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The 4G standard Long Term Evolution (LTE) has been developed for high-bandwidth mobile access for today's data-heavy applications, consequently, a better experience for the end user. To extend the user equipment battery lifetime, plus further support various services and large amount of data transmissions, the 3GPP standards for LTE/LTE-Advanced has adopted discontinuous reception (DRX). However, there is a need to optimize the DRX parameters, so as to maximize power saving without incurring network re-entry and packet delays. In this paper, we provide an overview of the fixed frame DRX cycle and compare it against an adjustable DRX cycle of the LTE/LTE-Advanced power saving mechanism, by modelling the system with bursty packet data traffic using a semi-Markov process. Based on the analytical model, we will show the trade-off relationship between the power saving and wake-up delay performance.