Robustness Analysis of Scaled Resource Allocation Models Using the Imperial PEPA Compiler

Abstract

The increase in scale provided by distributed computing systems has expanded scientific discovery and engineering solutions. Stochastic modeling with Performance Evaluation Process Algebra (PEPA) has been used to evaluate the robustness of static resource allocations in parallel and distributed computing systems. These evaluations have previously been performed through the PEPA Plug-In for the Eclipse Integrated Development Environment and have been limited by factors that include: i) the size and complexity of the underlying, in-use PEPA model, ii) a small number of resource allocation models available for analysis, and iii) the human interaction necessary to configure the PEPA Eclipse Plug-In, thus limiting potential automation. As the size and complexity of the underlying PEPA models increases, the number of states to be evaluated for each model also greatly increases, leading to a case of state space explosion. In this work, we validate the Imperial PEPA Compiler (IPC) as a replacement for the PEPA Eclipse Plug-In for the robustness analysis of resource allocations. We make available an implementation of the IPC as a Singularity container, as part of a larger online repository of PEPA resources. We then develop and test a programmatic method for generating PEPA models for resource allocations. When combined with our IPC container, this method allows automated analysis of resource allocation models at scale. The use of the IPC allows the evaluation of larger models than it is possible when using the PEPA Eclipse Plug-In. Moreover, the increases in scale in both model size and number of models, support the development of improved makespan targets for robustness metrics, including those among applications subject to perturbations at runtime, as found in typical parallel and distributed computing environments.