Addressing the Robustness of Resource Allocation in the Presence of Application and System Irregularities via PEPA Based Modeling

Applications executing in heterogeneous parallel and/or distributed computing (PDC) environments are often prone to unpredictable runtime due to variations in problem, algorithm, and system characteristics. This serves as a key motivation towards a study of the robustness of resource allocations required to maintain and guarantee a desired level of performance. Performance modeling and evaluation is often utilized to understand and predict the behavior of the application and the computational system from a performance point of view. In prior work, performance modeling for evaluating response times of static resource allocations in PDC systems was introduced by the authors as a proof of concept for validating the use of the performance evaluation process algebra (PEPA) for analyzing the robustness of static resource allocations. Herein, the authors present numerical modeling of several static resource allocations to evaluate their robustness in the presence of compound perturbations generated as combinations of variations in application workload and machine availability. The novelty of the approach is to introduce the compound effect as the variability of both, application workload and processor/machine availability, into the performance modeling of the overall computational system. The performance is obtained as a parallel execution time via a numerical analysis of the modeled execution of applications on non-dedicated parallel computational resources. A significant improvement in the robustness value (up to 143%) among the mappings yielding equal parallel execution times has been demonstrated via the analysis of the results. This notable difference in the robustness values strongly indicates the benefit of selecting one mapping versus the other for guaranteeing the best execution performance.