Delivery Delay Analysis of Selective Repeat ARQ in Underwater Acoustic Communications

Despite being the most efficient automatic repeat request (ARQ) protocol, the selective-repeat ARQ (SR-ARQ) is previously thought to be infeasible in underwater acoustic communications owing to the half-duplex property of typical underwater acoustic modems. However, with the help of the juggling-like stop-and-wait (JSW) transmission scheme, it has now become feasible. In this paper, we evaluate the delivery delay (consisting of transmission and resequencing delays) of the SR-ARQ operating over the JSW scheme under the static assumption that the relative radial velocity between the transmitter and the receiver is zero, aiming to provide system designers with a valuable reference for delay evaluation under more general scenarios. We model the underwater acoustic channel as a two-state Discrete Time Markov Channel, and derive the closed-form expression for the delivery delay under heavy traffic situation. Unlike most analytical approaches for the delay analysis of SR-ARQ in terrestrial communications whose computational complexities grow exponentially with round-trip delay, our proposed analytical approach is immune to the round-trip delay. This also makes our approach suitable for terrestrial communications. To highlight the accuracy of our approach, we also provide comparisons between analytical and simulation results.