The Age-of-Information Distribution in Slotted ALOHA

Age-of-Information (AoI) is a new performance metric for critical networked cyber-physical systems (CPS), where performance depends on how quickly fresh data is received in update packets. When multiple users communicate these updates over a shared channel in a random access manner, packet losses can occur due to overlapping transmissions. In this study, we analyse the AoI for slotted ALOHA, which is the classical medium access control protocol in communication networks. Our stochastic analysis provides exact results for the moments of the AoI at random slot boundaries and for the peak AoI, which is different from previous studies that rely on approximations. Additionally, we provide a recursive algorithm to calculate the probability mass function of the AoI. Finally, we explore how packet arrival and transmission probabilities impact the AoI through a numerical example. Our results, which characterise the AoI distribution in random access channels, have significant implications for the safety assessment of CPS in critical scenarios.