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Nowadays, data caching is being used as a high-speed data storage layer in mobile edge computing networks employing flow control methodologies at an exponential rate. This study shows how to discover the best architecture for backhaul networks with caching capability using a distributed offloading technique. This article used a continuous power flow analysis to achieve the optimum load constraints, wherein the power of macro base stations with various caching capacities is supplied by either an intelligent grid network or renewable energy systems. This work proposes ubiquitous connectivity between users at the cell edge and offloading the macro cells so as to provide features the macro cell itself cannot cope with, such as extreme changes in the required user data rate and energy efficiency. The offloading framework is then reformed into a neural weighted framework that considers convergence and Lyapunov instability requirements of mobile-edge computing under Karush Kuhn Tucker optimization restrictions in order to get accurate solutions. The cell-layer performance is analyzed in the boundary and in the center point of the cells. The analytical and simulation results show that the suggested method outperforms other energy-saving techniques. Also, compared to other solutions studied in the literature, the proposed approach shows a two to three times increase in both the throughput of the cell edge users and the aggregate throughput per cluster.