  In route selection problems, the driver's personal preferences will determine
whether she prefers a route with a travel time that has a relatively low mean
and high variance over one that has relatively high mean and low variance. In
practice, however, such risk aversion issues are often ignored, in that a route
is selected based on a single-criterion Dijkstra-type algorithm. In addition,
the routing decision typically does not take into account the uncertainty in
the estimates of the travel time's mean and variance. This paper aims at
resolving both issues by setting up a framework for travel time estimation. In
our framework, the underlying road network is represented as a graph. Each edge
is subdivided into multiple smaller pieces, so as to naturally model the
statistical similarity between road pieces that are spatially nearby. Relying
on a Bayesian approach, we construct an estimator for the joint per-edge travel
time distribution, thus also providing us with an uncertainty quantification of
our estimates. Our machinery relies on establishing limit theorems, making the
resulting estimation procedure robust in the sense that it effectively does not
assume any distributional properties. We present an extensive set of numerical
experiments that demonstrate the validity of the estimation procedure and the
use of the distributional estimates in the context of data-driven route
selection.
