Current real-time systems have typically been designed under the assumption that characteristics of the workload and the computing environment are both well-known and well-specified at the time of system design. Future real-time systems, however, will be required to operate in a more uncertain and stochastic environment. As a result, the designers of these future systems face a much more difficult task in developing resource scheduling algorithms and formally establishing their performance, timing, and fault-tolerance properties. This project is concerned with the design and performance evaluation of scheduling algorithms for real-time systems operating in a stochastic environment. The specific focus is on developing rigorous and formal approaches towards analyzing and designing such systems in a wide range of settings including uniprocessor, multiprocessor and fault-tolerant environments.