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

本提案中描述的工作旨在建立在申请人在上一个资助周期中所采取的领导地位，以及他的合著者，在推进被称为积累优先级队列（APQ）的理论。APQ的重要性在于，它是第一个平衡紧急情况与客户在系统中等待时间的服务准则。最初由Kleinrock在20世纪60年代提出，申请人与教授。Taylor （Melbourne）和Ziedins首先获得累积优先队列的等待时间分布；这是在单服务器设置中。在上一个周期中，由申请人的NSERC发现基金资助的博士生的扩展已被用于获得同质多服务器指数情况（Sharif等人（2014））和更难的异构多服务器指数情况（Li在资助周期中与学生一起研究各种APQ扩展）的等待时间分布。包括在仿射情况下，到达的客户可能获得最初的优先信用，然后在他们等待的过程中进一步积累。稍后，我们计划解决多服务器情况，其中服务速率取决于客户类别。***累积优先队列是一种建模工具，具有很大的潜力，可以改善在一套关键绩效指标（kpi）下运行的服务系统（其中包括卫生保健设施）的绩效。基于延迟的kpi为每一类客户指定了时间限制，并规定了在其时间限制内开始服务的客户的最小比例的遵从性目标。通过相应地选择APQ优先级累积率，可以确定是否有可能在给定的服务器人员配置级别上满足给定的一组kpi。*在建议下进行的一系列项目，旨在为以延误为基础的关键绩效指标系统确定适当的目标，并优化所产生的公式。***本研究计划提出在两种不同的环境下研究其他马尔可夫模型。在前者中，我们打算开发多方面的队列网络，以解决医疗保健中的一个慢性问题：将患者从医院的急症护理转移到康复或长期环境中的亚急性护理。跨越这一界限的困难导致医院病房严重拥挤，经常影响急诊室的等待时间。与此同时，病人占用了昂贵的床位，却无法提供所需的护理水平。***这条研究线的第二个设置涉及中风和其他致残条件下健康恢复的马尔可夫模型，这是精算和医疗保健组织感兴趣的交叉点。我们希望调查的情况下，保险公司控制其财务通过投资于特定的改进医疗保健设施，以确保及时护理。**

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. **