The 3GPP long term evolution (LTE) system is developed to enhance mobile services from the former 3G systems. In order to prolong the battery life time of mobile devices, the discontinuous reception (DRX) scheme is specified in the LTE standard to reduce the power consumption of user equipment. Existing analytical models did not comprehensively consider all essential sleep mode behaviors. Therefore, a performance analysis, including major DRX parameters is proposed in this paper for sleep mode operation. The correctness of proposed model is validated and the improvement can be observed via simulations. Furthermore, according to proposed analytical model, the DRX parameters can significantly influence the power-saving efficiency and quality-of-service (QoS) of LTE system. Hence, a traffic-based DRX cycles adjustment (TDCA) scheme is proposed to adaptively adjust the sleep cycles to balance the sleep ratio and mean packet delay based on traffic estimation. A partially observable Markov decision process is employed to conjecture the present traffic status. The policy for selecting DRX parameters can be constructed-based the evaluation metrics in TDCA scheme. Simulation results show that the proposed TDCA scheme can enhance the energy-saving efficiency while the QoS constraint is still satisfied.