We investigate how the flow of energy and the flow of jobs in a service system can be used to minimize the average response time to jobs that arrive according to random arrival processes at the servers. An interconnected system of workstations and energy storage units that are fed with randomly arriving harvested energy is analyzed by means of the Energy Packet Network (EPN) model. The system state is discretized, and uses discrete units to represent the backlog of jobs at the workstations, and the amount of energy that is available at the energy storage units. An Energy Packet (EP) which is the unit of energy, can be used to process one or more jobs at a workstation, and an EP can also be expended to move a job from one workstation to another one. The system is modeled as a probabilistic network that has a product-form solution for the equilibrium probability distribution of system state. The EPN model is used to solve two problems related to using the flow of energy and jobs in a multi-server system, so as to minimize the average response time experienced by the jobs that arrive at the system.