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To reduce energy consumption (EC), a mobile handset system can be designed in such a way that while the data-receiving unit in a mobile handset is receiving and monitoring data packets, the rest part of the handset (i.e., a processing unit and a user interface) is switched off into a sleep mode. In this paper, we study the timing when the rest part of the handset should wake up. Several schemes (i.e., Always-ON , Always-OFF, Wake-up upon Arrival, Wake-up upon Full, and the fractional threshold scheme) are studied and compared in terms of energy saving and the packet dropping probability (PDP). We formulate the total EC for all theses schemes analytically. Furthermore, we show how to choose optimal thresholds for the fractional threshold scheme for the following two-optimization problems: 1) minimizing the switch-on rate with a bound on the PDP and 2) minimizing the total EC with a bound on the PDP. Our study shows that the fractional threshold scheme is the best scheme. Simulations are carried out to validate analytic models.