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This paper summarizes some of our research in the area of robust static resource allocation for distributed computing systems operating under imposed quality of service (QoS) constraints. Often, these systems are expected to function in a physical environment replete with uncertainty, which causes the amount of processing required over time to fluctuate substantially. Determining a resource allocation that accounts for this uncertainty in a way that can provide a probabilistic guarantee that a given level of QoS is achieved is an important research problem. The stochastic robustness metric described in this research is based on a mathematical model where the relationship between uncertainty in system parameters and its impact on system performance are described stochastically.