Analysis of energy and delay for ARQ systems over time varying channels

We propose an analytical method to determine the joint distribution of the energy and delay of automatic repeat request (ARQ) protocols over time varying channels. By using a finite state machine (FSM) to model the operation of ARQ systems with a state transition diagram, the generating function of energy and delay can be evaluated according to Manson's gain formula. From the joint generating function of energy and delay, two performance metrics, throughput and energy efficiency are derived. As the numerical results demonstrate, the time-varying characteristic of the channel have a great influence on the system performance.