— Gupta and Kumar showed that throughput in a static random wireless network increases with the amount of hopping. In a subsequent paper (2004), it was shown that although throughput benefits from a large number of hops, this comes at the expense of higher delay. Separately, several studies have shown that in ad hoc networks, transmission energy decreases as hopping increases. However, when transceiver circuit energy is also taken into account, hopping as much as possible no longer maximizes energy efficiency and the optimal amount of hopping depends on the topology and size of the network. This paper attempts to unify these earlier results by establishing the optimal hopping for energy efficiency along with throughput and delay. A random network model with n nodes in area A(n) is considered. The effect of interference is captured by the Physical model and the signal is assumed to decay with distance r as r−δ
Abbas El Gamal, James P. Mammen