  We investigate algorithms to find short paths in spatial networks with
stochastic edge weights. Our formulation of the problem of finding short paths
differs from traditional formulations because we specifically do not make two
of the usual simplifying assumptions: (1) we allow edge weights to be
stochastic rather than deterministic; and (2) we do not assume that global
knowledge of a network is available. We develop a decentralized routing
algorithm that provides en route guidance for travelers on a spatial network
with stochastic edge weights without the need to rely on global knowledge about
the network. To guide a traveler, our algorithm uses an estimation function
that evaluates cumulative arrival probability distributions based on distances
between pairs of nodes. The estimation function carries a notion of proximity
between nodes and thereby enables routing without global knowledge. In testing
our decentralized algorithm, we define a criterion that allows one to
discriminate among arrival probability distributions, and we test our algorithm
and this criterion using both synthetic and real networks.
