Three Priority Queuing Models Motivated by Healthcare Management

• Main Author: Lu, Tianshu
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2021
• Subjects: Health care management; Operations research; Organizational behavior
• ISBN: 9798496546621

In this thesis, we study three priority queueing models in healthcare management. In the first chapter, we analyze the impact of incentive misalignment between ED and physicians. We analyze two scheduling rules: physician self-schedule and centralized schedule. For the first scheduling rule, we show, using Markov decision process, that the physician's optimal policy has a time-dependent pattern. More specifically, near the beginning of the shift, the physician is more willing to see new patients, while near the end of the shift, the physician is more willing to see reentrant patients. Using a fluid model, we demonstrate that the time-dependent behaviour increases the variance of the system, and thus raises the 90th percentile of time to physician initial assessment (TPIA). For the second scheduling rule, we show, using the fluid model, that the centralized scheduling rule decreases the 90th percentile of TPIA. In the second chapter, we analyze the practice of capacity rationing under the setting of a non-preemptive priority queueing model with c servers. In the model, an arriving low priority customer enters service without waiting only when the number of idle servers exceeds the capacity rationing level. When the service rates for high and low priority customers are equal, we demonstrate, using diffusion approximation, that the non-degenerative rationing level is at most (√c). When the service rates for two classes are different, we develop an algorithm, using queueing and Markov chain decomposition method, that calculates the performance measures of interest. In the third chapter, we study an M/G/1 preemptive priority queue with transition delays, which happen when high priority customers preempt low priority customers. Recent literature empirically shows the existence of transition delay. We build a queueing model to incorporate the transition delay into performance analysis. For queueing systems with two priority classes, we find the analytical solution of the expected waiting time of both classes. For systems with more than two priority classes, we summarize our preliminary results, and discuss the difficulty of extending the result of the two class model to multiple classes.