Average Age of Incorrect Information in Random Access Channels for IoT Systems

Age of incorrect information (AoII) has been proposed recently to overcome the shortcomings of age of information (AoI) in internet of things (IoT) systems. AoII takes into account the content of the information by penalizing the sink only when it has an incorrect perception of the monitored source. This is of paramount importance for scenarios where actuations are taken based on the current data sample. On the other hand, random access (RA) has been identified as a promising solution for supporting next-generation IoT systems. Therefore, a thorough understanding of the behaviors of RA policies from the perspective of AoII is key for the design of IoT systems. In this paper, we study two representative RA schemes, namely slotted ALOHA (SA) and irregular repetition slotted ALOHA (IRSA), with Markov sources. We track the AoII evolution for both schemes through a Markovian analysis, where state transition probabilities are derived and closed form expressions for the average AoII are obtained. Simulation results are provided to validate our analysis. The study reveals the influences of the Markov source on the system performance as well as the design trade-offs for IRSA. Furthermore, the performance of SA and IRSA are compared under various settings, showing the cases where IRSA can largely outperform SA in terms of average AoII.