This book investigates a problem of robust resource allocation for distributed computing systems operating under QoS constraints. Often, such systems function in a physical environment replete with uncertainty causing the amount of processing required over time to fluctuate substantially. The first two chapters show how an effective resource allocation can be achieved in the shipboard distributed computing system and IBM cluster based imaging system. The general form of stochastic robustness metric is presented next, where the relationship between uncertainty in system and its impact on performance are linked stochastically. The utility of the established metric is exploited for the large class of distributed systems operating on periodically updated data sets. One of the major reasons for possible QoS violations in distributed systems is a loss of resources, frequently caused by abnormal operating conditions. The last chapter describes a solution method based on the concepts of the Derman- Lieberman- Ross theorem. The experimental results indicate a significant potential of this approach to generate robust resource allocations in unstable distributed systems.