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Improving Productivity: An Emergency Service System in Which Cross-Trained Fire-Medics Respond to Medical Calls and Fire Incidents

We model and evaluate an emergency service system in which cross-trained fire-medics respond to both fire calls and medical emergencies. Compared to the traditional system, adding the server flexibility may be beneficial in terms of both cost savings and response time performance. A cross-trained fire-medic may be in one of three states: available, busy at an emergency medical incident, or busy at a fire call. We develop an exact spatial queuing model and an iterative approximation method that decouples the problem to two simpler systems. We prove that our method has a unique fixed point and provide the convergence condition. We demonstrate numerically that our algorithm will always converge in a few iterations. In constructed examples, performance errors are very small compared to the exact model. We apply our model to the fire-medic system in St. Paul, MN. and find close agreement between predicted and actual average response times. We compare St. Paul’s system to a traditional system having separate engine and medical units with the same number of personnel, and show the very large response time reductions achievable under the fire-medic system. The fire-medic approach and our modeling have widespread applicability to other cities.