitals, contact centers, and ride/bike sharing systems) has been the subject of extensive research in the past. The literature is predominantly concerned with continuous-time control, whereby the controller can interact with the system at any point in time. In many service settings, however, the system manager can only interact with the system at discrete and possibly long time-intervals. That is, although relevant information is becoming available, the controller cannot exercise control before the beginning of the next review time. The limitation of control to discrete-time or discrete-review policies often fundamentally changes the structure of the optimal control policy, making the corresponding continuous-time policy (if known) impractical and the insights from it hard to interpret. Despite applications and potential benefits, however, discrete-review control of queueing networks has remained mostly unexplored in the literature. The proposed research program aims to first provide fundamental insights on the impact of imposing the discrete-review limitation on the performance of dynamic control policies, and second, to develop practical and effective discrete-review policies for control of complex queueing networks. In particular, I will consider two important operational decisions, namely dynamic capacity allocation and capacity planning, and study queueing models that are mainly motivated by applications to patient flow management in Emergency Departments (EDs). Through collaboration with two large healthcare providers (Tritium Health Partners (THP) in Mississauga, ON, and New York Presbyterian (NYP) hospital in New York, NY) and using their data, the program will involve calibrating the models, estimating the performance of the proposed polices, and working towards their implementation in practice. An important characteristic of this research program is that it emphasises practical policies and relies on models that are informed by real-world data. Therefore, if successful, the outcome of the research can contribute to reduction of waiting times in EDs across Canada, where overcrowding is of growing concern. Further, although the proposed models are mainly motivated by applications to patient flow management, they capture dynamics and features that are present in various service systems. Therefore, it is expected that the methods and insights developed in this program will be useful and lead to further research for other service systems where continuous-time control is not feasible, due to either human-effects or high cost of interacting with the system.