Inspired by recent industrial efforts towards high altitude flying wireless access points powered by renewable energy, an online resource allocation problem for a mobile access point travelling at high altitude is formulated. The access point allocates its resources (available energy) to maximise 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, and the solution of which is quite open in the literature. We address the problem through deterministic and stochastic formulations followed by a model where the statistics of the underlying processes are not known and learned through rule-based and neural network approaches. For the deterministic problem, several online approximations including optimisation via genetic algorithm and rule-based approach 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 formulation, an approximate threshold-based policy is obtained. The performances of proposed policies are compared with that of the optimal solution obtained through dynamic programming. Copyright (C) 2016 John Wiley & Sons, Ltd.