Time-Dependent Statistical Characteristics of Age of Information Under Periodic Updating

This work investigates the time-dependent statistical characteristics of age of information (AoI) in the real-time Internet of Things systems with wireless periodic status updating. The periodic updating system is modeled as a discrete-time D/G/1/1 non-preemptive queue. The entire AoI process w.r.t. slot is split into a set of slot-specific AoI processes w.r.t. updating period. A Markov high-dimensional age process is introduced to track the evolution of the slot-specific AoI. Accordingly, the time-dependent AoI distribution, expected AoI (EAoI), and the time-average AoI are derived, forming a framework to study the time-dependent AoI statistical characteristics under periodic updating. Numerical results verify the effectiveness of theoretical analyses and usefulness of packet retransmission. It is found that the EAoI varies non-monotonously and greatly w.r.t. slot in an updating period; the EAoI variations are distinct for the update transmission times with different distributions; and the EAoI gains of channel enhancement differ greatly among slots.