TSDM: A Scheduling Policy for Joint Throughput-AoI Optimization in Multichannel Wireless Networks

Technical Summary: TSDM for Joint Throughput-AoI Optimization

Problem Statement
The paper addresses the challenge of jointly optimizing two competing performance metrics in multichannel wireless networks: throughput (data delivery rate) and Age of Information (AoI) (data freshness). This is critical for remote sensing applications where spatially distributed sensors transmit status updates over multiple heterogeneous and unreliable channels. While AoI minimization has been extensively studied, and throughput optimization is well-established, their joint optimization remains analytically difficult. The core challenge lies in balancing the trade-off between these metrics while managing resource competition among multiple nodes and the stochastic nature of packet deliveries in unreliable channels. The authors formulate this as a Network Utility Maximization (NUM) problem, where the utility function for each node depends on both its long-term average throughput and AoI.

Methodology: The TSDM Framework
The authors propose TSDM (Two-Stage Deficit Matching), a scheduling framework that decomposes the complex joint optimization problem into two distinct stages:

1. Stage 1: Second-Order Analytical Mapping

   • The framework employs a second-order analysis approach. Instead of optimizing throughput and AoI directly, it characterizes the packet delivery process by its mean ($\mu$) and temporal variance ($\sigma^2$).
   • Leveraging a known approximation where AoI is a function of mean and variance ($AoI \approx \frac{1}{2}(\frac{\sigma^2}{\mu^2} + \frac{1}{\mu}) + \frac{1}{2}$), the high-level utility maximization objective is translated into a concrete set of target statistics: desired mean throughput ($\mu_{ij}$) and temporal variance ($\sigma^2_{ij}$) for each node-channel pair.
   • This stage solves an optimization problem to find the optimal operating point $(\mu_{ij}, \sigma^2_{ij})$ that satisfies system constraints (channel reliability, matching feasibility) and the desired utility function. A key technical contribution is the decomposition of the total node variance into a sum of per-channel variances to handle cross-channel coupling, a step proven to preserve optimality in node-homogeneous systems.

2. Stage 2: Weighted Matching Deficit (WMD) Rule

   • Once target statistics are determined, a low-complexity real-time scheduling rule is applied.
   • The rule defines a deficit for each node-channel pair, representing the deviation of actual deliveries from the target mean, normalized by the target variance.
   • It calculates a channel-wide normalized deficit and assigns a weight to each node-channel pair based on the difference between the pair's deficit and the channel's average deficit.
   • The scheduler performs a maximum-weight bipartite matching at each time slot, selecting the set of node-channel assignments that maximizes the sum of these weights. This drives the system's long-term behavior toward the target statistics derived in Stage 1.

Key Contributions

• Novel Framework: Introduction of TSDM, a two-stage policy that bridges high-level utility optimization with low-complexity real-time scheduling using second-order statistics (mean and variance).
• Theoretical Guarantees:
  • Proof that the WMD rule ensures the system achieves the desired mean and temporal variance for each flow, thereby guaranteeing the target throughput and AoI.
  • Proof of optimality for the TSDM policy in node-homogeneous systems (where all nodes share the same channel reliability profile), demonstrating that the variance decomposition constraint does not incur performance loss.
• Handling Heterogeneity: The framework explicitly addresses heterogeneous and unreliable channels, a scenario often simplified in prior work.

Results
Extensive simulations were conducted on two representative NUM problems:

1. Utility Maximization with Soft Throughput Constraints: Minimizing AoI while penalizing throughput violations.
2. Weighted Proportional Fairness: Balancing throughput and AoI with specific weights for different nodes.

The results show that TSDM:

• Consistently outperforms existing baselines, including a multi-channel extension of the Max-Weight policy and a Partial Index policy (which ignores throughput).
• Achieves performance close to the theoretical upper bound (the numerical solution of the optimization problem).
• Demonstrates robustness under high load and in both homogeneous and heterogeneous channel settings. Specifically, TSDM manages to achieve significantly lower AoI than Max-Weight under high load by allowing controlled throughput violations, whereas Max-Weight sacrifices AoI to strictly meet throughput demands.

Significance and Claims
The paper claims that TSDM provides a practical and theoretically grounded solution to the underexplored problem of joint throughput-AoI optimization in multichannel networks. By leveraging second-order analysis, the authors successfully decouple the complex trade-off between throughput and freshness into a tractable scheduling problem. The significance lies in the ability to dynamically allocate limited channel resources to balance data delivery rates and timeliness without requiring complex iterative computations (like Whittle indices) at runtime. The authors conclude that TSDM offers a near-optimal solution that is computationally efficient and robust, making it suitable for critical remote sensing applications relying on unreliable wireless links. Future work is suggested to extend the framework to time-correlated channels and distributed architectures.