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This thesis focuses on two real-time scheduling algorithms: fixed-priority with preemption threshold (FPPT) and the reservation-based algorithm (RBA). FPPT is an important form of real-time scheduling algorithm that generalizes both fixed-priority preemptive (FPP) and fixed-priority non-preemptive (FPNP), i.e., FPP and FPNP are the two boundary cases for FPPT. The critical instant for FPPT is rephrased, and it is shown that FPPT is robust under its critical instant. When a task set is schedulable by FPPT with predefined regular priorities, there may exist multiple valid preemption threshold assignments, which are proved to be delimited by two special assignments, called minimal and maximal assignment respectively. This thesis presents effective algorithms to compute the minimal and maximal assignment by starting from FPNP In addition, algorithms are presented to compute the minimal (maximal) assignment when the other is known. The maximal assignment reduces the number of context switches and can eliminate some resource sharing issues. It is shown that the algorithm to find the maximal assignment can be used to perform a schedulability test for FPPT. Resource management protocols for FPPT are not addressed in this work, which is left for future study. RBA is a kind of bandwidth reservation algorithm in which an even duration of time (the bandwidth) is made available for executing aperiodic tasks to improve their response time. This thesis provides the theoretical support to compute the maximal size of the reserved bandwidth after guaranteeing schedulability of a periodic task set for earliest deadline first (EDF), rate monotonic (RMA), and FPPT algorithms. When RMA is used to schedule periodic tasks, the known algorithm to calculate the reservation size is complicated and ineffective. It is shown that the combination of RBA and FPPT can obtain a reservation size no smaller than that of RMA and avoid the high run-time cost of EDF. Combined with a background server, the response time of aperiodic tasks can be further improved. However, this thesis does not consider all practical issues. For example, the bandwidth may be too small and the practical costs of additional context switching may be expensive. To verify the research results of this thesis, a small real-time scheduling tool-kit was created as part of the thesis work. The tool-kit allows scheduling algorithms to be created and tested (via simulations), where scheduling results are presented as step-by-step Gantt-charts. The tool-kit was invaluable in generating examples to prove or disprove different aspects of the scheduling work for the thesis. The tool-kit has been extended with multiple scheduling algorithms, not just those specific to this thesis.