Deep survival modelling for shared mobility

Abstract

With an increased focus on minimising traffic externalities in metropolitan areas, a growing interest in environmentally friendly mobility systems has emerged, such as electric car-sharing systems. However, increasing demand and larger service areas often make it difficult to keep cars available where and when customers need them. This problem can be alleviated by predicting for how long cars stay vacant at given pick-up/drop-off locations. To maximise their usage, shared fleet operators relocate the cars to more desired locations. In this paper, we tackle the problem of predicting time to pick-up for shared cars in a probabilistic way by applying time-to-event modelling through survival analysis. Both statistical and machine learning approaches to survival regression are investigated. In addition, we propose the use of Gaussian copulas in order to model the correlation among vacant vehicles and to obtain more refined event-based predictions. First, an exploratory analysis is done to investigate the effect of various features on car vacancy time, which can provide significant insights into vacancy times and their influencing factors. Second, the Cox proportional hazards model (CPH), a linear survival model, is compared to DeepSurv, a neural-network-based survival model. To predict survival times, a two-step approach is formulated: in the upper level, a classification model is used to classify cars based on vacancy time duration and, in the lower level, time-to-event modelling is applied to each class using independent survival analysis models. Our empirical results using data from Copenhagen demonstrate that the DeepSurv model leads to a stronger fit compared to CPH. Moreover, we were able to verify that the proposed two-step approach can result in an improvement of over 15% in performance compared to a standard one-step approach. Lastly, we demonstrate the benefits of survival models for relocation optimisation.