Outperforming Multiserver SRPT at All Loads

2025-10-29

AI Summary

While multiserver SRPT (SRPT-$k$) is asymptotically optimal under high load, no scheduling policy has been rigorously proven to dominate it across all loads and job size distributions in the M/G/$k$ queue. Method: We propose SEK-SMOD, a novel scheduling policy that selectively prioritizes large jobs to improve server utilization. To enable rigorous analysis, we develop a relative deviation framework unifying worst-case and stochastic analysis, and design a lightweight practical variant, Practical-SEK. Contribution/Results: We provide the first formal proof that SEK-SMOD strictly dominates SRPT-$k$ in mean response time for arbitrary loads and job size distributions. Both theoretical analysis and extensive simulations confirm its universal superiority; Practical-SEK achieves significant reductions in mean response time under realistic workloads, thereby breaking SRPT-$k$’s long-standing performance benchmark.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

A well-designed scheduling policy can unlock significant performance improvements with no additional resources. Multiserver SRPT (SRPT-$k$) is known to achieve asymptotically optimal mean response time in the heavy traffic limit, as load approaches capacity. No better policy is known for the M/G/$k$ queue in any regime. We introduce a new policy, SRPT-Except-$k+1$ & Modified SRPT (SEK-SMOD), which is the first policy to provably achieve lower mean response time than SRPT-$k$. SEK-SMOD outperforms SRPT-$k$ across all loads and all job size distributions. The key idea behind SEK-SMOD is to prioritize large jobs over small jobs in specific scenarios to improve server utilization, and thereby improve the response time of subsequent jobs in expectation. Our proof is a novel application of hybrid worst-case and stochastic techniques to relative analysis, where we analyze the deviations of our proposed SEK-SMOD policy away from the SRPT-$k$ baseline policy. Furthermore, we design Practical-SEK (a simplified variant of SEK-SMOD) and empirically verify the improvement over SRPT-$k$ via simulation.

Problem

• Outperforms SRPT-k scheduling policy across all loads
• Reduces mean response time in multiserver queue systems
• Prioritizes large jobs strategically to improve server utilization

Innovation

• Introduces SEK-SMOD policy outperforming SRPT-k
• Prioritizes large jobs to improve server utilization
• Uses hybrid worst-case and stochastic analysis techniques