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The algorithms used for the optimal management of an ambulance fleet requirean accurate description of the spatio-temporal evolution of the emergencyevents. In the last years, several authors have proposed sophisticatedstatistical approaches to forecast ambulance dispatches, typically modellingthe data as a point pattern occurring on a planar region. Nevertheless,ambulance interventions can be more appropriately modelled as a realisation ofa point process occurring on a linear network. The constrained spatial domainraises specific challenges and unique methodological problems that cannot beignored when developing a proper statistical approach. Hence, this paperproposes a spatio-temporal model to analyse ambulance dispatches focusing onthe interventions that occurred in the road network of Milan (Italy) from 2015to 2017. We adopt a non-separable first-order intensity function with spatialand temporal terms. The temporal dimension is estimated semi-parametricallyusing a Poisson regression model, while the spatial dimension is estimatednon-parametrically using a network kernel function. A set of weights isincluded in the spatial term to capture space-time interactions, inducingnon-separability in the intensity function. A series of tests show that ourapproach successfully models the ambulance interventions and captures thespace-time patterns more accurately than planar or separable point processmodels.

A non-separable first-order spatio-temporal intensity for events on linear networks: an application to ambulance interventions