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With the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road network as a weighted graph; it blasts trajectories into small fragments that fit the underlying edges to assign weights to edges; and it then applies a routing algorithm to the resulting graph. We propose a new paradigm, the hybrid graph, that targets more accurate and more efficient path cost distribution estimation. The new paradigm avoids blasting trajectories into small fragments and instead assigns weights to paths rather than simply to the edges.We show how to compute path weights using trajectory data while taking into account the travel cost dependencies among the edges in the paths. Given a departure time and a query path, we show how to select an optimal set of weights with associated paths that cover the query path and such that the weights enable the most accurate joint cost distribution estimation for the query path. The cost distribution of the query path is then computed accurately using the joint distribution. Finally, we show how the resulting method for computing cost distributions of paths can be integrated into existing routing algorithms. Empirical studies with substantial trajectory data from two different cities offer insight into the design properties of the proposed method and confirm that the method is effective in real-world settings.

Path representations are critical in a variety of transportation applications, such as estimating path ranking in path recommendation systems and estimating path travel time in navigation systems. Existing studies often learn task-specific path representations in a supervised manner, which require a large amount of labeled training data and generalize poorly to other tasks. We propose an unsupervised learning framework Path InfoMax (PIM) to learn generic path representations that work for different downstream tasks. We first propose a curriculum negative sampling method, for each input path, to generate a small amount of negative paths, by following the principles of curriculum learning. Next, PIM employs mutual information maximization to learn path representations from both a global and a local view. In the global view, PIM distinguishes the representations of the input paths from those of the negative paths. In the local view, PIM distinguishes the input path representations from the representations of the nodes that appear only in the negative paths. This enables the learned path representations encode both global and local information at different scales. Extensive experiments on two downstream tasks, ranking score estimation and travel time estimation, using two road network datasets suggest that PIM significantly outperforms other unsupervised methods and is also able to be used as a pre-training method to enhance supervised path representation learning.

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