# Workflow Scheduling in the Cloud with Weighted Upward-rank Priority Scheme Using Random Walk and Uniform Spare Budget Splitting

## TL;DR

This paper introduces a novel workflow scheduling method in cloud environments that combines Markovian importance-based prioritization with uniform spare budget splitting, outperforming existing algorithms in various workflow scenarios.

## Contribution

It proposes a new prioritization scheme using Markovian chain stationary probabilities and a uniform spare budget splitting strategy for improved cloud workflow scheduling.

## Key findings

- Markovian prioritization improves workflow makespan.
- Uniform spare budget splitting outperforms proportional splitting.
- Algorithms outperform state-of-the-art in diverse workflows.

## Abstract

We study a difficult problem of how to schedule complex workflows with precedence constraints under a limited budget in the cloud environment. We first formulate the scheduling problem as an integer programming problem, which can be optimized and used as the baseline of performance. We then consider the traditional approach of scheduling jobs in a prioritized order based on the upward-rank of each job. For those jobs with no precedence constraints among themselves, the plain upward-rank priority scheme assigns priorities in an arbitrary way. We propose a job prioritization scheme that uses Markovian chain stationary probabilities as a measure of importance of jobs. The scheme keeps the precedence order for the jobs that have precedence constraints between each other, and assigns priorities according to the jobs' importance for the jobs without precedence constraints. We finally design a uniform spare budget splitting strategy, which splits the spare budget uniformly across all the jobs. We test our algorithms on a variety of workflows, including FFT, Gaussian elimination, typical scientific workflows, randomly generated workflows and workflows from an in-production cluster of an online streaming service company. We compare our algorithms with the-state-of-art algorithms. The empirical results show that the uniform spare budget splitting scheme outperforms the splitting scheme in proportion to extra demand in average for most cases, and the Markovian based prioritization further improves the workflow makespan.