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

This work investigates the time-dependent statistical characteristics (SCs) of age of information (AoI) in V2I periodic-updating. The D/G/1/1 (non-)preemptive discrete-time (slotted) queue model is employed. The entire AoI process is split into a set of slot-specific AoI processes w.r.t. updating period (UP). A Markov multi-dimensional age process w.r.t. UP is used to track the evolution of slot-specific AoI. Accordingly, the time-dependent AoI distribution and expected AoI (EAoI) are derived, forming a framework to study the time-dependent AoI SCs under periodic updating. Based on the AoI SCs, we optimize the decision-making (DM) process at roadside unit to minimize age upon decisions, improving information freshness when conducting DMs. A quasiperiodic DM mechanism is regarded, where one DM slot is probabilistically determined in each UP. The optimal DM probabilities are obtained in closed-form. In the D/Geo/1/1 case, we find that the preemption-induced EAoI gains are identical among slots; for extremely reliable/error-prone channels, conducting DM at the second/middle slot in UP is optimal. Numerical results verify the effectiveness of theoretical analyses and DM process optimization.