The power saving operation, called discontinuous reception (DRX), in Third-Generation Partnership Project (3GPP) Long-Term Evolution Advanced (LTE Advanced) has recently been discussed in many studies. However, most of them focus only on the first moments, i.e. means, of interested performance metrics such as power-saving factor, transmission delay, etc. In order to gain full quality of service (QoS) control for real-time applications, it is imperative to obtain the distribution function of, in particular, the transmission delay. Thus, in this paper, extensive simulations are performed to examine the effects of various DRX parameters on the distribution function of the transmission delay.