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Machine type communications (MTC) are considered as key applications in LTE/LTE-A networks, for which lowering power consumption is among the primary requirements. In this paper, we model the LTE/LTE-A discontinuous reception (DRX) mechanism for MTC applications based on a Semi-Markov chain model. With our model the power saving factor and wake up latency can be accurately estimated for a given choice of DRX parameters, thus allowing to select the ones presenting the best tradeoff. The proposed model is validated through simulations. We also investigate the effect of different DRX parameters on performance.