A Parsimonious Monte Carlo Model for Verifying Ambulance System Dynamics and Time-Dependent Blocking from Dispatch Records

Abstract

Emergency medical service (EMS) systems operate under finite vehicle availability and stochastic, time-varying demand. When all ambulances are occupied, additional calls experience blocking. Dispatch records typically document served missions but might not capture unserved incidents. We present a parsimonious Monte Carlo (MC) simulation to estimate time-dependent blocking risk from dispatch data alone. The model fits two components: A censoring-corrected incident rate and a time-dependent duration distribution. Duration parameters correlate strongly with the lagged incident rate, which we exploit by collapsing per-bin duration fits into a compact linear model. Together with vehicle duty schedules estimated from the same source, these form a complete simulation. Unlike piecewise Erlang B formulas, it captures transient effects such as missions spanning shift and hour boundaries. Validated against one year of data from a mid-sized German city, the simulation reproduces the observed distribution of concurrent active missions – a quantity not used directly in calibration.