An expected coverage model with a cutoff priority queue

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.