Analysis of Age of Incorrect Information under Generic Transmission Delay

TL;DR

This paper analyzes the Age of Incorrect Information in a communication system with random delays, focusing on threshold policies and providing exact and closed-form performance metrics.

Contribution

It introduces a Markov chain-based analysis of threshold policies for AoII under delay, with exact and closed-form solutions for performance evaluation.

Findings

Threshold policies can outperform constant transmission strategies.

Exact AoII performance can be computed via finite linear systems.

Closed-form expressions are derived for specific thresholds.

Abstract

This paper investigates the Age of Incorrect Information (AoII) in a communication system whose channel suffers a random delay. We consider a slotted-time system where a transmitter observes a dynamic source and decides when to send updates to a remote receiver through the communication channel. The threshold policy, under which the transmitter initiates transmission only when the AoII exceeds the threshold, governs the transmitter's decision. In this paper, we analyze and calculate the performance of the threshold policy in terms of the achieved AoII. Using the Markov chain to characterize the system evolution, the expected AoII can be obtained precisely by solving a system of linear equations whose size is finite and depends on the threshold. We also give closed-form expressions of the expected AoII under two particular thresholds. Finally, calculation results show that there are better strategies than the transmitter constantly transmitting new updates.