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Long-term evolution (LTE) of the UMTS terrestrial radio access and radio access network is considered to ensure the competitiveness of 3GPP radio-access technology in a longer time frame. To minimize/optimize the user equipment (UE) power consumption, and further to support various services and large amount of data transmissions, a discontinuous reception (DRX) mechanism with adjustable DRX cycles has been adopted in LTE RRC_CONNECTED mode. In this paper, we take an overview of the DRX cycle adjustable feature of the LTE power saving mechanism and further modeling the mechanism with bursty packet data traffic using a semi-Markov process. The analytical results, which are validated against simulation experiments, show that LTE DRX achieves power saving gains over UMTS DRX at the price of prolonging wake-up delay. Based on the analytical model, effects of the DRX parameters on the power saving and wake-up delay performance are also investigated, and the results verify a trade-off relationship between the power saving and wake-up delay performance.