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In this paper, issues involved in the design of real-time on-demand broadcast system which maintains data temporal constraints are discussed. We propose a new online scheduling algorithm, called RDDS that incorporates access frequency, data size, request-deadline and data-deadline of pending requests for real-time on-demand broadcast system with dual deadlines. Furthermore, the concepts of deferrable requests and non-deferrable requests are introduced, cases of non-deferrable requests are analyzed, and Non-deferrable Request First policy is proposed and integrated into RDDS to form another new algorithm, called RDDS-W. We have performed a series of simulation experiments to evaluate the performance of our algorithms as compared with other previously proposed methods. The experimental results show that our algorithms can substantially outperform other algorithms under a wide range of scenarios, especially when combining with Non-deferrable Request First policy, which improves the performance significantly.