An optimal stopping approach to ARQ protocols with variable success probabilities per retransmission

In the current work tie conceptual framework of optimally stopping a stochastic process is used to determine the optimal maximum number of retransmissions in an ARQ chain. The process sequentially observed is the binary ARQ feedback after each packet (re)transmission (AC /NA ). A reward-cost process Y is constructed as a function of the observed sequence up to time n with a certain reward and cost per trial as well as a final penalty in case the retransmission process is inalised before correct packet reception. Two problems are investigated , namely the cases without and with cost. In the ARQ stopping problem without cost ergodicity conditions of the ARQ Markov chain are stated and proved. These guarantee with probability one inite waiting times until the irst AC is received. The solution of the ARQ stopping problem with cost provides an explicit expression for the optimal truncation time of ARQ protocols as a function of the costs and rewards and suggests a tradeoff between delay and dropping probability. Conditions for cases when the ARQ chain should not be truncated as well as when no retransmissions should be allowed at all are presented. The stopping rule is applied to practical ARQ scenarios where the behavior of the truncation time with respect to different supported rate9 delay and dropping is investigated.