Multi-hop wireless networks play a crucial role in extending the coverage of monitoring and automation applications in the Internet of Things arena. In this paper, we propose an analytical model for analyzing the performance of IEEE 802.15.4 based multi-hop networks. We accurately model the IEEE 802.15.4 MAC for three different kinds of nodes (leaf, relay and pre-gateway nodes) using 3D Markov chains. Performance of the proposed model is analyzed using reliability, channel congestion and duty cycle as the key performance metrics. The proposed model analyzes the network behavior accurately by achieving less than 5% error when compared with simulation outcomes. © 2017, Springer Science+Business Media, LLC, part of Springer Nature.