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This paper considers a general scheduling problem for a vital class of cyber-physical systems, the Physical Networks (PhyNets), where the physical laws in the plant can be abstracted into a physical graph. Such graph structure often allows efficient distributed algorithms for inference and control. Important application of PhyNets include packet scheduling in wireless ad hoc networks and the coordinated Electric Vehicle (EV) charging in power grids. This paper first formulates the general scheduling problem, and then proposes an optimal scheduling algorithm, which employs a combination of Lyapunov optimization and Markov Chain Monte Carlo (MCMC) sampling techniques. The algorithm is fully distributed, and does not require any knowledge of the statistics of the arrival processes and network states. Finally, as the main application focus of this paper, the algorithm is applied to the important case of distributed EV charging scheduling, where its performance is demonstrated by simulation results.