In this paper, we investigate the impact of individual variable-range power control on the physical and network connectivity, network capacity, and power savings of wireless multihop networks such as ad hoc and sensor networks. First, using previous work by Steele [18] , we show that, for a path attenuation factor ¼ 2, the average range of links in a planar random network of A m 2 having n nodes is $ c ffiffiffi A p nÀ1 . We show that this average range is approximately half the range obtained

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... hen common-range transmission control is used. Combining this result and previous work by Gupta and Kumar [8], we derive an expression for the average traffic carrying capacity of variable-range-based multihop networks. For ¼ 2, we show that this capacity remains constant even when more nodes are added to the network. Second, we derive a model that approximates the signaling overhead of a routing protocol as a function of the transmission range and node mobility for both route discovery and route maintenance. We show that there is an optimum setting for the transmission range, not necessarily the minimum, which maximizes the capacity available to nodes in the presence of node mobility. The results presented in this paper highlight the need to design future MAC and routing protocols for wireless ad hoc and sensor networks based, not on common-range which is prevalent today, but on variable-range power control.