When computing resources are consolidated in a few huge data centers, a massive amount of data is transferred to each data center over a wide area network (WAN). This results in increased power consumption in the WAN. A distributed computing network (DCN), such as a content delivery network, can reduce the traffic from/to the data center, thereby decreasing the power consumed in the WAN. In this paper, we focus on the energy-saving aspect of the DCN and evaluate its effectiveness, especially considering traffic locality, i.e., the amount of traffic related to the geographical vicinity. We first formulate the problem of optimizing the DCN power consumption and describe the DCN in detail. Then, numerical evaluations show that, when there is strong traffic locality and the router has ideal energy proportionality, the system's power consumption is reduced to about 50% of the power consumed in the case where a DCN is not used; moreover, this advantage becomes even larger (up to about 30%) when the data center is located farthest from the center of the network topology.