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Age of Information Minimization for Heterogenous Transmissions.

In this paper, we consider a status update system, in which update packets are sent to the destination via a channel that allow for multiple rates, where a higher rate also naturally corresponds to a higher error probability. The date freshness is measured using age of information (or simply age), which is defined as the age of the recent update at the destination. A packet that is transmitted with a higher rate, will encounter a shorter delay and a higher error probability. The two properties have an opposite impact on age. Thus, the choice of the transmission rate affects the AoI at the destination. We aim to design a low-complexity scheduler that chooses the appropriate transmission rate error probability pair in order to minimize the average AoI at the destination. We focus on a a two-rate scenario and investigate the problem of which transmission rate should be used at each transmission epoch. This problem can be cast as a Markov Decision Process. We show that there exists a threshold-type policy that is age-optimal. More importantly, we show that the objective function is convex or quasi-convex in the threshold, based on to the system parameters values. This enables us to devise a \emph{low-complexity algorithm} to minimize the age. Finally, we provide a discussion in which we illustrate the insights we obtain from studying the two rates scenario in order to solve the problem with more than two rates.