Sampling for Data Freshness Optimization: Non-linear Age Functions
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In this paper, we study how to take samples from an information source, where the samples are forwarded to a remote receiver through a queue. The optimal sampling problem for maximizing the freshness of received samples is formulated as a constrained Markov decision process (MDP) with a possibly uncountable state space. We present a complete characterization of the optimal solution to this MDP: The optimal sampling policy is a deterministic or randomized threshold policy, where the threshold and the randomization probabilities are determined by the optimal objective value of the MDP and the sampling rate constraint. The optimal sampling policy can be computed by bisection search, and the curse of dimensionality is circumvented. This solution is optimal under quite general conditions, including (i) general data freshness metrics represented by monotonic functions of the age of information, (ii) general service time distributions of the queueing server, and (iii) both continuous-time and discrete-time sampling problems. Numerical results suggest that the optimal sampling policies can be much better than zero-wait sampling and the classic uniform sampling.
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