One commonly used workload metric in Emergency Medical Services (EMS) is the Unit Hour Utilization (UHU). The UHU is a productivity measure that, by definition, represents the ratio of patient transport calls to the total hours that ambulances are staffed. It is often misinterpreted as a utilization measure representing the percentage of crews' available working hours that are spent performing work. This paper investigates a surrogate model to estimate a measure of EMS crew utilization that considers not only call response, but also indirect work tasks, such as documentation and shift start activities. We explored Kriging, KPLS, RBF, and physics-based models based on EMS work dynamics. The true measure of utilization was based on Montecarlo samples of estimated work time patterns associated with a year's worth of dispatch data augmented with the results of a work measurement study. The best performing model in terms of the root mean square error (RSME), the symmetric mean absolute percent error (sMAPE), and Pearson correlation estimates, was the physics-based model. This model requires time studies to estimate the average time spent in shift start activities and documenting calls, geographic information systems to estimate the average time driving back to the post, and dispatch data analysis to estimate the average time to respond to calls. Sensitivity analysis was used to provide recommendations for when to update these parameters and general recommendations were given to implement this approach in other EMS systems.