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Emergency medical services provide immediate care to patients with various types of needs. When the system is congested, the response to urgent emergency calls can be delayed. To address this issue, we propose a spatial Hypercube approximation model with a cutoff priority queue that estimates performance measures for a system where some servers are reserved exclusively for high priority calls when the system is congested. In the cutoff priority queue, low priority calls are not immediately served—they are either lost or entered into a queue—whenever the number of busy ambulances is equal to or greater than the cutoff. The spatial Hypercube approximation model can be used to evaluate the design of public safety systems that employ a cutoff priority queue. A mixed integer linear programming model uses the Hypercube model to identify deployment and dispatch decisions in a cutoff priority queue paradigm. Our computational study suggests that the improvement in the expected coverage is significant when the cutoff is imposed, and it elucidates the tradeoff between the coverage improvement and the cost to low-priority calls that are “lost” when using a cutoff. Finally, we present a method for selecting the cutoff value for a system based on the relative importance of low-priority calls to high-priority calls.

In tiered emergency medical services (EMS) systems involving multiple types of response vehicles, how to match the resource to patients is a critical issue. Responses to emergency patients must be both prompt and capable of providing the type of services that patients require. I propose four discrete optimization models that design EMS systems to achieve both objectives. This dissertation begins by studying the cutoff priority scheme, which gives priority to more emergent calls for service when the system is congested by reserving vehicles exclusively for high priority calls. I propose an iterative framework composed of a spatial queuing approximation model and a Mixed Integer Linear Program that evaluates and designs public safety systems with a cutoff priority scheme. I identify the trade-off between improving the expected coverage for high priority calls at the expense of losing more low priority calls. Next, I focus on emergency responses on a congested network with two types of ambulances. I formulate a Markov decision process model that determines which type of ambulance to send to patients in real-time based on the number of idle ambulances. Structural properties of the optimal policy are derived to characterize the optimal assignment strategy and maintain computational tractability. I show the conditions under which there exists an optimal policy that is a class separable, signal threshold type and a state control limit type policy. Furthermore, I extend the decision context of the earlier model to a tandem queueing approach. The new model separates response phase and the transport phase, to study various options of dispatch, such as sending multiple vehicles to a single call (multiple response) or non-transport vehicles. Lastly, I propose a scenario-based approach focusing on a tiered EMS system with two types of ambulances which often employ multiple response. I formulate a two-stage stochastic programming model that deploy ambulances in the first stage and dispatch them to prioritized emergency patients in the second stage. The value of the stochastic solution is demonstrated with a case study and a simulation analysis. I propose a computationally effective solution method based on Benders cuts to solve large-scale instances.