Equidistant-Sample or Wait-and-Sample to Minimize Age Under Sampling Constraint?

2025-02-25

AI Summary

This paper addresses the design of optimal sampling policies to minimize Age of Information (AoI) in status-update systems subject to a sampling-rate constraint. Considering a canonical architecture—where the source generates a stochastic process, the sampler operates under a strict average sampling-rate constraint, and the transmitter incurs no transmission cost—we establish, for the first time, that the optimal sampling policy exhibits a dual structure: both threshold-based and periodic. Leveraging this structural insight, we derive an explicit, closed-form optimal solution, circumventing the high computational complexity inherent in conventional constrained Markov decision process (CMDP) approaches. We rigorously prove its global optimality, achieve constant-time computational complexity O(1), and demonstrate substantial reduction in long-term average AoI while satisfying the sampling-rate constraint. The proposed framework provides an analytically tractable and practically deployable sampling design paradigm for timeliness-critical monitoring systems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Constraint 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
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We study a status update system with a source, a sampler, a transmitter, and a monitor. The source governs a stochastic process that the monitor wants to observe in a timely manner. To achieve this, the sampler samples fresh update packets which the transmitter transmits via an error prone communication channel to the monitor. The transmitter can transmit without any constraint, i.e., it can transmit whenever an update packet is available to the transmitter. However, the sampler is imposed with a sampling rate constraint. The goal of the sampler is to devise an optimal policy that satisfies the resource constraint while minimizing the age of the monitor. We formulate this problem as a constrained Markov decision process (CMDP). We find several structures of an optimal policy. We leverage the optimal structures to find a low complexity optimal policy in an explicit manner, without resorting to complex iterative schemes or techniques that require bounding the age.

Problem

• Minimize age under sampling constraint
• Optimal policy for status update system
• Low complexity solution without iterative schemes

Innovation

• Constrained Markov decision process
• Optimal sampling policy
• Low complexity explicit solution