Browsing by Subject "Discrete-time queues"

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    Discrete-time queueing model of age of information with multiple information sources
    (IEEE, 2021-01-22) Akar, Nail; Doğan, Ozancan
    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 discrete-time 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.
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    ItemOpen Access
    A matrix analytical method for the discrete time Lindley equation using the generalized Schur decomposition
    (ACM, 2006) Akar, Nail
    In this paper, we study the discrete time Lindley equation governing an infinite size GI/GI/1 queue. In this queuing system, the arrivals and services are independent and identically distributed but they obey a discrete time matrix geometric distribution not necessarily with finite support. Our GI/GI/1 model allows geometric batch arrivals and also treats late, early, and hybrid arrival models in a unified manner. We reduce the problem of finding the steady state probabilities for the Lindley equation to finding the generalized ordered Schur form of a matrix pair (E, A) where the size of these matrices are the sum, not the product, of the orders of individual arrival and service distributions. The approach taken in this paper is purely matrix analytical and we obtain a matrix geometric representation for the related quantities (queue lengths or waiting times) for the discrete time GI/GI/1 queue using this approach.