Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


Prof. David A. Stanford

2nd Supervisor

Prof. Gregory S. Zaric

Joint Supervisor


This thesis consists of four contributing chapters; two of which are inspired by practical problems related to emergency department (ED) operations management and the remaining two are motivated by the theoretical problem related to the time-dependent priority queue. Unlike classical priority queue, priorities in the time-dependent priority queue depends on the amount of time an arrival waits for service in addition to the priority class they belong. The mismatch between the demand for ED services and the available resources have direct and indirect negative consequences. Moreover, ED physician pay in some jurisdictions reflects pay-for-performance contracts based on operational benchmarks. To assist in capacity planning and meeting these benchmarks, in chapter 4, I built a forecasting model to produce short-term forecasts of ED arrivals. In chapter 5, I empirically investigated the effect of workload on the productivity of ED services. Specifically, under discretionary work setting, different statistical models were fitted to identify the effect of workload and census on four measures of ED service processes, namely, number discharged, length of stay, service time, and waiting time. The time-dependent priority model was first proposed by Kleinrock (1964), and, more recently, naming it accumulating priority queue (APQ), Stanford et al. (2014) derived the waiting time distributions for the various priority classes when the queue has a single server. In chapter 6, I derived expressions for the waiting time distributions for a multi-server APQ with Poisson arrivals for each class, and a common exponential service time distribution. In chapter 7, I worked with a KPI based service system where there are specific time targets by which each class of customers should commence their service and a compliance probability indicating the proportion of customers from that class meeting the target. Recognizing the fact that customer who misses their KPI target is of greater, not lesser importance, I seek to minimize a weighted sum of the expected amount of excess waiting for each class. When minimizing the total expected excess, our numerical examples lead to an easily-implemented rule of thumb for the optimal priority accumulation rates, which can have an immediate impact on health care delivery.