This paper presents an analytical model, based on a semi-Markov process, for determining the power savings achieved in a User Equipment (UE) device of a Long Term Evolution (LTE) network using the Discontinuous Reception (DRX) mechanism. Systems with and without packet buffers and the UE and enodeB are presented in this paper. Using the models, it is possible to determine the savings in power attainable by the UE when different DRX sleep cycles and timers are used. The analytical models has been validated using a discrete-event simulation model. The numerical results show that it is possible to obtain UE power savings of up to 63%.