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There are wafer fabrication processes in cluster tools that require wafer revisiting. If a swap strategy is applied to dual-arm cluster tools handling wafer revisiting, a three-wafer periodical process is formed with three wafers completed in each period. Such a period contains three cycles in a revisiting process and three cycles in a nonrevisiting one. Hence, analysis and scheduling of such tools become very complicated. In this paper, a Petri net (PN) model is developed to describe their operations. Based on it, it is found that, if a swap strategy is applied, such tools are always in a transient state. A systematic method is then presented to analyze their performance. With the help of the proposed PN model, this work, for the first time, derives the optimality conditions of three-wafer period scheduling. Industrial application examples are given to show the results.