As an increasing proportion of the world population moves to urban areas, quality of life and economic productivity of an increasing proportion of the world population are getting impacted by traffic congestion phenomena of increasing severity. In the context of urban transportation networks of growing complexity, the management of non-recurrent road traffic events, estimated to account for close to 50% of the total travel-time delay on road networks, requires advanced predictive methods, supporting both response plan deployment and traveller information. In this work, we consider the problem of predicting how a non-recurrent traffic event, such as a road incident, impacts traffic conditions at the incident location in the future. Based on a detailed statistical analysis of a large dataset of traffic incidents, we propose a parametric piecewise-affine incident model. The model is calibrated offline using a combination of constrained and unconstrained non-linear regression methods, and is shown to provide a good fit. The prediction of local incident impact is achieved via the design of a neural network model learning the parametric fit of the incident model based on available incident features. The neural network-based prediction model is shown to outperform state-of-the-art prediction methods such as multivariate decision trees. Empirical performance of the method introduced in this work is illustrated on a large dataset of more than 50000 incidents from the city of Lyon, France, for the months of September 2013 to January 2014. Practical deployment and applicability of the proposed method in operational conditions are also discussed.