Parallel and distributed computing has led to a proliferation in solving computationally intensive mathematical, science, or engineering problems. However, such computational environments are often prone to unpredictable variations due to problem, algorithm, and system characteristics. Therefore, a robustness study of resource allocations and application scheduling is required to guarantee a desired level of performance. Given an initial workload, a mapping of applications to resources is considered to be robust if it optimizes the execution performance and guarantees a desired level of performance in the presence of unpredictable perturbations at runtime. In this research work, a stochastic process algebra, performance evaluation process algebra, is used for obtaining performance of various resource allocations via a numerical analysis of performance modeling of the parallel execution of applications on parallel computing resources. Further, a robustness analysis of various allocations is performed for finding a robust mapping from a set of initial mapping schemes. The numerical results obtained from this performance modeling of resource allocations have been validated by the simulation results of earlier research, which are available from the existing literature, thus underscoring the significance of using stochastic process algebra models in providing a cost-effective and low overhead analysis of robustness. Copyright (C) 2016 John Wiley & Sons, Ltd.