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Age Optimal Sampling and Routing under Intermittent Links and Energy Constraints

Adem Utku Atasayar, Aimin Li, Çağrı Arı, Elif Uysal

TL;DR

The paper tackles the challenge of keeping information fresh in networks with multiple, heterogeneous routes that may intermittently become available and incur different energy costs. It formulates joint sampling and routing as an infinite-horizon constrained semi-Markov decision process and solves it with a novel Bisec-ReaVI algorithm, leveraging fractional programming, Dinkelbach's method, and Lagrangian relaxation. The authors establish structural results showing threshold-based routing and piecewise-linear sampling policies, and provide an efficient numerical framework to compute them without discretizing the state space. Through satellite-terrestrial simulations, the work reveals that carefully orchestrated use of diverse routes can improve AoI even when some routes have worse mean delays or availability, offering practical guidance for next-generation TN-NTN systems.

Abstract

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, nonlinear 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-ReaVI, to solve this problem. We reveal a well-defined jointly optimal policy structure: (i) the optimal routing policy is a monotonic handover policy that adapts to the availability of routes and their mean delays; and (ii) the optimal sampling policy is a piecewise linear waiting policy, with at most "N choose 2 + N" breakpoints given N routes. Numerical experiments in a satellite-terrestrial integrated routing scenario demonstrate that the proposed scheme efficiently balances energy usage and information freshness, and reveal a counter-intuitive insight: even routes with higher average delay, higher delay variance, or lower availability can still play a critical role in minimizing monotonic functions of AoI.

Age Optimal Sampling and Routing under Intermittent Links and Energy Constraints

TL;DR

The paper tackles the challenge of keeping information fresh in networks with multiple, heterogeneous routes that may intermittently become available and incur different energy costs. It formulates joint sampling and routing as an infinite-horizon constrained semi-Markov decision process and solves it with a novel Bisec-ReaVI algorithm, leveraging fractional programming, Dinkelbach's method, and Lagrangian relaxation. The authors establish structural results showing threshold-based routing and piecewise-linear sampling policies, and provide an efficient numerical framework to compute them without discretizing the state space. Through satellite-terrestrial simulations, the work reveals that carefully orchestrated use of diverse routes can improve AoI even when some routes have worse mean delays or availability, offering practical guidance for next-generation TN-NTN systems.

Abstract

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, nonlinear 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-ReaVI, to solve this problem. We reveal a well-defined jointly optimal policy structure: (i) the optimal routing policy is a monotonic handover policy that adapts to the availability of routes and their mean delays; and (ii) the optimal sampling policy is a piecewise linear waiting policy, with at most "N choose 2 + N" breakpoints given N routes. Numerical experiments in a satellite-terrestrial integrated routing scenario demonstrate that the proposed scheme efficiently balances energy usage and information freshness, and reveal a counter-intuitive insight: even routes with higher average delay, higher delay variance, or lower availability can still play a critical role in minimizing monotonic functions of AoI.

Paper Structure

This paper contains 39 sections, 9 theorems, 78 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Motivation
  4. Related Works and Contributions
  5. System Model
  6. Persistent and Intermittent Links
  7. Correlated Random Delays
  8. Heterogeneous Energy Costs
  9. Age of Information
  10. Problem Formulation
  11. Fractional programming reformulation
  12. Lagrangian Techniques
  13. Average-Cost MDP for a Given $\lambda$ and $c$
  14. Main Results
  15. Structural Results of Optimal Policies
  16. ...and 24 more sections

Key Result

Lemma 1

For any fixed $c \ge 0$, the following assertions hold:

Figures (8)

  • Figure 1: A remote monitoring system, where status updates are transmitted through $N$ heterogeneous routes.
  • Figure 2: Sample evolution of the AoI process $\Delta(t)$.
  • Figure 3: Visualization of the jointly optimal policies.
  • Figure 4: AoI vs. $E_{\max}$
  • Figure 5: Simulation results of systems with $N=3$ and competitive route $1$.
  • ...and 3 more figures

Theorems & Definitions (18)

  • Lemma 1
  • proof
  • Theorem 1
  • proof : Proof Sketch
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • ...and 8 more