Towards Robust Resource Allocations via Performance Modeling with Stochastic Process Algebra

Recent developments in the field of parallel and distributed computing have led to a proliferation in solving large and computationally intensive mathematical, science, or engineering problems, which consist of several parallelizable parts and several non-parallelizable (sequential) parts. 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 that mapping optimizes the execution performance and guarantees a desired level of performance in the presence of unpredictable perturbations at runtime. In this research, a stochastic process algebra, Performance Evaluation Process Algebra (PEPA), 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. The PEPA performance model is translated into an underlying mathematical Markov chain model for obtaining performance measures. 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 were made available in the existing literature, thus underscoring the significance and benefits of using stochastic process algebra models and the related numerical analysis in providing a cost effective and low overhead analysis of robustness.