Data-Driven Queueing Models for Healthcare: Accounting for Stochastic Dependence and Time Dependence

一些急诊科（ED）病人在从急诊科转到主医院的病床时经历了很长时间的延误，这种现象被称为急诊科登机。虽然急诊科登机可能是由急诊科的需求激增引起的，但也可能是由病人需要床位的医院病房的操作政策引起的。要正确理解急诊科登机，有必要以更广阔的视野，除了急诊科本身，还要看医院的其他部分。医院急诊科登机和其他病人流问题可以建模为多类排队网络。因此，本研究将开发新的方法来分析医疗保健中复杂的数据驱动排队网络模型。本研究将借鉴排队网络模型的丰富经验，以减少拥塞，提高制造、计算机和通信系统的效率。医疗保健中所需的排队网络模型更为复杂，因为它们需要(i)根据优先级对患者和资源进行分类，以及（ii）考虑患者流中随时间变化的到达率和复杂的随机依赖。医疗保健为这些排队网络模型的有效应用提供了新的机会，因为这些模型可以适合医疗保健患者流数据，这些数据正在迅速变得可用。在进行这项研究时，PI仍然致力于帮助从传统上代表性不足的群体中培养新的研究人员。本项目将为时变多类别排队网络模型开发新的易于处理的数据驱动分析近似和仿真方法。新的近似方法将结合最近开发的鲁棒优化和基于繁忙交通限制和随机依赖的部分特征（如分散指数）的随机过程的已建立的近似。提出了一种新的鲁棒排队（RQ）公式，以揭示流中时间依赖性和随机依赖性对性能的影响。新的RQ公式基于每个类别的每个流程的累积速率和方差，表示为作为时间函数的总工作输入。研究将探讨新的RQ优化是否有效和易于处理；即，如果它确实可以暴露时间依赖性和随机依赖性对队列性能的影响。还将研究优先事项的影响。计算机模拟将用于评估近似，也直接作为性能分析工具。本研究将探讨这些时变模型的新模拟方法，包括时变单服务器队列的罕见事件模拟新方法。本文将通过仿真实验和系统数据对这些方法进行验证。

Some emergency department (ED) patients experience long delays in being transferred from the ED to a bed within the main hospital, a phenomenon called ED boarding. While ED boarding can be caused by surges of demand in the ED, it also can be caused by operating policies in the hospital wards where the patient needs a bed. To properly understand ED boarding, it is necessary to take a broader view, looking at the rest of the hospital in addition to the ED itself. The problem of ED boarding and other patient flows in hospitals can be modeled as multi-class networks of queues. Accordingly, this research will develop new ways to analyze complex data-driven queueing network models in healthcare. This research will draw on the extensive experience with queueing network models to reduce congestion and improve the efficiency of manufacturing, computer and communication systems. The queueing network models needed in healthcare are more complicated because they require (i) classifying patients and resources, with priorities, and (ii) accounting for time-varying arrival rates and complicated stochastic dependence in the patient flows. Healthcare presents a new opportunity for fruitful applications of these queueing network models because the models can be fit to healthcare patient flow data, which are rapidly becoming available. In undertaking this research, the PI remains committed to helping to develop new researchers from traditionally under-represented groups.This project will develop new tractable data-driven analytical approximations and simulation methods for time-varying multi-class queueing network models. New approximation methods will combine the recently developed robust optimization with established approximations for stochastic processes based on heavy-traffic limits and partial characterizations of stochastic dependence, such as indices of dispersion. A new robust queueing (RQ) formulation is proposed for exposing the performance impact of the time dependence and stochastic dependence in the flows. The new RQ formulation is based on the cumulative rate and variance of each flow for each class, represented as the total input of work as functions of time. The research will investigate if the new RQ optimization is effective and tractable; i.e., if it can indeed expose the impact of the time dependence and stochastic dependence on the performance of the queue. The impact of priorities also will be studied. Computer simulation will be used to evaluate the approximations and also directly as a performance analysis tool. This research will investigate new simulation methods for these time-varying models, including a new rare-event simulation method for the time-varying single-server queue. The methods will be tested by experiments with simulation and system data.