Abstract : In this paper, we study how to take samples at a datasource for improving the freshness of received data samples at aremote receiver. We use non-linear functions of the age of informationto measure data freshness, and provide a survey of non-linearage functions and their applications. The sampler design problemis studied to optimize these data freshness metrics, even when thereis a sampling rate constraint. This sampling problem is formulatedas a constrained Markov decision process (MDP) with a possiblyuncountable state space. We present a complete characterizationof the optimal solution to this MDP: The optimal sampling policyis a deterministic or randomized threshold policy, where thethreshold and the randomization probabilities are characterizedbased on the optimal objective value of the MDP and the samplingrate constraint. The optimal sampling policy can be computed bybisection search, and the curse of dimensionality is circumvented.These age optimality results hold for (i) general data freshness metricsrepresented by monotonic functions of the age of information,(ii) general service time distributions of the queueing server, (iii)both continuous-time and discrete-time sampling problems, and(iv) sampling problems both with and without the sampling rateconstraint. Numerical results suggest that the optimal samplingpolicies can be much better than zero-wait sampling and the classicuniform sampling.
Index terms : Age of information, data freshness, Markov decision process, sampling. I