Exact distribution of age of information (AoI) and peak AoI in single-source and multi-source status update systems
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In this thesis, we ﬁrst study buﬀerless and single-buﬀer single-source queueing models of a status update system with various accompanying buﬀer manage-ment schemes. Next, we study the buﬀerless multi-source queueing model of a status-update system with probabilistic preemption. For both single-source and multi-source queueing models, we obtain the exact distributions of the associ-ated Age of Information (AoI) and Peak Age of Information (PAoI) processes. For this purpose, we propose a Markov Fluid Queue (MFQ) model for both scenarios out of which the exact AoI distributions are derived. The numerical so-lution obtained from the proposed model provides the distributional expressions in matrix-exponential form out of which one can easily obtain their high order moments. We validate the accuracy of our proposed algorithm by comparing our results with simulations and also existing results in the literature in certain sub-cases. Numerical results are presented to provide engineering insight on how state update systems need to be conﬁgured and operated.