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We present a guaranteed real-time scheduling algorithm for multiple real-time tasks subject to (m,k)-firm deadlines on homogeneous multiprocessors. The scheduling objective of the proposed algorithm is to provide guaranteed performance by bounding the probability of missing (m,k)-firm deadline constraints while improving the probability of deadline satisfactions as much as possible. This goal is established to satisfy the minimum requirements expressed by (m,k)-firm deadlines and simultaneously provide the best possible quality of service. We analytically establish that the proposed algorithm provides assurance on the bounded probability of missing (m,k)-firm constraints. Experimental studies validate our analytical results and confirm the effectiveness and superiority of the proposed scheme in achieving our scheduling objective.