Beyond Freshness and Semantics: A Coupon-Collector Framework for Effective Status Updates

Youssef Ahmed; Arnob Ghosh; Chih-Chun Wang; Ness B. Shroff

eess.SYMar 27, 2026

Beyond Freshness and Semantics: A Coupon-Collector Framework for Effective Status Updates

Authors: Youssef Ahmed, Arnob Ghosh, Chih-Chun Wang, Ness B. Shroff

Organizations: Department of ECE, The Ohio State University, Columbus, OH, USA · Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ, USA · Elmore Family School of ECE, Purdue University, West Lafayette, IN, USA · Department of CSE, The Ohio State University, Columbus, OH, USA

Abstract

For status update systems operating over unreliable energy-constrained wireless channels, we address Weaver's long-standing Level-C question: do my packets actually improve the plant's behavior? Each fresh sample carries a stochastic expiration time -- governed by the plant's instability dynamics -- after which the information becomes useless for control. Casting the problem as a coupon-collector variant with expiring coupons, we (i) formulate a two-dimensional average-reward MDP, (ii) prove that the optimal schedule is doubly thresholded in the receiver's freshness timer and the sender's stored lifetime, (iii) derive a closed-form policy for deterministic lifetimes, and (iv) design a Structure-Aware Q-learning algorithm (SAQ) that learns the optimal policy without knowing the channel success probability or lifetime distribution. Simulations validate our theoretical predictions: SAQ matches optimal Value Iteration performance while converging significantly faster than baseline Q-learning, and expiration-aware scheduling achieves up to 50% higher reward than age-based baselines by adapting transmissions to state-dependent urgency -- thereby delivering Level-C effectiveness under tight resource constraints.

Figures & tables

Metric	Definition	Level	Insight
AoI	$\Delta(n)=n-U(n)$	A	Data freshness
MSE	$\mathbb{E}[\\|x_{n}-\hat{x}_{n}\\|^{2}]$	A	Estimation accuracy
AoSync	$n-S(n)$	A	Synchronization gap
AoA	$n-A(n)$	A	Actuation staleness
AoL	$t-\hat{t}_{j}$ ; $t-t_{i}$	A	Round-trip freshness
AoC	$n-U_{\mathrm{comp}}(n)$	A	Computation freshness

TABLE I : Key update metrics mapped to Shannon-Weaver layers. Symbols:

n

: current slot;

U(n)

: generation time of latest received update;

\Delta(n)=n-U(n)

;

x_{n},\hat{x}_{n}

: true/estimated states;

A(n)

: last action time;

\hat{t}_{j}

: freshest command time;

t_{i}

: status update time causing latest action;

S(n)

: last sync time;

U_{\mathrm{comp}}(n)

: generation time of latest computation result;

w(n)

: urgency weight;

C(\cdot)

: cost function;

r_{k}

: reward at age

k

;

\epsilon

: tolerance.

Panel of Figure 2 — Fig. 1 : Impact of observation age and noise $\sigma_{\max}$ on controller performance.

Panel of Figure 3 — Fig. 2 : Expiration Analysis and Scheduling Performance.

Panel of Figure 4 — Fig. 3 : Coupon-collector model with expiring samples.

Fig. 4 : Optimal policy regions for varying $p_{s}$ values ( $K=20$ , $c/r=0.5$ ). Blue (shaded) regions: the sender transmits ( $a=1$ ); white regions: the sender remains silent ( $a=0$ ). The diagonal $T_{r}=T_{s}$ marks the boundary above which the receiver already holds fresher data, so transmission is never optimal (Theorem 3 (ii)). As $p_{s}$ decreases from left to right, the send region expands to compensate for higher packet-loss probability.

Panel of Figure 6 — Fig. 5 : Average reward vs. system parameters for Baseline Q, SAQ, and optimal VI.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Category	Feature	Ctrl.	Pred.	Per.
State	Current observation ( $\mathbf{y}_{n}$ )	–	✓	–
State	Stale observation ( $\hat{\mathbf{y}}_{n}$ )	✓	–	–
Context	Observation age ( $\delta_{n}$ )	✓	–	✓
	Target position ( $t_{n}$ )	✓	✓	–
	Last action ( $u_{n-1}$ )	✓	✓	–
Error	Tracking error ( $x_{n}-t_{n}$ )	✓	✓	–

Appendix

TABLE II : Input features for Controller, Predictor, and Periodic agents.

Age of Information

Age of Information (AoI) measures how stale received data is and guides timely updates in communication, control, and distributed systems.

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When Mean Age Is Not Enough: Distribution-Aware Scheduling for Networked LQR Control

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Open paper AskPDF arXiv

Age of Information (AoI) has become a central metric for the design of wireless update systems, especially in applications where fresh measurements support tracking, estimation, and control. Despite its popularity, the use of mean AoI or peak AoI as a surrogate for closed-loop performance is often motivated by intuition rather than by a control-theoretic derivation. This paper examines whether minimizing the mean AoI is in fact optimal for networked control systems. For scalar linear time-invariant systems with delayed intermittent updates, we show that, under state-independent scheduling policies, the infinite-horizon LQR tracking problem reduces to an optimization over the distribution of inter-scheduling intervals. The resulting objective depends on higher-order statistical moments, and in unstable or correlated regimes on exponential moments, of the inter-scheduling process rather than only on its mean. Consequently, policies with identical mean AoI can induce substantially different tracking costs. We further extend the analysis to disturbances with exponentially decaying autocorrelation and derive equivalent cost formulations that expose the role of the full interval distribution. Finally, we evaluate the theory using real vehicle trajectories from the NGSIM US-101 dataset. The empirical results match the predicted performance trends, demonstrating that mean AoI alone is insufficient for control-oriented network design.

Abstract

Age of Information

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