The energy expenditure of cellular networks is increasing rapidly due to high demand of data services by the subscribers. This subsequently gives rise to the CO2 emission which is a critical issue nowadays. A hybrid cellular network comprised of macrocell and several femtocells is required to achieve reliability, continuous connectivity, and energy efficiency. To address the issue of energy efficiency, in this paper we present a queuing model of an energy efficient femtocell network. The transmission of data traffic in this type of network is modeled using M/M/1 queue where server FAP (Femtocell Access Point) takes vacation to save energy during inactivity period. The network model is solved using a MGM (Matrix Geometric Method). The performance of the system is evaluated in terms of average system delay and power savings for different sleep cycle durations. Results reveal that the maximum energy can be saved with higher sleep cycle duration at a cost of increased system delay