A Markov Chain Model for an EMS System with Repositioning

We propose and analyze a two-dimensional Markov chain model of an Emergency Medical Services system that repositions ambulances using a compliance table policy, which is commonly used in practice. The model is solved via a fixed-point iteration. We validate the model against a detailed simulation model for several scenarios. We demonstrate that the model provides accurate approximations to various system performance measures, such as the response time distribution and the distribution of the number of busy ambulances, and that it can be used to identify near-optimal compliance tables. Our numerical results show that performance depends strongly on the compliance table that is used, indicating the importance of choosing a well-designed compliance table.