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arXiv · 2002.08798

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

Antzela Kosta·Nikolaos Pappas·Anthony Ephremides·Vangelis Angelakis
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Abstract

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

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Antzela Kosta, Nikolaos Pappas, Anthony Ephremides, Vangelis Angelakis. 2020-02-20. The Age of Information in a Discrete Time Queue: Stationary Distribution and Non-linear Age Mean Analysis. https://arxiv.org/abs/2002.08798

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