Optimal Hopping in Ad Hoc Wireless Networks
Abbas El Gamal, J. Mammen · 2006
Abstract — 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, δ> 1. Both transmission and transceiver circuit energy are taken into account. Optimal trade-offs between throughput, delay and energy-per-bit scaling for this random network model are established. These results show that the amount of hopping still determines the optimal trade-off and yield the amount of hopping that should be used to achieve any point of the optimal trade-off. In a constant area network, where A(n) = 1, Θ(1) hops result in the best energy and delay scaling of Θ(1) at the cost of the worst throughput scaling of Θ(1/n). At the other “ extreme, pn/ in” a constant density network, where A(n) = n, Θ log n hops result in the best throughput scaling of Θ ` 1 / √ n log n ´ and the best energy scaling but at the cost of the worst delay scaling. For intermediate values of A(n), p “p ” B(n) = Θ min{A(n), n / log n} hops should be used “ to obtain the minimum energy-per-bit scaling, which is Θ A(n) δ B(n) 1 2 −δ