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In the past decades, distributed systems have been widely applied to real-time applications, most of which have fault-tolerance requirements to assure high reliability. Due to the stringent space constraints of real-time systems, the issue of schedulability becomes a major concern in the design of fault-tolerant and real-time distributed systems. Most existing real-time and fault-tolerant scheduling algorithms, which are based on the primary-backup scheme for periodic real-time tasks, introduce unnecessary redundancies by aggressively using active-backup copies. To solve this problem, we propose two novel fault-tolerant techniques, which are seamlessly integrated with fixed-priority-based scheduling algorithms. These techniques leverage redundancies to enhance schedulability in fault-tolerant and real-time distributed systems. Our fault-tolerant techniques make use of the primary-backup scheme to tolerate permanent hardware failures. The first technique (referred to as Tercos) terminates the execution of active-backup copies, when corresponding primary copies are successfully completed. Tercos is designed to reduce scheduling lengths in fault-free scenarios to enhance schedulability by virtue of executing portions of active-backup copies in passive forms. The second technique (referred to as Debus) uses a deferred-active-backup scheme to further minimize schedule lengths to improve the schedulability performance. Debus schedules active-backup copies as late as possible, while terminating active-backup copies when their primary copies are completed. Experimental results show that, compared with existing algorithms in literature, Tercos can significantly improve schedulability by up to 17.0% (with an average of 9.7%). Furthermore, empirical results reveal that Debus can enhance schedulability over Tercos by up to 12% (with an average of 7.8%).