Discrete-time Queueing Model of Age of Information with Multiple Information Sources

TL;DR

This paper models and analyzes the Age of Information in multi-source IoT systems using a discrete-time queueing framework, providing exact AoI distributions for different queueing disciplines and optimizing system parameters.

Contribution

It introduces a matrix-analytic method to exactly compute AoI and PAoI distributions in a multi-source IoT queueing model with three different disciplines, advancing analytical tools in this area.

Findings

Exact AoI and PAoI distributions obtained for three queueing disciplines.

Numerical validation confirms model accuracy and effectiveness.

Optimal Bernoulli parameters identified for diverse AoI requirements.

Abstract

Information freshness in IoT-based status update systems has recently been studied through the Age of Information (AoI) and Peak AoI (PAoI) performance metrics. In this paper, we study a discrete-time server arising in multi-source IoT systems which accepts incoming information packets from multiple information sources so as to be forwarded to a remote monitor for status update purposes. Under the assumption of Bernoulli information packet arrivals and a common geometric service time distribution across all the sources, we numerically obtain the exact per-source distributions of AoI and PAoI in matrix-geometric form for three different queueing disciplines: i) Non-Preemptive Bufferless (NPB) ii) Preemptive Bufferless (PB) iii) Non-Preemptive Single Buffer with Replacement (NPSBR). The proposed numerical algorithm employs the theory of Discrete-Time Markov Chains (DTMC) of Quasi-Birth-Death (QBD) type and is matrix analytical, i.e, the algorithm is based on numerically stable and efficient vector-matrix operations.Numerical examples are provided to validate the accuracy and effectiveness of the proposed queueing model. We also present a numerical example on the optimum choice of the Bernoulli parameters in a practical IoT system with two sources with diverse AoI requirements.