Essays on Decision-Making with Queueing Models for Service Systems

This thesis consists of three essays that propose simple dynamic time- and/or state-dependent policies to improve the performance of queueing-based service systems. The first essay analyzes a single-physician emergency department (ED) model with heterogeneous new and in-progress (IP) patients over a finite shift with end-of-shift handoff penalties. The system is formulated as a transient optimal control problem, and the analysis shows that the optimal policy has a time-threshold-type structure. For prioritizing between different customer classes, the essay derives time-dependent rules that can be viewed as generalizations of well-known index-based prioritization rules in the literature. It also provides closed-form approximations for the optimal time thresholds as functions of model parameters. Numerical results based on a simulation calibrated with real hospital data show that the proposed policy can significantly outperform current practices and alternative policies in terms of several performance measures, including waiting times, throughput, and handoffs. The second essay extends the first essay to a more general shift-based system with a generic, rather than ED-specific, application and formulates a finite-horizon Markov decision process (MDP). It is shown that the optimal policy is a state- and time-dependent threshold rule on the number of IP customers, and demonstrates that this policy can outperform purely time-dependent rule proposed in the first essay, especially under moderate load. To make the policy easier to use, the essay parameterizes the threshold as a function of time and uses supervised learning to map model parameters to threshold parameters. The third essay studies an infinite-horizon, misclassification-aware MDP for routing patients from emergency medical services (EMS) to either a hospital ED or an alternative urgent care center when only predicted-discharge patients are eligible for diversion and the prehospital classifier is imperfect. It shows that the optimal routing policy has a state-dependent threshold form in the urgent care workload. The classifier design is also parameterized through effort and a propensity threshold. A heuristic method is proposed to solve the joint problem of routing, effort, and classification threshold. Structural analysis as well as numerical experiments show how optimal routing decisions depend on misclassification rates and unit workloads. It is also shown that the optimal effort level is strictly positive but typically small relative to the maximum feasible range.