Energy consumption is one of the most important challenges in Millimeter Wave (mmWave) 5G wireless communications since higher data rate and lower latency are required. Thus, User Equipment (UE) battery suffers from its energy absorption. To investigate a green communication, Discontinuous Reception (DRX) mode is introduced when no traffic arrival from the Base Station (BS) to extend UE battery lifetime but delay is increased. This paper introduces an advanced DRX, which can achieve extended UE battery lifetime with a reasonable reduced delay due to a proposed sub-frame size. Generally, traffic which arrives may be data packet or paging message. This paper evaluates two proposed system models based on traffic which arrives during wake up periods of the UE. The first system model is called Signaling Based DRX and the second system model is called Enhanced Paging Monitoring (EPM). The both system models utilize two different indicators; they are Power Saving Indicator (PSI) and Paging Early Indicator (PEI), respectively. These indicators enhance power saving and delay compared to that of the traditional approach. The evaluation of the both system models performance is by measuring the power saving factor and the average delay of the UE over the same data/paging traffic arrival rate. A MATLAB simulation program is used to validate the system model and the numerical analysis. Analytical and numerical results are considered.