The Case for Phase-Aware Scheduling of Parallelizable Jobs

Abstract

Parallelizable workloads are ubiquitous and appear across a diverse array of modern computer systems. Data centers, supercomputers, machine learning clusters, distributed computing frameworks, and databases all process jobs designed to be parallelized across many servers or cores. Unlike the jobs in more classical models, such as the M/G/k queue, that each run on a single server, parallelizable jobs are capable of running on multiple servers simultaneously. When a job is parallelized across additional servers or cores, the job receives a speedup and can be completed more quickly.

Scheduling for Multi-Phase Parallelizable Jobs

“…The choice of which jobs to process by the algorithm is defined by the number of jobs in each of the two-phases. Compared to the algorithm [15] that always prioritises jobs that are in their in-elastic phases, our algorithm prioritises jobs that are in their in-elastic phase only when there are sufficiently many of them and the total number of jobs is less compared to the total number of servers.…”

“…In addition to the analytical results, we also present average-case simulation results to illustrate the actual performance of the proposed algorithm. We compare the performance of our proposed algorithm with EQUI, the inelastic first algorithm [15], as well as the phase aware FCFS [19], and observe that the performance of our algorithm is comparable or better than EQUI and the inelastic first algorithm, while outperforming phase aware FCFS always.…”

“…Note that with the continuous allocation model, it is possible that k j (t) < 1. Following [2], [9], [15], however, we let s j (t) = k j (t) 1/α even when k j (t) < 1.…”

“…For example in a MapReduce framework [14], initially, jobs have full/limited parallelizability, while in the May 3, 2022 DRAFT concluding stages they become sequential. Given practical considerations as described in detail in [15], it is reasonable to consider the case of jobs having either limited parallelizability [2] (called elastic phase), or are sequential (called in-elastic phase), where 2 ≤ α ≤ 3 is the most relevant regime for limited parallelizability.…”

“…Some partial results have been derived in [20] for the two-phase scheduling problem. In very recent work, [15] characterized an optimal scheduling policy, for the two-phase scheduling problem as studied in this paper, however, with two strong assumptions, i) the size of jobs in the elastic and in-elastic phases are exponentially distributed with the same parameters for all jobs, and are independent of each other, and ii) the job always completes when it is in its in-elastic phase. We avoid all these assumptions in this paper, by letting the job sizes in each phase to be arbitrary, and the first and the last phase of a job can either be elastic or in-elastic.…”