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In this paper, resource allocation and outage control are considered for solar-powered WLAN mesh networks. Solar-powered nodes are a very cost effective option in WLAN mesh deployments where continuous power sources are not practical. In such nodes, the cost of the solar panel and battery can be a significant fraction of the total and, therefore, reducing AP power consumption is very important. A solar panel/battery configuration methodology is introduced based on a proposed AP power-aware version of IEEE 802.11. Public meteorological data is used to provision each node based on an averaged offered capacity profile. Since a node is configured statistically, it is possible that future loading may result in nonzero outage even when negligible outage is the design target. Control algorithms are introduced which can improve node outage performance by sometimes introducing an access point capacity deficit. Results are presented which show the value of the proposed configuration methodology and show that the control algorithms can prevent outage even at high levels of excess loading.