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

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.