The Age of Information in a Discrete Time Queue: Stationary Distribution and Non-Linear Age Mean Analysis

In this work, we investigate information freshness in a status update communication system consisting of source-destination link. Initially, study the properties sample path age (AoI) process at destination. We obtain general formula stationary distribution AoI, under assumption ergodicity. relate result to discrete time queueing and provide expression generating function AoI relation with peak (PAoI) metric. Furthermore, consider three different single-server models closed-form expressions functions distributions PAoI. The first model is first-come-first-served (FCFS) queue, second preemptive last-come-first-served (LCFS) last bufferless packet dropping. build upon these results methodology for analyzing non-linear type systems, using representations as power series.