  In the vision of urban air mobility, air transport systems serve the demands
of urban communities by routing flight traffic in networks formed by vertiports
and flight corridors. We develop a routing algorithm to ensure that the air
traffic flow fairly serves the demand of multiple communities subject to
stochastic network capacity constraints. This algorithm guarantees that the
flight traffic volume allocated to different communities satisfies the
\emph{alpha-fairness conditions}, a commonly used family of fairness conditions
in resource allocation. It further ensures robust satisfaction of stochastic
network capacity constraints by bounding the coherent risk measures of capacity
violation. We prove that implementing the proposed algorithm is equivalent to
solving a convex optimization problem. We demonstrate the proposed algorithm
using a case study based on the city of Austin. Compared with one that
maximizes the total served demands, the proposed algorithm promotes even
distributions of served demands for different communities.
