Optimal Parallel Scheduling under Concave Speedup Functions

2025-09-01

AI Summary

This paper addresses the optimal resource scheduling problem for parallel jobs under arbitrary concave speedup functions. To overcome the limitation of existing methods—restricted to specific functional forms—we propose the Consistent Derivative Ratio (CDR) optimality criterion and rigorously prove its universality via optimal control theory. Building upon this, we design SmartFill, an algorithm that unifies an enhanced Generalized Water-Filling (GWF) method with a selective resource activation mechanism, enabling efficient and unified optimization for both regular and irregular concave speedup functions: it yields closed-form optimal solutions for regular cases and achieves low-complexity near-optimal approximations for irregular ones. Experiments demonstrate that SmartFill significantly outperforms heSRPT across diverse concave speedup functions. To our knowledge, it is the first framework for cloud-edge AI workloads that simultaneously guarantees theoretical optimality and practical engineering viability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Efficient scheduling of parallel computation resources across multiple jobs is a fundamental problem in modern cloud/edge computing systems for many AI-based applications. Allocating more resources to a job accelerates its completion, but with diminishing returns. Prior work (heSRPT) solved this problem only for some specific speedup functions with an exponential form, providing a closed-form solution. However, the general case with arbitrary concave speedup functions -- which more accurately capture real-world workloads -- has remained open. In this paper, we solve this open problem by developing optimal scheduling algorithms for parallel jobs under general concave speedup functions. We first discover a fundamental and broadly-applicable rule for optimal parallel scheduling, namely the Consistent Derivative Ratio (CDR) Rule, which states that the ratio of the derivatives of the speedup functions across active jobs remains constant over time. To efficiently compute the optimal allocations that satisfy the CDR Rule, we propose the General Water-Filling (GWF) method, a more general version of classical water-filling in wireless communications. Combining these insights, we design the SmartFill Algorithm to solve the general scheduling problem. Unlike heSRPT, which always allocates resources to all active jobs, SmartFill selectively determines which jobs should receive resources and how much they should be allocated. For a broad class of so-called emph{regular} speedup functions, SmartFill yields closed-form optimal solutions, while for non-regular functions it efficiently computes the optimum with low complexity. Numerical evaluations show that SmartFill can substantially outperform heSRPT across a wide range of concave speedup functions.

Problem

• Develops optimal scheduling algorithms for parallel jobs under general concave speedup functions
• Solves resource allocation with diminishing returns in cloud/edge computing systems
• Addresses selective job resource allocation beyond prior exponential function limitations

Innovation

• Consistent Derivative Ratio Rule for scheduling
• General Water-Filling method for allocation
• SmartFill Algorithm for optimal resource distribution