Before revision:  Our numerical study shows an overall transmit power savings of up to 95\% when compared to a fixed power allocation . We also apply our algorithm to a realistic WirelessHART network setup and observe that link heterogeneity can significantly influence network lifetime when no efficient power management is applied.
After revision:  Our numerical study shows an overall transmit power savings of up to 95\% when compared to a fixed power allocation scheme when using a service model in terms of the Shannon capacity limit. For a more realistic set-up, we evaluate the performance of the suggested algorithm in a WirelessHART network, which is a widely used communication standard for process automation and other industrial applications. We find that link heterogeneity can significantly influence network lifetime when no efficient power management is applied.