Modelling emergency medical services with phase‐type distributions

Effective and efficient emergency medical services (EMS) are a critical part of a national healthcare system. This paper describes research to model EMS by better capturing ambulance service times using Coxian phase‐type (PH) distributions. Distributions are fitted to both the overall cycle time for different classes of patient priorities, as well as to sub‐cycles. Sub‐cycles are the distinct identifiable parts of the ambulance cycle time, such as travel times, time on scene and turnaround time at the hospital. The Coxian PH fits have then been used within a priority simulation model to provide guidance on the number of ambulances required to meet response time targets. Results from using various numbers of phases from the fitted Coxian distributions are compared. The proposed benefit of using sub‐cycle fits is that it more readily permits scenario modelling within the simulation, such as evaluating the impact of reducing the turnaround time on the overall response times in the ambulance system.