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

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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 & Stanford (2016)). ***This proposal intends 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. **