Optimizing Information Freshness in Two-Hop Status Update Systems under a Resource Constraint
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This paper considers a two-hop status update system, in which an information source aims for the timely delivery of status updates to the destination with the aid of a relay. The relay is assumed to be an energy-constraint device and our goal is to devise scheduling policies that adaptively switch between the information decoding and information forwarding to minimize the long-term average Age-of-Information (AoI) at the destination, under a resource constraint on the average number of forwarding operations at the relay. We first identify an optimal scheduling policy by modelling the considered scheduling problem as a constrained Markov decision process (CMDP) problem. We resolve the CMDP problem by transforming it into an unconstrained Markov decision process (MDP) using a Lagrangian method. The structural properties of the optimal scheduling policy is analyzed, which is shown to have a multiple threshold structure. For implementation simplicity, based on the structural properties of the CMDP-based policy, we then propose a low-complexity double threshold relaying (DTR) policy with only two thresholds, one for relay's age and the other one for the age gain between destination and relay. We manage to derive approximate closed-form expressions of the average AoI at the destination, and the average number of forwarding operations at the relay for the DTR policy, by modelling the tangled evolution of age at the relay and destination as a Markov chain (MC). Numerical results are provided to verify all the theoretical analysis, and show that the low-complexity DTR policy can achieve near optimal performance compared with the optimal scheduling policy derived from the CMDP problem. The simulation results also unveil that only one threshold for the relay's age is needed in the DTR policy when there is no resource constraint or the resource constraint is loose.
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