  Using 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 graph, assigns weights to the graph's edges by fragmenting
trajectories into small pieces that fit the underlying edges, and then applies
a routing algorithm to the resulting graph. We propose a new paradigm that
targets more accurate and more efficient estimation of the costs of paths by
associating weights with sub-paths in the road network. The paper provides a
solution to a foundational problem in this paradigm, namely that of computing
the time-varying cost distribution of a path.
  The solution consists of several steps. We first learn a set of random
variables that capture the joint distributions of sub-paths that are covered by
sufficient trajectories. Then, given a departure time and a path, we select an
optimal subset of learned random variables such that the random variables'
corresponding paths together cover the path. This enables accurate joint
distribution estimation of the path, and by transferring the joint distribution
into a marginal distribution, the travel cost distribution of the path is
obtained. The use of multiple learned random variables contends with data
sparseness, the use of multi-dimensional histograms enables compact
representation of arbitrary joint distributions that fully capture the travel
cost dependencies among the edges in paths. Empirical studies with substantial
trajectory data from two different cities offer insight into the design
properties of the proposed solution and suggest that the solution is effective
in real-world settings.
