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On-demand broadcast is an effective wireless data dissemination technique to enhance system scalability and capability to handle dynamic user access patterns. Previous studies on time-critical on-demand data broadcast were under the assumption that each client requests only one data item at a time. Little work, however, has considered the on- demand broadcast with time-critical multi-item requests. In this paper, we study the problem arising in this new environment and observe that existing single item based scheduling algorithms are unable to manage multi-item requests efficiently. Thus, a new scheduling algorithm that combines the benefit of data item scheduling and request scheduling is proposed. The performance results show that the proposed algorithm is superior to other classical algorithms under a variety of factors. Our algorithm not only reduces deadline-missing ratio of requests, but also saves broadcast channel bandwidth.