This paper investigates the adaptive trajectory and communication scheduling design for an unmanned aerial vehicle (UAV) relaying random data traffic generated by ground nodes to a base station.The goal is to minimize the expected average communication delay to serve requests, subject to an average UAV mobility power constraint. It is shown that the problem can be cast as a semi-Markov decision process with a two-scale structure, which is optimized efficiently: in the outer decision, the UAV radial velocity for waiting phases and end radius for communication phases optimize the average longterm delay-power trade-off; given outer decisions, inner decisions greedily minimize the instantaneous delay-power cost, yielding the optimal angular velocity in waiting states, and the optimal relay strategy and UAV trajectory in communication states. A constrained particle swarm optimization algorithm is designed to optimize these trajectory problems, demonstrating 100× faster computational speeds than successive convex approximation methods. Simulations demonstrate that an intelligent adaptive design exploiting realistic UAV mobility features, such as helicopter translational lift, reduces the average communication delay and UAV mobility power consumption by 44% and 7%, respectively, with respect to an optimal hovering strategy and by 2% and 13%, respectively, with respect to a greedy delay minimization scheme.