In wireless ad hoc sensor networks, energy use is in many cases the most important constraint since it corresponds directly to operational lifetime. Topology management schemes such as GAF put the redundant nodes for routing to sleep in order to save the energy. The radio range will affect the number of neighbouring nodes, which collaborate to forward data to a base station or sink. In this paper we study a simple linear network and deduce the relationship between optimal radio range and traffic. We find that half of the power can be saved if the radio range is adjusted appropriately compared with the best case where equal radio ranges are used.

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