Optimal Scheduling of Parallelizable Jobs with Varying Levels of Parallelizability

Core Concepts

The optimal scheduling policy depends on the scaling behavior of the system. When the system has more spare capacity, deferring parallelizable work is more important. When the system is heavily loaded, prioritizing short jobs is more important.

Abstract

The paper considers a system with k homogeneous servers and ℓ classes of parallelizable jobs. Each job class i has an associated job size distribution Si and parallelizability level ci, where ci represents the maximum number of servers the job can utilize.
The key insights are:

When all job classes have the same exponential size distribution, the Least-Parallelizable-First (LPF) policy, which prioritizes jobs from the least parallelizable classes, is optimal for minimizing mean response time.

In the conventional heavy-traffic regime as ρ→1, the Shortest-Expected-Remaining-Processing-Time (SERPT) policy, which prioritizes jobs with the shortest expected remaining processing time, is asymptotically optimal.

In lighter-load scaling regimes (Sub-Halfin-Whitt), LPF is asymptotically optimal because deferring parallelizable work is more important than prioritizing short jobs when there is a high probability of having idle servers.

In heavier-load scaling regimes (Super-NDS), SERPT is asymptotically optimal because minimizing queueing time becomes the dominant concern when the probability of having idle servers vanishes.

The paper also discusses practical considerations, such as how to schedule when the scaling behavior is unknown and the challenges of scheduling with non-exponential job size distributions.

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Key Insights Distilled From

Asymptotically Optimal Scheduling of Multiple Parallelizable Job Classes

by Benjamin Ber... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00346.pdf

Deeper Inquiries

What are the implications of the results in this paper for real-world systems that may not fit neatly into the scaling regimes analyzed

The implications of the results in this paper for real-world systems that may not fit neatly into the scaling regimes analyzed are significant. The findings suggest that the optimal scheduling policies, such as LPF and SERPT, are tailored to specific scaling behaviors. In real-world systems where the scaling behavior may not align perfectly with the analyzed regimes, the challenge lies in determining the most suitable policy.
For systems that do not fall into the defined scaling regimes, a more adaptive approach to scheduling may be necessary. This could involve dynamically switching between policies based on the observed system behavior. Implementing a hybrid approach that combines the principles of LPF and SERPT could be beneficial in such cases. By monitoring the system's performance metrics and adjusting the scheduling policy accordingly, real-world systems can strive to achieve optimal performance even in non-standard scaling scenarios.

How might the scheduling policies need to be adapted if job sizes are not exponentially distributed

If job sizes are not exponentially distributed, the scheduling policies may need to be adapted to accommodate different size distributions. Exponential distributions simplify the analysis and allow for elegant mathematical solutions, but in practice, job sizes can follow various distributions.
When job sizes are not exponentially distributed, the scheduling policies may need to incorporate additional parameters to account for the characteristics of the specific distribution. Policies that consider the variance, skewness, or other statistical properties of the job size distribution may be more effective in optimizing response times.
Adapting the scheduling policies to handle non-exponential size distributions could involve recalibrating the prioritization criteria, adjusting the server allocation strategies, or introducing new heuristics to account for the variability in job sizes. By incorporating the characteristics of the actual job size distribution, the scheduling policies can be more robust and efficient in real-world scenarios.

Are there other factors, beyond parallelizability and job size, that should be considered when designing optimal scheduling policies for parallelizable workloads

Beyond parallelizability and job size, several other factors should be considered when designing optimal scheduling policies for parallelizable workloads. Some of these factors include:

Resource Constraints: Taking into account the limitations of the system resources, such as memory, bandwidth, and storage, is crucial in designing efficient scheduling policies. Ensuring that the allocation of resources aligns with the system's capacity can prevent bottlenecks and optimize performance.

Priority Levels: Differentiating between job priorities based on criticality, deadlines, or importance can influence the scheduling decisions. Policies that incorporate priority levels can ensure that high-priority tasks are completed in a timely manner, even in the presence of parallelizable workloads.

Communication Overhead: Considering the communication overhead between parallel tasks and the impact on overall system performance is essential. Minimizing communication delays and optimizing data transfer between parallel tasks can improve efficiency and reduce response times.

Fault Tolerance: Building resilience into the scheduling policies to handle failures, errors, or disruptions is important for maintaining system stability. Implementing fault-tolerant mechanisms can ensure continuous operation and prevent job failures from affecting the entire workload.

By integrating these additional factors into the design of scheduling policies, real-world systems can achieve optimal performance and responsiveness in managing parallelizable workloads.