Abstract. Energy cost is the main constraint in modern wireless communication system. A powerful scheme due to optimal energy cost is provided for a single node server in this paper. In wireless communications, the total energy for transmitting packets can be reduced by proper regulating the service rate due to different packet sizes. In our study, a generic method applying the Lagrange Multiplier methods for optimizations is proposed. We show the energy cost is a convex function and it is easy to achieve the optimization. Our contribution focused on minimizing the total energy cost induced by the transmission energy in a single server with multi-queues. The methodology presented in this paper can effectively save the energy cost due to energy consumption in wireless communication systems.