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

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.Comment: 15 pages, 3 figure

The Multi-Source Preemptive M/PH/1/1 Queue with Packet Errors: Exact Distribution of the Age of Information and Its Peak

Age of Information (AoI) and Peak AoI (PAoI) and their analytical models have recently drawn substantial amount of attention in information theory and wireless communications disciplines, in the context of qualitative assessment of information freshness in status update systems. We take a queueing-theoretic approach and study a probabilistically preemptive bufferless $M/PH/1/1$ queueing system with arrivals stemming from $N$ separate information sources, with the aim of modeling a generic status update system. In this model, a new information packet arrival from source $m$ is allowed to preempt a packet from source $n$ in service, with a probability depending on $n$ and $m$. To make the model even more general than the existing ones, for each of the information sources, we assume a distinct PH-type service time distribution and a distinct packet error probability. Subsequently, we obtain the exact distributions of the AoI and PAoI for each of the information sources using matrix-analytical algorithms and in particular the theory of Markov fluid queues and sample path arguments. This is in contrast with existing methods that rely on Stochastic Hybrid Systems (SHS) which obtain only the average values and in less general settings. Numerical examples are provided to validate the proposed approach as well as to give engineering insight on the impact of preemption probabilities on certain AoI and PAoI performance figures.Comment: 16 pages, 6 figures, 3 table