To ensure timing constraints, traditional real-time system designs usually adopt a worst-case based deterministic approach. However, such an approach is becoming out of sync with the continuous evolution of IC technology and increased complexity of real-time applications. As IC technology continues to evolve into the deep submicron domain, process variation causes processor performance to vary from die to die, chip to chip, and even core to core. The extensive resource sharing on multicore platforms also significantly increases the uncertainty when executing real-time tasks. The traditional approach can only lead to extremely pessimistic, and thus, unpractical design of real-time systems.Our research seeks to address the uncertainty problem when designing real-time systems on multi-core platforms. We first attacked the uncertainty problem caused by process variation. We proposed a virtualization framework and developed techniques to optimize the system's performance under process variation. We further studied the problem on peak temperature minimization for real-time applications on multi-core platforms. Three heuristics were developed to reduce the peak temperature for real-time systems. Next, we sought to address the uncertainty problem vi in real-time task execution times by developing statistical real-time scheduling techniques. We studied the problem of fixed-priority real-time scheduling of implicit periodic tasks with probabilistic execution times on multi-core platforms. We further extended our research for tasks with explicit deadlines. We introduced the concept of harmonic to a more general task set, i.e. tasks with explicit deadlines, and developed new task partitioning techniques. Throughout our research, we have conducted extensive simulations to study the effectiveness and efficiency of our developed techniques.The increasing process variation and the ever-increasing scale and complexity of real-time systems both demand a paradigm shift in the design of real-time applications. Effectively dealing with the uncertainty in design of real-time applications is a challenging but also critical problem. Our research is such an effort in this endeavor, and we conclude this dissertation with discussions of potential future work.