Performance Modeling of Scalable Resource Allocations with the Imperial PEPA Compiler

Advances in computational resources have led to corresponding increases in the scale of large parallel and distributed computer (PDC) systems. With these increases in scale, it becomes increasingly important to understand how these systems will perform as they scale when they are planned and defined, rather than post deployment. Modeling and simulation of these systems can be used to identify unexpected problems and bottlenecks, verify operational functionality, and can result in significant cost savings and avoidance if done prior to the often large capital expenditures that accompany major parallel and distributed computer system deployments. In this paper, we evaluate how PDC systems perform while they are subject to increases in both the number of applications and the number of machines. We generate 42,000 models and evaluate them with the Imperial PEPA Compiler to determine the scaling effects across both an increasing number of applications and an increasing number of machines. These results are then utilized to develop a heuristic for predicting the makespan time for sets of applications mapped onto a number of machines where the applications are subjected to perturbations at runtime. While in the current work the estimated application rates and perturbed rates considered are based on the uniform probability distribution, future work will include a wider range of probability distributions for these rates.