# Age-optimal Sampling and Transmission Scheduling in Multi-Source Systems

## TL;DR

This paper addresses age minimization in multi-source systems by establishing a separation principle that decouples scheduling and sampling, and proposes near-optimal strategies using dynamic programming and water-filling approximations.

## Contribution

It proves the independence of scheduling and sampling strategies, introduces the MAF scheduling policy, and develops an approximate water-filling solution for optimal sampling.

## Key findings

- Maximum Age First (MAF) scheduling outperforms other strategies.
- Zero-wait sampling is optimal for minimizing total average peak age.
- Water-filling approximation closely matches the optimal sampling strategy.

## Abstract

In this paper, we consider the problem of minimizing the age of information in a multi-source system, where samples are taken from multiple sources and sent to a destination via a channel with random delay. Due to interference, only one source can be scheduled at a time. We consider the problem of finding a decision policy that determines the sampling times and transmission order of the sources for minimizing the total average peak age (TaPA) and the total average age (TaA) of the sources. Our investigation of this problem results in an important separation principle: The optimal scheduling strategy and the optimal sampling strategy are independent of each other. In particular, we prove that, for any given sampling strategy, the Maximum Age First (MAF) scheduling strategy provides the best age performance among all scheduling strategies. This transforms our overall optimization problem into an optimal sampling problem, given that the decision policy follows the MAF scheduling strategy. While the zero-wait sampling strategy (in which a sample is generated once the channel becomes idle) is shown to be optimal for minimizing the TaPA, it does not always minimize the TaA. We use Dynamic Programming (DP) to investigate the optimal sampling problem for minimizing the TaA. Finally, we provide an approximate analysis of Bellman's equation to approximate the TaA-optimal sampling strategy by a water-filling solution which is shown to be very close to optimal through numerical evaluations.