Accumulating Priority Queues & Markov Models for Health Care Wait Times & Health Recovery Modelling

本提案中将描述的工作旨在建立在申请者在上一个资金周期中与他的合著者一起在提出所谓的累积优先队列(APQ)理论方面所发挥的领导作用。APQ的重要性在于，它是第一个在紧急程度与客户在系统中的等待时间之间取得平衡的服务规程。最初是由克莱恩罗克在20世纪60年代提出的，申请者与教授一起。Taylor(墨尔本)和Ziedins将首先获得累积优先级队列的等待时间分布；这是在其单一服务器设置中。在上一个周期，由申请人的NSERC发现补助金资助的博士生的延期被用来获得同质多服务器S指数情况(谢里夫等人(2014年))和更难的异质多服务器指数情况(Li)的等待时间分布，以在资助周期内与学生研究各种APQ扩展，包括仿射情况，在到达的客户可以获得初始优先学分，然后在他们等待期间进一步积累。稍后，我们计划解决服务速率取决于客户类别的多服务器情况。*累积优先级队列是一种建模工具，它有很大的潜力来改进在一组关键性能指标(KPI)下运行的服务系统(其中包括卫生保健设施)的性能。基于延迟的关键绩效指标规定了每类客户的时限，以及规定了在时限内开始服务的客户的最低比例的合规目标。通过相应地选择APQ优先级累积率，人们可以尝试在给定的服务器人员水平上是否有可能满足给定的一组KPI。*根据该提案将进行的一系列项目寻求确定基于延迟的KPI系统的适当目标，并优化由此产生的公式。*该研究计划建议在两个不同的环境中研究其他马尔可夫模型。在前者中，我们打算发展多方面的排队网络，以解决医疗服务的一个长期问题：将病人从医院的急症护理转移到康复或长期环境下的亚急性护理。过关的困难导致医院病房严重挤迫，经常影响急症室的轮候时间。与此同时，患者占用昂贵的床位，无法提供所需的护理水平。*这一系列研究的第二个背景是关于中风和其他致残条件下的健康恢复的马尔科夫模型，这是精算和卫生保健组织感兴趣的交叉点。我们希望调查保险公司通过投资于特定的改善医疗设施以确保及时护理来控制其财务状况的情况。**

The work to be described in this proposal intends to build upon the leadership the applicant has taken during the last funding cycle, along with his co-authors, in advancing the theory for what have come to be known as Accumulating Priority Queues(APQ). The importance of the APQ is that it is the first service discipline to balance urgency with the waiting times of customers in the system. initially proposed by Kleinrock in the 1960s, the applicant together with Profs. Taylor (Melbourne) and Ziedins were to first to obtain waiting time distributions for the Accumulating Priority Queue; this was in its single server setting. Extensions with PhD students funded by the applicant's NSERC Discovery Grant in the last cycle have been used to obtain the waiting time distributions for the homogeneous multi-server s exponential case (Sharif et al (2014)) and the harder heterogeneous multi-server exponential case (Li to study a variety of APQ extensions with students during the funding cycle, including the affine case in which arriving customers may obtain an initial priority credit which then further accumulates while they wait. Later, we plan to address the multi-server case where the rate of service depends upon the customer class. ***Accumulating Priority Queues are a modelling tool that has a large potential to improve performance of service systems (among them, health care facilities) that operate under a set of Key Performance Indicators (KPIs). Delay-based KPIs specify a time limit for each class of customer, and a compliance target stipulating the minimum proportion of the customers to commence service by their time limit. By choosing the APQ priority accumulation rates accordingly, one can seek if it is possible to meet a given set of KPIs at a given staffing level of servers.*A series of projects to be pursued under the proposal seeks to identify appropriate objectives for delay-based KPI systems, and to optimise the resulting formulations.***The research program proposes to study other Markovian models in two distinct settings. In the former, we intend to develop multi-faceted networks of queues to address a chronic problem in health care: the moving of patients across the boundary from acute care in a hospital to sub-acute care in a rehabilitation or long term setting. The difficulty in crossing this boundary leads to heavily congested hospital wards that frequently impact upon wait times in Emergency Departments. Meanwhile, patients occupy expensive beds which do not provide the required level of care. ***The second setting of this line of research pertains to Markovian models for health recovery from stroke and other disabling conditions, which lie at the intersection of interest for actuarial and health care organizations. We hope to investigate situations where insurers contain their financial by investing in specific improved health care facilities to ensure timely care. **