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

翻译：用于优化救护车队管理的算法需要精确描述紧急事件的时空演变。近年来，多位学者提出了复杂的统计方法来预测救护车调度，通常将数据建模为平面区域上的点模式。然而，救护车干预更适合建模为线性网络上点过程的实现。受约束的空间域带来了特定的挑战和独特的方法论问题，在开发适当的统计方法时不可忽视。因此，本文提出一种时空模型来分析救护车调度，重点关注2015年至2017年意大利米兰道路网络上的干预事件。我们采用包含空间和时间项的不可分一阶强度函数。时间维度通过泊松回归模型进行半参数估计，空间维度则通过网络核函数进行非参数估计。在空间项中引入一组权重以捕捉时空交互，从而在强度函数中产生不可分性。一系列测试表明，我们的方法成功建模了救护车干预，并且比平面或可分点过程模型更准确地捕捉了时空模式。