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Security requirements of security-critical real-time applications must be met in addition to satisfying timing constraints. However, conventional real-time scheduling algorithms ignore the applications' security requirements. In recognition that an increasing number of applications running on clusters demand both real-time performance and security, we investigate the problem of scheduling a set of independent real-time tasks with various security requirements. We propose a security overhead model that is capable of measuring security overheads incurred by security-critical tasks. Further, we propose a security-aware scheduling strategy, or SAREC, which integrates security requirements into scheduling for real-time applications by employing our security overhead model. To evaluate the effectiveness of SAREC, we implement a security-aware real-time scheduling algorithm (SAREC-EDF), which incorporates the earliest deadline first (EDF) scheduling algorithm into SAREC Extensive simulation experiments show that SAREC-EDF significantly improves overall system performance over three baseline scheduling algorithms (variations of EDF) by up to 72.55%.