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Age of Synchronization Minimization in Wireless Networks with Random Updates and Time-Varying Timeliness Requirement

Yuqiao He, Yuchao Chen, Jintao Wang, Jian Song

TL;DR

This work addresses minimizing the weighted sum of AoS in a multi-user wireless network with random status updates and time-varying sensor importance. By relaxing the instantaneous bandwidth constraint to a time-average constraint and applying a Lagrangian decomposition, the authors derive per-node MDPs solved via linear programming, yielding stationary policies for the relaxed problem. The overall policy combines two per-node policies to meet the original constraint, producing a near-stationary scheduling rule with theoretical asymptotic optimality under fixed load and large bandwidth. Simulations show the proposed approach outperforms Max-Weight in scenarios with non-iid weight dynamics and confirms convergence toward the relaxed lower bound as bandwidth increases.

Abstract

This study considers a wireless network where multiple nodes transmit status updates to a base station (BS) via a shared, error-free channel with limited bandwidth. The status updates arrive at each node randomly. We use the Age of Synchronization (AoS) as a metric to measure the information freshness of the updates. The AoS of each node has a timely-varying importance which follows a Markov chain. Our objective is to minimize the weighted sum AoS of the system. The optimization problem is relaxed and formulated as a constrained Markov decision process (CMDP). Solving the relaxed CMDP by a linear programming algorithm yields a stationary policy, which helps us propose a near-stationary policy for the original problem. Numerical simulations show that in most configurations, the AoS performance of our policy outperforms the policy choosing the maximum AoS regardless of weight variations.

Age of Synchronization Minimization in Wireless Networks with Random Updates and Time-Varying Timeliness Requirement

TL;DR

This work addresses minimizing the weighted sum of AoS in a multi-user wireless network with random status updates and time-varying sensor importance. By relaxing the instantaneous bandwidth constraint to a time-average constraint and applying a Lagrangian decomposition, the authors derive per-node MDPs solved via linear programming, yielding stationary policies for the relaxed problem. The overall policy combines two per-node policies to meet the original constraint, producing a near-stationary scheduling rule with theoretical asymptotic optimality under fixed load and large bandwidth. Simulations show the proposed approach outperforms Max-Weight in scenarios with non-iid weight dynamics and confirms convergence toward the relaxed lower bound as bandwidth increases.

Abstract

This study considers a wireless network where multiple nodes transmit status updates to a base station (BS) via a shared, error-free channel with limited bandwidth. The status updates arrive at each node randomly. We use the Age of Synchronization (AoS) as a metric to measure the information freshness of the updates. The AoS of each node has a timely-varying importance which follows a Markov chain. Our objective is to minimize the weighted sum AoS of the system. The optimization problem is relaxed and formulated as a constrained Markov decision process (CMDP). Solving the relaxed CMDP by a linear programming algorithm yields a stationary policy, which helps us propose a near-stationary policy for the original problem. Numerical simulations show that in most configurations, the AoS performance of our policy outperforms the policy choosing the maximum AoS regardless of weight variations.
Paper Structure (8 sections, 1 theorem, 22 equations, 2 figures)

This paper contains 8 sections, 1 theorem, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Resolution
  4. Relaxed Problem
  5. Problem for individual node
  6. Finding appropriate Lagrange multiplier
  7. Simulation Results
  8. Conclusion

Key Result

Theorem 1

There exists an optimal stationary policy $\pi_i^*$ and a set of threshold $\{\tau_r\}_{r\in\mathcal{R}}$ such that the node transmits to the BS with probability 1 in the states with $r$ satisfying $s\ge\tau_r$ and keeps idle with probability 1 while $s<\tau_r$.

Figures (2)

  • Figure 1: The time-average weighted sum AoS varies with self-transition probability.
  • Figure 2: The time-average weighted sum AoS varies with bandwidth limitation.

Theorems & Definitions (2)

  • Theorem 1
  • Proof 1