A Markov Chain Monte Carlo Approach to Cost Matrix Generation for Scheduling Performance Evaluation

TL;DR

This paper introduces a Markov Chain Monte Carlo method to generate cost matrices with a known distribution for scheduling performance evaluation in high-performance computing, ensuring unbiased and uniform instance sampling.

Contribution

It presents a novel MCMC-based approach for generating cost matrices with controlled distribution, improving the reliability of scheduling performance assessments.

Findings

Provides formal guarantees on instance distribution

Ensures uniform sampling among heterogeneous task-machine configurations

Enhances simulation accuracy for scheduling algorithms

Abstract

In high performance computing, scheduling of tasks and allocation to machines is very critical especially when we are dealing with heterogeneous execution costs. Simulations can be performed with a large variety of environments and application models. However, this technique is sensitive to bias when it relies on random instances with an uncontrolled distribution. We use methods from the literature to provide formal guarantee on the distribution of the instance. In particular, it is desirable to ensure a uniform distribution among the instances with a given task and machine heterogeneity. In this article, we propose a method that generates instances (cost matrices) with a known distribution where tasks are scheduled on machines with heterogeneous execution costs.