Heterogeneous parallel and distributed computing systems may operate in an environment where certain system performance features degrade due to unpredictable circumstances. Robustness can be defined as the degree to which a system can function correctly in the presence of parameter values different from those assumed. This work develops a model for quantifying robustness in a dynamic heterogeneous computing environment where task execution time estimates are known to contain errors. This mathematical expression of robustness is then applied to two different problem environments. Several heuristic solutions to both problem variations are presented that utilize this expression of robustness to influence mapping decisions. © 2007 Springer Science+Business Media, LLC.