Bufferless and single-buffer queueing systems have recently been shown to be effective in coping with escalated Age of Information (AoI) figures arising in systems with large buffers and FCFS scheduling. In this paper, we propose a numerical algorithm for obtaining the exact distribution of both the AoI and the peak AoI (PAoI) in the bufferless P H/P H/1/1 and P H/P H/1/1/P -LCFS queues as well as the single-buffer M/P H/1/2 and M/P H/1/2 * queues, the latter one involving the replacement of the packet in the queue by the new arrival. The proposed exact models are based on the well-established theory of Markov fluid queues and the numerical algorithms rely on numerically stable and efficient vector-matrix operations. Moreover, the obtained exact distributions are in matrix exponential form making it amenable to calculate the tail distributions and the associated moments straightforwardly. We validate the proposed algorithms with simulations and we also comparatively study the AoI performance of the four queueing systems of interest as a function of the system load as well as the squared coefficient of variation (scov) of the service time. A similar study is also pursued for assessing the impact of the scov of the interarrival time for the two bufferless queueing systems.

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 article, we study a discrete-time server arising in multisource 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 general discrete phase-type 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: 1) nonpreemptive bufferless; 2) preemptive bufferless; and 3) nonpreemptive single buffer with replacement. The proposed numerical algorithm employs the theory of discretetime Markov chains of quasi-birth-death type and is matrix analytical. 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. Index Terms-Age of Information (AoI), discrete-time queues, Peak AoI (PAoI), Markov chains of quasi-birth-death (QBD) type.

Ozancan Doǧan is supported in part by the 5G and Beyond Scholarship granted by the Information and Communication Technologies (ICTA) of Turkey and Vodafone Turkey. The associate editor coordinating the review of this article and approving it for publication was N. Pappas.

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/P H/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.1 Mr. Dogan is supported in part by the 5G and Beyond scholarship granted by the Information and Communication Technologies Authority (ICTA) of Turkey and Vodafone Turkey.