Peak Age of Incorrect Information of Reactive ALOHA Reporting Under Imperfect Feedback

Age of Incorrect Information (AoII) is particularly relevant in systems where real time responses to anomalies are required, such as natural disaster alerts, cybersecurity warnings, or medical emergency notifications. Keeping system control with wrong information for too long can lead to inappropriate responses. In this paper, we study the Peak AoII (PAoII) for multi-source status reporting by independent devices over a collision channel, following a zero-threshold ALOHA access where nodes observing an anomaly immediately start transmitting about it. If a collision occurs, nodes reduce the transmission probability to allow for a resolution. Finally, wrong or lost feedback messages may lead a node that successfully updated the destination to believe a collision happened. The PAoII for this scenario is computed in closed-form. We are eventually able to derive interesting results concerning the minimization of PAoII, which can be traded against the overall goodput and energy efficiency, but may push the system to the edge of congestion collapse.