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The major challenge to achieving efficient power management for local computers that serve as edge devices of the Internet is to achieve long sleeping times while at the same time maintaining network connectivity. By modifying the network interface card (NIC) with a low-weight proxy module that can handle a certain amount of network protocol semantics and hence still keep the local computer alive on the Internet, a longer host sleeping time can be achieved, while keeping many of the components, including CPU, memory, motherboard, hard drive, etc, remain in a very-low-energy mode. In this paper, we pursue a power-proxy solution to the widely-used Instant Messenger (IM) applications. Yahoo!Â® Messenger is selected for a case study to investigate its communication protocol YMSG. Furthermore, the decision on inactivity time-out values is a crucial factor for energy savings, but the random nature of idle periods makes the decision another challenge. We formulate the decision problem into a stochastic program and propose an adaptive algorithm to set up appropriate inactivity time-out values. Simulations show that the proposed power-proxy solution combined with the inactivity time-out setup algorithm can efficiently reduce the power consumption of an edge computer.