Minimizing the Sum of Age of Information and Transmission Cost under Stochastic Arrival Model

TL;DR

This paper studies an optimal update policy balancing Age of Information and transmission costs in stochastic arrival scenarios, providing explicit solutions for Poisson arrivals and a competitive randomized algorithm for general distributions.

Contribution

It derives an explicit optimal online policy for Poisson arrivals and introduces a competitive randomized algorithm for arbitrary inter-arrival distributions.

Findings

Optimal policy for Poisson arrivals derived.

Proposed randomized algorithm with competitive ratio bounds.

Competitive ratio is at most 2 for common distributions.

Abstract

We consider a node-monitor pair, where updates are generated stochastically (according to a known distribution) at the node that it wishes to send to the monitor. The node is assumed to incur a fixed cost for each transmission, and the objective of the node is to find the update instants so as to minimize a linear combination of AoI of information and average transmission cost. First, we consider the Poisson arrivals case, where updates have an exponential inter-arrival time for which we derive an explicit optimal online policy. Next, for arbitrary distributions of inter-arrival time of updates, we propose a simple randomized algorithm that transmits any newly arrived update with a fixed probability (that depends on the distribution) or never transmits that update. The competitive ratio of the proposed algorithm is shown to be a function of the variance and the mean of the inter-arrival time distribution. For some of the commonly considered distributions such as exponential, uniform, and Rayleigh, the competitive ratio bound is shown to be 2.