Abstract
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 Unite 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.