Demand modelling for emergency medical service system with multiple casualties cases: k-inflated mixture regression model

In most of the literature on emergency medical service (EMS) system design and analysis, arrivals of EMS calls are assumed to follow Poisson process. However, it is not uncommon for real-world EMS systems to experience batch arrivals of EMS requests, where a single call involves more than one patient. Properly capturing such batch arrivals is needed to enhance the quality of analyses, thereby improving the fidelity of a resulting system design. This paper proposes a spatio-temporal demand model that incorporates batch arrivals of EMS calls. Specifically, we construct a spatio-temporal compound Poisson process which consists of a call arrival model and call size model. We build our call arrival model by combining two models available in the existing EMS demand modeling literature—artificial neural network and spatio-temporal Gaussian mixture model. For the call size model, we develop a k-inflated mixture regression model. This model reflects the characteristics of EMS call arrivals that most calls involve one patient while some calls involve multiple patients. The utility of the proposed EMS demand model is illustrated by a probabilistic ambulance location model, where we show ignoring batch arrivals leads to overestimation of ambulance availability.