Models for Capacity Allocation in Anticipation of Time-Varying Demand

In this dissertation, we propose and investigate several stationary capacity allocation methods that anticipate time-varying demand. We apply these techniques to three practical settings in customer acquisition and retention, cloud computing, and healthcare.

In the first part of this dissertation, we model the trade-off between customer acquisition and retention as a multi-class queueing network with returning customers, time-dependent arrivals, and abandonment. Based on its fluid approximation, we propose an approach to determine optimal stationary staffing levels by partitioning the time-limiting solution of the dynamical system. We test our method by applying it to two real-world applications, i.e., advertising campaigns and a clinical setting, and demonstrate its superiority when comparing to other state-of-the-art approaches.

In the second part, we analyze a cloud computing system where a provider wants to determine the optimal number of servers and retrial interval for incoming jobs when all servers are busy. Servers in this setting represent components of a computer network and customers are jobs attempting to access the cloud computing infrastructure. By modeling the system as a fluid queue and using a calculus-of-variations approach, we derive the optimal amount of service capacity and retrial interval in anticipation of time-varying dynamics. We conduct a case study using data collected from a real cloud service provider and show that significant savings can be realized.

Finally, we estimate the demand for personal protective equipment (PPE) in the general internal medicine (GIM) department of a hospital during the COVID-19 pandemic. We derive closed-form estimates of demand for multiple types of PPE using a queueing framework with generally distributed service times that models medical interactions with heterogeneous patients whose hospital admissions are time-varying. We parametrize our predictive model using a data set containing patients' clinical and operational records over a period of 9 years. We find that gloves and surgical masks represent approximately 90% of predicted PPE usage. We also find that while demand for gloves is driven entirely by patient-practitioner interactions, 86% of the predicted demand for surgical masks can be attributed to the requirement that medical practitioners will need to wear them when not interacting with patients.