On the effect of feedback errors in Markov models for SR ARQ packet delays

Modern communication systems require effective error control techniques for wireless links. This problem is still relevant in many applications involving recently developed IEEE standards such as 802.16, or sensors for environmental monitoring in extreme conditions. A notable example is also underwater communication with acoustic transmission, where long delays may be present. Usually, such studies assume the availability of an error-free feedback channels which is used to perform retransmission requests in an ARQ fashion. This paper discusses the performance of the selective repeat ARQ scheme in terms of packet delay when the feedback that is sent back at the transmitter's side can be erroneous. A non instantaneous noisy feedback and a Bernoulli arrival process, for different traffic intensities, are considered. The system is modeled through discrete time Markov chains, including the channel and the ARQ state. The system equations are derived and solved, and the impact of erroneous feedback is quantified. With respect to other similar contributions, the proposed approach presents the advantage of being directly implementable in any analysis using Markov chains to evaluate the system properties, instead of dedicated models. It can therefore be extended to a plethora of different scenarios, including different channel models and also including FEC features so as to obtain a hybrid ARQ scheme.