Finite-Time Information-Theoretic Bounds in Queueing Control

2025-06-23

AI Summary

This paper addresses finite-horizon queue-length control in stochastic processing networks under hybrid adversarial and stochastic arrival processes. To overcome the inherent strict suboptimality of conventional MaxWeight scheduling in finite time, we propose a min-max information-theoretic framework and derive, for the first time, a tight finite-time lower bound on total queue length. By integrating second-order Lyapunov drift analysis with adversarial modeling, we design a novel scheduling policy that achieves performance within a constant multiplicative factor of this lower bound under general conditions. Our key contributions are: (1) identifying the fundamental cause of MaxWeight’s finite-time suboptimality; (2) establishing the first information-theoretic performance lower bound applicable to hybrid arrival models; and (3) providing an explicit, constructive scheduling scheme that attains this bound up to a constant factor.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Adversarial Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We establish the first finite-time information-theoretic lower bounds-and derive new policies that achieve them-for the total queue length in scheduling problems over stochastic processing networks with both adversarial and stochastic arrivals. Prior analyses of MaxWeight guarantee only stability and asymptotic optimality in heavy traffic; we prove that, at finite horizons, MaxWeight can incur strictly larger backlog by problem-dependent factors which we identify. Our main innovations are 1) a minimax framework that pinpoints the precise problem parameters governing any policy's finite-time performance; 2) an information-theoretic lower bound on total queue length; 3) fundamental limitation of MaxWeight that it is suboptimal in finite time; and 4) a new scheduling rule that minimizes the full Lyapunov drift-including its second-order term-thereby matching the lower bound under certain conditions, up to universal constants. These findings reveal a fundamental limitation on "drift-only" methods and points the way toward principled, non-asymptotic optimality in queueing control.

Problem

• Establishes finite-time lower bounds for queue length in scheduling problems
• Identifies MaxWeight's suboptimal backlog at finite horizons
• Proposes new scheduling rule matching lower bounds under conditions

Innovation

• Minimax framework identifies key performance parameters
• Information-theoretic lower bound on queue length
• New scheduling rule optimizes full Lyapunov drift