In order to improve the management mechanisms of the electric energy transport infrastructures, the smart grid networks have associated data networks that are responsible for transporting the necessary information between the different elements of the electricity network and the control center. Besides, they make possible a more efficient use of this type of energy. Part of these data networks is comprised of the Neighborhood Area Networks (NANs), which are responsible for interconnecting the different smart meters and other possible devices present at the consumers’ premises with the control center. Among the proposed network technologies for NANs, wireless technologies are becoming more relevant due to their flexibility and increasing available bandwidth. In this paper, some general modifications are proposed for the routing protocol of the wireless multi-hop mesh networks standardized by the IEEE. In particular, the possibility of using multiple paths and transmission channels at the same time, depending on the quality of service needs of the different network traffic, is added. The proposed modifications have been implemented in the ns-3 simulator and evaluated in situations of high traffic load. Simulation results show improvements in the network performance in terms of packet delivery ratio, throughput and network transit time.