Cluster tools with chamber revisiting-modeling and analysis using timed Petri nets

Timed Petri nets are formal models of discrete concurrent systems. Since the durations of all activities are included in the model descriptions, many performance characteristics can be derived from such models. In the case of cluster tools, net models represent the flow of wafers through the chambers of the tool as well as consecutive actions performed by the robotic transporter. Steady-state performance of cluster tools with chamber revisiting is investigated in this paper. A systematic development of detailed tool schedules, based on a general behavioral description of the tool, is proposed and is used to derive the corresponding Petri net models. Symbolic performance characteristics of the modeled tools are obtained by using place invariants, without exhaustive reachability analysis. Simple examples presented in the paper can be easily extended in many ways.