Taming the Heavy Tail: Age-Optimal Preemption

2026-01-23

AI Summary

This work addresses the degradation of Age of Information (AoI) caused by heavy-tailed delays under general service time distributions. The authors model the joint sampling and preemption system as a piecewise-deterministic Markov process (PDMP) with impulse control, deriving coupled integral average-cost optimality equations via dynamic programming and reformulating the preemption decision as an optimal stopping problem on a one-dimensional boundary. The study uncovers the counterintuitive phenomenon that delay variance can be leveraged into an AoI advantage under preemption. Exploiting the busy-period invariance structure, they design an efficient policy iteration algorithm incorporating a hybrid uniform/logarithmic action grid, far-field linear truncation, and heavy-tail acceleration techniques. Under Pareto and log-normal service times, the proposed method achieves up to a 30-fold reduction in average cost compared to non-preemptive AoI-optimal and zero-wait baselines.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

This paper studies a continuous-time joint sampling-and-preemption problem, incorporating sampling and preemption penalties under general service-time distributions. We formulate the system as an impulse-controlled piecewise-deterministic Markov process (PDMP) and derive coupled integral average-cost optimality equations via the dynamic programming principle, thereby avoiding the smoothness assumptions typically required for an average-cost Hamilton-Jacobi-Bellman quasi-variational inequality (HJB-QVI) characterization. A key invariance in the busy phase collapses the dynamics onto a one-dimensional busy-start boundary, reducing preemption control to an optimal stopping problem. Building on this structure, we develop an efficient policy iteration algorithm with heavy-tail acceleration, employing a hybrid (uniform/log-spaced) action grid and a far-field linear closure. Simulations under Pareto and log-normal service times demonstrate substantial improvements over AoI-optimal non-preemptive sampling and zero-wait baselines, achieving up to a 30x reduction in average cost in heavy-tailed regimes. Finally, simulations uncover a counterintuitive insight: under preemption, delay variance, despite typically being a liability, can become a strategic advantage for information freshness.

Problem

• Age of Information
• preemption
• heavy-tailed service times
• sampling
• average-cost optimization

Innovation

• impulse-controlled PDMP
• average-cost optimality equations
• optimal stopping
• heavy-tail acceleration
• preemption control