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WiMax/802.16 mesh network is an emerging infrastructure that offers a cost-effective deployment for high-speed wireless broadband access to the back haul network. In order to provide the best cost-effective deployment solution, nodes must be powered by batteries which do not require electrical cables and voltage transformers deployment (city power lines voltage is not suited to WiMax/802.16 nodes voltage). Moreover this deployment approach (the only one compatible with a mobile nodes topology) is environment constraint free since not all cities have easy-reachable power lines (e.g. rural cities). However it requires a predictive mechanism to calculate the lifetime of the network, in purpose to provide the adequate maintenance (recharge/change nodes batteries, reconfigure the nodes) at the appropriate time. We study the problem of maximizing the network lifetime (MNL) in order to minimize the maintenance of WiMax/802.16 mesh centralized scheduling networks powered by batteries which causes them to go off line. Moreover our study incorporates an explicit novel modeling of interference and hidden terminal nodes using an appropriate time slot allocation. Results show that power aware routing and a convenient frame size improve the network lifetime.