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Recent advances in mobile media cloud (MMC) make it possible for users to enjoy the multimedia applications at anytime and anywhere. Most existing scheduling algorithms for MMC assume that the system parameters, such as user demand rate and server service time, are known to the scheduler. However, this assumption is invalid in many practical scenarios. In this paper, we consider a blind scenario where the above system parameters are unavailable. We aim at developing a blind scheduling algorithm (BSA) that performs well across magnitudes of fairness, simplicity and asymptotic optimality for a relatively general MMC. Specifically, the blind scheduling is first formulated as a finite time horizon optimization problem and fairness is required to be maintained at each time point with a given probability from the scheduler. Next, BSA routes the new users to the media service provider (MSP) whose weighted idle time is the longest, then assigns the available MSPs according to the fairness on the idle time. Importantly, we demonstrate that BSA is asymptotically optimal in the Halfin-Whitt heavy traffic (HWHT) regime. The asymptotic optimality is in the sense that the scheduling asymptotically and stochastically minimizes the steady-state waiting time of all the users. Our analysis also shows that in the HWHT regime the heterogeneous MSP system outperforms its homogeneous MSP counterpart in terms of the user waiting time. Moreover, we apply BSA to the program recommendation system and investigate its property.