Analysis on Asymptotic Optimality of Round-Robin Scheduling for Minimizing Age of Information with HARQ

In a heterogeneous unreliable multiaccess network, wherein terminals share a common wireless channel with distinct error probabilities, existing works have shown that a persistent round-robin (RR-P) scheduling policy can be arbitrarily worse than the optimum in terms of Age of Information (AoI) under standard Automatic Repeat reQuest (ARQ). In this paper, practical Hybrid ARQ (HARQ) schemes which are widely-used in today's wireless networks are considered. We show that RR-P is very close to optimum with asymptotically many terminals in this case, by explicitly deriving tight, closed-form AoI gaps between optimum and achievable AoI by RR-P. In particular, it is rigorously proved that for RR-P, under HARQ models concerning fading channels (resp. finite-blocklength regime), the relative AoI gap compared with the optimum is within a constant of 6.4% (resp. 6.2% with error exponential decay rate of 0.5). In addition, RR-P enjoys the distinctive advantage of implementation simplicity with channel-unaware and easy-to-decentralize operations, making it favorable in practice. A further investigation considering constraint imposed on the number of retransmissions is presented. The performance gap is indicated through numerical simulations.