Using the Energy Packet Network (EPN) model, we show how energy can be shared between heterogenous servers at the edge to minimize the overall average response time of jobs. The system is modeled as a probabilistic network where energy and jobs are being dispatched to the edge servers using G-Networks with a product-form solution for the equilibrium probability distribution of system state. The approach can also be used to design energy dispatching systems when renewable energy is used to improve the sustainability of edge computing.