Timely Trajectory Reconstruction in Finite Buffer Remote Tracking Systems

TL;DR

This work studies the trade-off between real-time state freshness and offline trajectory reconstruction in remote tracking with finite buffers. It introduces AoI as a complementary metric to reconstruction error (RE) and analyzes several packet-dropping policies—Keep-Old, Keep-Fresh, and Inter-arrival-Aware (IaA)—across M/M/1/2 and M/M/1/B+1 queue models, providing closed-form RE and AoI expressions where possible and numerical insights otherwise. The key finding is that AoI-minimizing policies can hurt reconstruction accuracy, while IaA-based strategies offer a favorable balance, achieving improved RE with modest AoI impact; a threshold-based IaA provides tunable trade-offs. These results inform buffer-management design for resource-constrained IoT networks requiring both timely updates and accurate historical analyses.

Abstract

Remote tracking systems play a critical role in applications such as IoT, monitoring, surveillance and healthcare. In such systems, maintaining both real-time state awareness (for online decision making) and accurate reconstruction of historical trajectories (for offline post-processing) are essential. While the Age of Information (AoI) metric has been extensively studied as a measure of freshness, it does not capture the accuracy with which past trajectories can be reconstructed. In this work, we investigate reconstruction error as a complementary metric to AoI, addressing the trade-off between timely updates and historical accuracy. Specifically, we consider three policies, each prioritizing different aspects of information management: Keep-Old, Keep-Fresh, and our proposed Inter-arrival-Aware dropping policy. We compare these policies in terms of impact on both AoI and reconstruction error in a remote tracking system with a finite buffer. Through theoretical analysis and numerical simulations of queueing behavior, we demonstrate that while the Keep-Fresh policy minimizes AoI, it does not necessarily minimize reconstruction error. In contrast, our proposed Inter-arrival-Aware dropping policy dynamically adjusts packet retention decisions based on generation times, achieving a balance between AoI and reconstruction error. Our results provide key insights into the design of efficient buffer management policies for resource-constrained IoT networks.

Figures (14)

• Figure 1: System model.
• Figure 2: Sample path of age $\Delta(t)$, where packet $2$ is delivered after packet $3$, making it stale and thus not reducing the age. Consequently $i_2 = 3$.
• Figure 3: Sample path of packet arrivals and departures under the Keep-Old policy.
• Figure 4: Sample path of packet arrivals and departures under the Keep-Fresh policy.
• Figure 5: Comparison of three packet-dropping policies in an M/M/1/2 queueing system with service rate is $\mu=1$.