Road traffic estimation and algorithmic routing in a spatially dependent network

This work concerns a procedure to estimate the joint distribution of the per-edge travel times in a road traffic network with spatial dependence. The constructed estimator, based on the realized travel times of a collection of independently operating probe vehicles traversing the network, is shown to be consistent and rate-optimal. The obtained estimates of the joint travel-time distribution can be used in routing policies. In particular, as realized travel times are observed en route to the destination, spatial dependence can be leveraged to iteratively update the predictive distribution of the remaining travel time. Importantly, we can deal with general objective functions, reflecting the individual traveler's specific risk aversion, including ones that involve the uncertainty of the estimates. Through a series of numerical experiments, we systematically study the estimator's performance in combination with specific routing policies and objective functions.