# heSRPT: Optimal Parallel Scheduling of Jobs With Known Sizes

## TL;DR

This paper introduces heSRPT, an optimal parallel job scheduling policy that minimizes mean flow time by balancing short job prioritization with system efficiency, outperforming existing policies significantly.

## Contribution

The paper derives the first optimal server allocation policy for minimizing mean flow time with jobs having diminishing returns from parallelization.

## Key findings

- heSRPT outperforms existing policies by at least 30%.
- The policy allocates servers proportionally to job size, balancing efficiency and priority.
- Optimal scheduling is achieved by completing jobs in size order while maintaining some parallelism.

## Abstract

When parallelizing a set of jobs across many servers, one must balance a trade-off between granting priority to short jobs and maintaining the overall efficiency of the system. When the goal is to minimize the mean flow time of a set of jobs, it is usually the case that one wants to complete short jobs before long jobs. However, since jobs usually cannot be parallelized with perfect efficiency, granting strict priority to the short jobs can result in very low system efficiency which in turn hurts the mean flow time across jobs. In this paper, we derive the optimal policy for allocating servers to jobs at every moment in time in order to minimize mean flow time across jobs. We assume that jobs follow a sublinear, concave speedup function, and hence jobs experience diminishing returns from being allocated additional servers. We show that the optimal policy, heSRPT, will complete jobs according to their size order, but maintains overall system efficiency by allocating some servers to each job at every moment in time. We compare heSRPT with state-of-the-art allocation policies from the literature and show that heSRPT outperforms its competitors by at least 30%, and often by much more.