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 device, a novel discontinuous reception (DRX) scheme is specified in LTE standards to reduce the power consumption of user equipment. Since the existing analytical models are not accurate enough in some situations. A performance analysis including more parameters is proposed for DRX operation in this thesis. For the proposed model, the correctness is validated and the improvement can be observed by performing simulations. Besides, according to performance evaluations of DRX operation, the DRX parameters may significantly influence the power saving efficiency and quality-of-service (QoS). Hence, a traffic-based DRX cycles adjustment (TDCA) scheme is proposed to adaptively control the DRX operation. The proposed TDCA scheme will adjust the sleep cycles to balance the sleep ratio and mean packet delay based on traffic estimation. A partially observable Markov decision process is applied in this thesis to conjecture the present traffic state and offer a decision policy. Simulation results show that the TDCA scheme can enhance the energy saving efficiency for the existing DRX operation while the QoS constraint is still satisfied.