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With the widespread use of the Internet, reducing power consumption to extend network lifetime while maintaining the communication connectivity and covering the target region completely has become one of the most important challenges in designing future Internet networks. After the comparison of some existing methods, such as measuring networks state and evaluating flow-jamming attack on network flow, we present a new form of network traffic flows, in which end systems or hosts have three basic states: on, off and asleep. In this paper, we first give a brief review on the existing techniques, and particularly consider ldquoresearch on architecturerdquo as a process rather than an event. Then, we propose a framework for initial exploration of supporting selective connectivity, whereby a host or a router can choose whether to be ldquoconnectedrdquo or ldquodisconnectedrdquo. The proposed approach is formulated as an optimization problem for both selective connectivity and resource exhaustion in Internet. We show that this technique is able to provide a foundation for design of future protocols to improve the actual Internet architecture.