Age Optimal Sampling and Routing under Intermittent Links and Energy Constraints

Links in practical systems, such as satellite–terrestrial integrated networks, exhibit distinct delay distributions, intermittent availability, and heterogeneous energy costs. These characteristics pose significant challenges to maintaining timely and energy-efficient status updates. While link availability restricts feasible transmission routes, routing decisions determine the actual delay and energy expenditure. This paper tackles these challenges by jointly optimizing sampling and routing decisions to minimize monotonic, non-linear Age of Information (AoI). The proposed formulation incorporates key system features, including multiple routes with correlated random delays, stochastic link availability, and route-dependent energy consumption. We model the problem as an infinite-horizon Constrained Semi-Markov Decision Process (CSMDP) with a hybrid state–action space and develop an efficient nested algorithm, termed Bisec-\textsc{ReaVI}, to solve this problem. We analyze the structural properties of the solution and reveal a well-defined jointly optimal policy structure: (i) For general monotonic penalty functions, the optimal sampling policy is a piecewise linear waiting policy with at most $N$ breakpoints given $N$ routes; and (ii) under a derived Expected Penalty Ordering condition, the optimal routing policy is a monotonic threshold-based handover policy characterized by at most $\binom{N}{2}$ thresholds. Numerical experiments in a \textit{satellite–terrestrial} integrated routing scenario demonstrate that the proposed scheme efficiently balances energy usage and information freshness, and reveal a counter-intuitive insight: \textit{even routes with higher average delay, higher delay variance or lower availability can still play a critical role in minimizing monotonic functions of AoI}.

💡 Research Summary

The paper addresses the problem of maintaining fresh information in a remote monitoring system where status updates can be sent through multiple heterogeneous routes that differ in delay statistics, stochastic availability, and energy consumption. Building on the Age of Information (AoI) framework, the authors consider a general, monotonic, non‑linear age penalty function f(Δ) rather than the usual linear metric, thereby capturing a wider range of application‑specific freshness requirements.

System model.

• Routes: N routes are divided into persistent routes (always available, p_k = 1) and intermittent routes (available with probability 0 < p_k < 1). This captures terrestrial links (fiber, cellular) and non‑terrestrial links (satellite) that experience visibility windows and weather‑induced outages.
• Delays: At each transmission epoch i, the vector of delays Y_i = (Y_{i,1},…,Y_{i,N}) is drawn from a stationary multivariate distribution Q. While the components may be correlated, the authors prove that the optimal control depends only on the marginal distributions Q_k, because the system state resets after each successful delivery and the decision maker observes only the delay of the selected route.
• Energy: Two energy costs are modeled: a fixed sampling cost C_s incurred each time a new sample is generated, and a per‑unit‑time transmission cost G_k for route k. The long‑term average energy consumption must not exceed a given budget E_max, which is realistic for battery‑powered ground terminals or solar‑powered satellites.
• AoI dynamics: AoI Δ(t) grows linearly between deliveries and drops to the most recent transmission delay Y_i at each delivery instant. The performance objective is the infinite‑horizon average expected penalty 𝔼