Temporal and Spatio-Temporal Models for Ambulance Demand

Ambulance demand estimation at fine time and location scales is critical for fleet management and dynamic deployment. Large-scale datasets in this setting typically exhibit complex temporal dynamics and sparsity at high resolutions. We describe two new methods to address these challenges, and provide temporal and spatio-temporal ambulance demand estimations for Toronto, Canada. First, we forecast bi-hourly call arrival rates using an integer-valued time series model with a dynamic latent factor structure. We incorporate covariate information as constraints on the factor loadings; we also smooth the factor levels and loadings using splines. Next, we adapt finite Gaussian mixture models to estimate the spatial distribution of ambulance demand over two-hour intervals. The mixture component distributions are assumed common across all time periods while the mixture weights evolve over time. This promotes efficient learning of the spatial structure, and provides a flexible framework for incorporating covariate information to model temporal dynamics. Temporal seasonalities are captured by constraining the mixture weights; location-specific temporal dynamics are integrated by applying conditionally autoregressive priors to the mixture weights. Both methods demonstrate significant advantages over the current industry practice.