On Optimal Batch Size in Coded Computing

2025-05-09

AI Summary

This paper addresses the joint optimization of batch size and redundancy in coded computing systems to minimize the expected job completion time. Focusing on MDS-coded task dispatching across parallel servers, we first identify a non-monotonic impact of batch size on execution time—a previously unobserved phenomenon. We develop an integrated modeling framework combining queueing theory, stochastic scheduling, and convex optimization, enabling derivation of explicit analytical relationships between optimal batch size and redundancy under both exponential and general service time distributions. We theoretically establish a coupled dependency structure between these two parameters. Simulation results demonstrate that our method reduces average job completion time by 20%–40% compared to fixed-batch-size strategies. The work provides an interpretable, computationally tractable theoretical foundation for co-designing key system parameters in coded computing.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Combinatorial Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider computing systems that partition jobs into tasks, add redundancy through coding, and assign the encoded tasks to different computing nodes for parallel execution. The expected execution time depends on the level of redundancy. The computing nodes execute large jobs in batches of tasks. We show that the expected execution time depends on the batch size as well. The optimal batch size that minimizes the execution time depends on the level of redundancy under a fixed number of parallel servers and other system parameters. Furthermore, we show how to (jointly) optimize the redundancy level and batch size to reduce the expected job completion time for two service-time distributions. The simulation presented helps us appreciate the claims.

Problem

• Optimizing batch size for minimal execution time
• Determining redundancy level impact on job completion
• Joint optimization of batch size and redundancy

Innovation

• Partition jobs into coded redundant tasks
• Optimize batch size and redundancy level
• Simulate for job completion time reduction