Buffer Management for Timely Reconstruction: Lower Bounds and Near-Optimal Policies

초록

Remote tracking systems play a critical role in applications such as IoT sensing, monitoring, surveillance, and healthcare, where updates must be sufficiently fresh for real-time decisions while also informative enough to reconstruct past trajectories. We study this dual objective for a single-source system whose state follows a Wiener process, with updates generated at rate lambda and transmitted over a non-preemptive M/M/1/2 communication link, i.e., a single-server link with exponential service times of rate mu and a buffer that can store at most one waiting packet. Freshness is measured using the average peak Age of Information (AoI) and the time-average AoI, while historical fidelity is captured by a long-run reconstruction error (RE) derived from LMMSE interpolation. We first analyze a stationary randomized replacement (SRP) rule that, upon an arrival to a full system, keeps the fresh packet with probability alpha, and derive closed-form expressions for AoI and RE. Our results show that AoI decreases monotonically with alpha, where as RE varies non-monotonically. In the heavy-traffic limit (lambda to infinity), RE converges to 1/(3 mu) regardless of alpha, revealing a fundamental lower bound. To further navigate the timeliness-fidelity trade-off, we introduce a threshold-based dropping policy with parameter gamma. Analysis and numerical results show that thresholding can reduce RE relative to keep-fresh with only a modest age penalty, providing practical guidelines for selecting alpha and gamma.

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