In this paper, we propose a novel Autonomous Decentralized Control (ADC) scheme for indirectly controlling a system performance variable of large-scale and wide-area networks. In a large-scale and wide-area network, since it is impractical for any one node to gather full information of the entire network, network control must be realized by inter-node collaboration using information local to each node. Several critical network problems (e.g., resource allocation) are often formulated by a system performance variable that is an amount to quantify system state. We solve such problems by designing an autonomous node action that indirectly controls, via the Markov Chain Monte Carlo method, the probability distribution of a system performance variable by using only local information. Analyses based on statistical mechanics confirm the effectiveness of the proposed node action. Moreover, the proposal is used to implement traffic-aware virtual machine placement control with load balancing in a data center network. Simulations confirm that it can control the system performance variable and is robust against system fluctuations. A comparison against a centralized control scheme verifies the superiority of the proposal.