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Long-term evolution (LTE) has been heralded as the 4G mobile communication standard to meet the demand for high-speed data transmission. But the heavy processing requirement on the user equipment (UE) leads to excessive power consumption. Discontinuous reception (DRX) is an important mechanism to tackle the issue. Delay and power saving are two contradictory performance indicators associated with DRX. This paper makes a rigorous analysis of the delay incurred and power saving achieved by a DRX scheme that uses a mix of short and long cycles. The correctness of the analysis is validated by simulation. Moreover, the values of key parameters values are varied to assess their impact on the performance of DRX.