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On-demand broadcast is an effective wireless data dissemination technique to enhance system scalability and deal with dynamic user access patterns. With the rapid growth of time-critical information services in emerging applications, there is an increasing need for the system to support timely data dissemination. This paper investigates online scheduling algorithms for time-critical on-demand data broadcast. We propose a novel scheduling algorithm called SIN-α that takes the urgency and number of outstanding requests into consideration. An efficient implementation of SIN-α is presented. We also analyze the theoretical bound of request drop rate when the request arrival rate rises toward infinity. Trace-driven experiments show that SIN-α significantly outperforms existing algorithms over a wide range of workloads and approaches the analytical bound at high request rates.