Age-Energy Tradeoff for Two-Hop Status Update Systems with Heterogeneous Truncated ARQ

Age of information (AoI) and energy cost (EC) are two key metrics in real-time remote monitoring systems. In this letter, we investigate the age-energy tradeoff for a short packet-based two-hop status update system, where the packet transmission may fail because of channel errors. In this case, the source can either retransmit the failed update to save EC for sensing, or generate a new one to maintain the AoI. Accordingly, we consider the truncated automatic repeat request (ARQ) scheme in both the first and second hops with different retransmission thresholds. Closed-form average AoI and average EC are given as a function of the failure probability and the thresholds of two hops. Moreover, a weighted sum of AoI and EC is minimized to tradeoff the age and energy. Numerical results demonstrate that increasing the difference between the thresholds of two hops can reduce the average AoI but increase the average EC, and an optimal packet length can always be identified to achieve age-energy tradeoff.