Robustness Prediction and Evaluation of Divisible Load Scheduling on Computing Systems with Unpredictable Variations

Abstract

This work addresses the problem of predicting and evaluating the robustness of divisible load scheduling of data parallel workloads (also called arbitrarily divisible workloads) onto high performance parallel and distributed computing systems with unpredictable variations. Divisible load scheduling is based on the divisible load theory (DLT) which offers a linear, deterministic, and tractable model for scheduling arbitrarily divisible workloads. High performance parallel and distributed computing systems operate in an environment characterized by unpredictable variations (or perturbations) such as system load or unexpected resource failures. In this work, we analytically evaluate and empirically determine the robustness of divisible load scheduling algorithms (called DLT algorithms) with respect to variations in processor availability via realistic simulation. The realism arises from modeling the characteristics of two applications from the NAS parallel benchmark suite, as well as from modeling the target system as a 3D torus topology, one of the most widely used interconnection networks. Extending prior related work, we conduct an analytical evaluation as well as a simulation-based study of the robustness of divisible load scheduling for scheduling the two NAS parallel benchmarks, namely, embarrassingly parallel (EP) which is computationally intensive and integer sort (IS) which is communication intensive. The simulation results indicate that the robustness observed via simulation of scheduling the EP benchmark is always within the analytically predicted range, and that the robustness observed via simulation of scheduling the IS benchmark is within the analytically predicted range in the best case, and within 6.56% on average in the worst case.