The next-generation 5G networks are being developed with high promised capabilities. Beyond just multitudes faster data speed, 5G is expected to serve billions of connected devices and the Internet of Things (IoT), with the right trade-offs between speed, latency, and energy at an affordable cost. 5G radio networks will strongly depend on using ultra-dense integrated Small Cells (SCs) beside the Macro Cells (MCs). This kind of Ultra-Dense Networks (UDN) consisting of a large number of MCs and SCs will significantly increase network energy demands. A practical method to control energy consumption is by dynamically controlling power-saving modes in radio networks. In this paper, we propose a novel cooperative energy management framework for 5G UDN using graph theory. The 5G network is first modeled as a graph, then graph theory methods are exploited to determine the order of nodes at which power-off/on procedure is applied. We also show that significant power savings are achievable by considering only a subset of network nodes and thus reduce traffic migration and control plane signaling. We evaluated the proposed algorithm at different network densification levels and several load factors including two real-life networks. We also present the convergence of the proposed algorithm and the robustness of networks optimized using it. We also show that power savings up to 25% at full load and 65% during off-peak can be achieved using the proposed algorithm. These power savings increase further if no constraints are imposed on traffic migration and control signaling.
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