A Probabilistic Bound for Peak Age of Information Guarantee

TL;DR

This paper develops a probabilistic bound for the peak Age of Information (AoI) in general queuing systems using martingale theory, providing a new analytical tool for performance guarantees in information freshness.

Contribution

It introduces a general probabilistic bound on peak AoI applicable to various models, linking AoI to inter-arrival and service times through a novel analysis approach.

Findings

Derived a probabilistic bound for peak AoI using martingale theory.

Validated the bound with M/M/1 and D/M/1 queuing models.

Numerical results confirm the bound's effectiveness.

Abstract

This paper considers the distribution of a general peak age of information (AoI) model and develops a general analysis approach for probabilistic performance guarantee from the time-domain perspective. Firstly, a general relationship between the peak AoI and the inter-arrival and service times of packets is revealed. With the help of martingale theory, a probabilistic bound on the peak AoI is then derived for the general case of endogenous independently and identically distributed increments in information generation and transmission processes. Thereafter, the application of the obtained bound is illustrated with the M/M/1 and D/M/1 queuing models. The validity of the proposed bound is finally examined with numerical results.