We introduce statistical methods to address two forecasting problems arising in the management of ambulance fleets: (1) predicting the time it takes an ambulance to drive to the scene of an emergency; and (2) space-time forecasting of ambulance demand. These predictions are used for deciding how many ambulances should be deployed at a given time and where they should be stationed, which ambulance should be dispatched to an emergency, and whether and how to schedule ambulances for non-urgent patient transfers. We demonstrate the accuracy and operational impact of our methods using data from Toronto Emergency Medical Services.

For travel time estimation the relevant data are Global Positioning System (GPS) recordings from historical lights-and-sirens ambulance trips. Challenges include the typically large size of the road network and dataset (70,000 network links and 160,000 historical trips for Toronto), the lack of trips in the historical data that follow precisely the route of interest, and uncertainty regarding the instantaneous location of ambulances in the historical trips (due to sparsity of the GPS recordings). For space-time demand forecasting, challenges include complex weekly and daily patterns in demand as well as changes in the spatial demand density over time. I will describe our methods and results, and discuss ongoing commercialization efforts.