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At present, the adjustment of train operation plans is undertaken generally before a comparatively long planning horizon such as 3 hours by the dispatchers via the workstation of train scheduling, which can not meet the requirements of optimization and real-time processing in the networked operation with medium- and high-speed trains. This paper establishes the generalized formal description for train scheduling, and proposes a framework and algorithm for the real-time train scheduling and control based on model predictive control, i.e. real-time predictive scheduling (RTPS), which provides automatic and intelligent decision support for the optimization of train operation. The simulation results demonstrate the advantages of the proposed approach over the current heuristic scheduling strategies such as FCFS (first come first served), FLFS (first leave first served), and AMCC (avoid most critical completion time). The proposed RTPS considers the effects of future selection of alternative arcs on the current selection of them with performance improvement of total railway network in the prediction horizon rather than that of one train for the selection of alternative arcs.