To solve the challenges of ever-increasing energy consumption, wireless mesh networks (WMNs) consisting of routers using renewable energy sources have been emerging as a promising solution. In this paper, we jointly consider the node placement and energy management in a hybrid WMN consisting of electricity-powered Internet gateways and solar-powered rechargeable routers. We introduce a new metric of failure rate to evaluate network performance and formulate the problem as a constrained optimization problem with the objective of minimizing both capital expenses on installation and operational expenses related to energy consumption. The network Quality of Service (QoS) requirements include meeting the failure rate requirement, the users' dynamic traffic demand requirements in both downlink and uplink, the gateways' and routers' capacity constraints, the maximal transmission power constraints, and the rechargeable routers' energy consumption constraints. Furthermore, we propose a minimum cost association algorithm to connect mesh clients to the Internet in different slots and a greedy placement algorithm to find approximate solutions for hybrid node placement. Simulation results show that the hybrid placement with rechargeable routers reveals its advantage for large scale networks in terms of more energy saving. Compared with the optimal placement achieved by the exhaustive search, our proposed algorithm can achieve good performance with the significantly reduced computation complexity.
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