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With wafer residency time constraints for some wafer fabrication processes, the schedulability and scheduling problems of cluster tools are still open. Addressing these issues, this paper conducts their schedulability analysis. A Petri net (PN) model, called resource-oriented PN (ROPN), is developed for the system. This model describes when the robot should wait and a robot wait is modeled as an event in an explicit way. Based on this model, for the first time, we present the necessary and sufficient conditions under which a single-arm cluster tool with residency time constraints is schedulable, which can be checked analytically. Meanwhile, an analytical scheduling algorithm is developed to find an optimal periodic schedule if it is schedulable.