Generating function analysis of wireless networks and ARQ systems

In this thesis, there are two main themes. The first part of the thesis is to study the trade-off between energy and delay for wireless networks. A network using a request-to-send (RTS) and clear-to-send (CTS) type medium access control (MAC) protocol is considered. We first determine the average delay incurred and the average energy consumed when the effects of an imperfect channel are incorporated in the model. In order to incorporate the relation between packet error probability, energy, and delay, we use the reliability function bounds for different channel models on the error probability of a coded system. Further, we present a generic framework that allows us to obtain the joint statistics of energy and delay through their joint generating function. Several important design trade-offs are studied from the joint generating function, such as the average energy with an out-age delay constraint. This framework allows us to optimize over the system parameters for various objective functions, such as average delay. An approximation method is also proposed to calculate the average energy and average delay analytically. This approximation is found to be quite accurate for a wide range of lengths. The inhomogeneous and time varying effects for the trade-off between energy and delay are also studied.; The second part of the thesis is to propose an analytical method to determine the joint distribution of the joint distribution of the energy and delay of automatic repeat request (ARQ) protocols over time varying channels. A finite state machine (FSM) is used to model the transmitter, receiver and channel. From the state transition diagram of the FSM, the generating function of energy and delay consumption can be evaluated according to the Manson's gain formula while incorporating physical layer characteristics (packet error probability as a function of energy and delay). We also consider a receiver containing memory of previously received samples and derive the cutoff rate for two different receiver structures. As the numerical results demonstrate, the time-varying characteristic of the channel have a great influence on the system performance.