  Travel time estimation is a crucial application in navigation apps and web
mapping services. Current deterministic and probabilistic methods primarily
focus on modeling individual trips, assuming independence among trips. However,
in real-world scenarios, we often observe strong inter-trip correlations due to
factors such as weather conditions, traffic management, and road works. In this
paper, we propose to model trip-level link travel time using a Gaussian
hierarchical model, which can characterize both inter-trip and intra-trip
correlations. The joint distribution of travel time of multiple trips becomes a
multivariate Gaussian parameterized by learnable link representations. To
effectively use the sparse GPS trajectories, we also propose a data
augmentation method based on trip sub-sampling, which allows for fine-grained
gradient backpropagation in learning link representations. During inference, we
estimate the probability distribution of the travel time of a queried trip
conditional on the completed trips that are spatiotemporally adjacent. We refer
to the overall framework as ProbTTE. We evaluate ProbTTE on two real-world GPS
trajectory datasets, and the results demonstrate its superior performance
compared to state-of-the-art deterministic and probabilistic baselines.
Additionally, we find that the learned link representations align well with the
physical geometry of the network, making them suitable as input for other
applications.
