Energy expended in a discrete manufacturing system can be saved by turning idle machines off. Utilizing this idea, previous research has contributed preliminary models in which mainly M/M/1 machines are considered. To generalize existing approaches, this paper proposes a new energy model based on a Gi/M/1 queueing network. To start, a simulation model is built with Gi/M/1 machines. The proposed model is then built by fitting each GED (Generalized Erlang Distribution) to the observed first two moments of simulated interarrival times of all machines. Consumed energy is calculated separately by the proposed and simulation models, and, in the comparison between two estimations, the proposed method shows at most 4% different energy estimation from simulated values, suggesting that the proposed approach is promising for the energy analysis about a Gi/M/1 queueing network.