The Probability Distribution of AoI for Multi-Connectivity Short-Packet Transmission in Industrial IoT

Age of Information (AoI) has been proposed to measure the freshness of information for emerging real-time applications in industrial Internet of Things (IIoT), where short packets and multi-connectivity via multiple links are employed to enable the reduction in AoI. However, the probability distribution analysis of AoI for multi-connectivity systems remains unexplored, especially for short-packet transmission. Motived by this open issue, the closed-form expressions for the average AoI and peak AoI (PAoI) over Rayleigh fading channels are deduced to characterize the average freshness performance in multi-connectivity short-packet systems. The probability density function (PDF) and cumulative distribution function (CDF) of PAoI have been derived in closed forms. Then PAoI violation probability is formulated as an exponential function of PAoI threshold to indicate the outage performance of AoI. Simulation results verify our analysis and demonstrate that the AoI and PAoI performance gain will saturate at a large number of connections.