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In this study, we consider an environment composed of a heterogeneous cluster of multicore-based machines used to analyze satellite images. The workload involves large data sets, and is typically subject to deadline constraints. Multiple applications, each represented by a directed acyclic graph (DAG), are allocated to a dedicated heterogeneous distributed computing system. Each vertex in the DAG represents a task that needs to be executed and task execution times vary substantially across machines. The goal of this research is to assign applications to multicore-based parallel system in such a way that all applications complete before a common deadline, and their completion times are robust against uncertainties in execution times. We define a measure that quantifies robustness in this environment. We design, compare, and evaluate two resource allocation heuristics that attempt to maximize robustness.