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Over the past few years, as multicore technology has become cost-effective, multiprocessor systems have become increasingly prevalent. The growing availability of such systems has spurred the development of computationally-intensive applications for which single-processor designs are insufficient. Many such applications have timing constraints; such timing constraints are often not static, but may change in response to both external and internal stimuli. Examples of such applications include tracking systems and many multimedia applications. Motivated by these observations, this dissertation proposes several different adaptive scheduling algorithms that are capable of guaranteeing flexible timing constraints on multiprocessor platforms. Under traditional task models (e.g., periodic, sporadic, etc.), the schedulability of a system is based on each task’s worst-case execution time (WCET), which defines the maximum amount of time that each of its jobs can execute. The disadvantage of using WCETs is that systems may be deemed unschedulable even if they would function correctly most of the time when deployed. Adaptive real-time scheduling algorithms allow the timing constraints of applications to be adjusted based upon runtime conditions, instead of always using fixed timing constraints based upon WCETs. While there is a substantial body of prior work on scheduling applications with static timing constraints on multiprocessor systems, prior to this dissertation, no adaptive multiprocessor scheduling approach existed that is capable of ensuring bounded “error” (where error is measured by comparison to an ideal allocation). In this dissertation, this limitation is addressed by proposing five different multiprocessor scheduling algorithms that allow a task’s timing constraints to change at runtime. The five proposed adaptive algorithms are based on different non-adaptive multiprocessor scheduling algorithms that place different restrictions on task migrations and preemptions. The relative advantages of these algorithms are compared by simulating both the Whisper human tracking system and the Virtual Exposure Camera (VEC), both of which were developed at The University of North Carolina at Chapel Hill. In addition, a feedback-based adaptive framework is proposed that not only allows timing constraints to adapt at runtime, but also detects which adaptions are needed. An implementation of this adaptive framework on a real-time multiprocessor testbed is discussed and its performance is evaluated by using the core operations of both Whisper and VEC. From this dissertation, it can be concluded that feedback and optimization techniques can be used to determine at runtime which adaptions are needed. Moreover, the accuracy of an adaptive algorithm can be improved by allowing more frequent task migrations and preemptions; however, this accuracy comes at the expense of higher migration and preemption costs, which impacts average-case performance. Thus, there is a tradeoff between accuracy and average-case performance that depends on the frequency of task migrations/preemptions and their cost.