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In the fourth generation or next generation networks, services of non-real-time variable bit rate (NRT-VBR) and best effort (BE) will dominate over 85% of the total traffic in the networks. In this paper, we study the power saving mechanism of NRT-VBR and BE services for mobile handsets (MHs) to prolong their battery lifetime (i.e., the sustained operation duration) in the fourth generation networks. Because the priority of NRT-VBR and BE is lower than that of real-time VBR (RT-VBR) or guaranteed bit rate (GBR) services, we investigate an extended sleep mode for lower priority services (e.g., NRT-VBR and BE) in an MH to conserve the energy. The extended sleep mode is used when the MH wakes up from the sleep mode but it cannot obtain the bandwidth from base station (BS). The proposed mechanism, named extra power saving scheme (EPSS), uses the Markovian queuing model to estimate the extended sleep duration to let MHs conserve their battery energy when the networks traffic is congested. To study the performance of EPSS, an accurate analysis model of energy is presented and validated by taking a series of simulations. Numerical experiments show that EPSS can achieve 43% extra energy conservation at most when downlink resource is saturated. We conclude that the energy of MHs can be conserved further by applying EPSS when the traffic load is saturated. The effect of energy saving becomes more obvious when the portion of NRT-VBR and BE services is greater than that of RT-VBR and GBR services. [ABSTRACT FROM AUTHOR]