  In a heterogeneous unreliable multiaccess network, wherein terminals share a
common wireless channel with distinctive error probabilities, existing works
have showed that a persistent round-robin (RR-P) scheduling policy (i.e.,
greedy policy) can be arbitrarily worse than the optimum in terms of Age of
Information (AoI) under standard Automatic Repeat reQuest (ARQ), and one must
resort to Whittle's index approach for optimal AoI. 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 $(\sqrt{e}-1)^2/4\sqrt{e} \cong 6.4\%$ (resp. $6.2\%$ with
error exponential decay rate of $0.5$). In addition, RR-P enjoys the distinct
advantage of implementation simplicity with channel-unaware and
easy-to-decentralize operations, making it favorable in practice.
