Average age of information with hybrid ARQ under a resource constraint

Scheduling the transmission of status updates over an error-prone communication channel is studied in order to minimize the long-term average age of information at the destination under a constraint on the average number of transmissions at the source node. After each transmission, the source receives an instantaneous ACK/NACK feedback, and decides on the next update without prior knowledge on the success of future transmissions. The optimal scheduling policy is first studied under different feedback mechanisms when the channel statistics are known; in particular, the standard automatic repeat request (ARQ) and hybrid ARQ (HARQ) protocols are considered. The structural results are derived for the optimal policy under HARQ, while the optimal policy is determined analytically for ARQ. For the case of unknown environments, an average-cost reinforcement learning algorithm is proposed that learns the system parameters and the transmission policy in real time. The effectiveness of the proposed methods is verified through the numerical results.