  Inspired by recent industrial efforts toward high altitude flying wireless
access points powered by renewable energy, an online resource allocation
problem for a mobile access point (AP) travelling at high altitude is
formulated. The AP allocates its resources (available energy) to maximize the
total utility (reward) provided to a sequentially observed set of users
demanding service. The problem is formulated as a 0/1 dynamic knapsack problem
with incremental capacity over a finite time horizon, the solution of which is
quite open in the literature. We address the problem through deterministic and
stochastic formulations. For the deterministic problem, several online
approximations are proposed based on an instantaneous threshold that can adapt
to short-time-scale dynamics. For the stochastic model, after showing the
optimality of a threshold based solution on a dynamic programming (DP)
formulation, an approximate threshold based policy is obtained. The
performances of proposed policies are compared with that of the optimal
solution obtained through DP.
