A reward-based task typically consists of a mandatory part that must be accomplished before the given deadline, and an optional part that is associated with rewards for partial completion. In this paper, we consider a hierarchical framework of reward-based tasks. These types of tasks are characterized by positive rewards, tree-like order-dependency and identical service times. We propose a near-optimal scheduling algorithm for such tasks under hard-real time constraints. In our technique, tasks are pre-sorted by their potential rewards and real-time scheduling can be achieved with no prior knowledge of the hard deadlines. We also demonstrate how this approach could be utilized for uninterrupted transfer of multimedia in varying network conditions, while delivering near-best results.