Petri net-based scheduling of time-constrained dual-arm cluster tools with bounded activity time variation

For time-constrained cluster tool in semiconductor manufacturing, activity time variation can make an originally feasible schedule infeasible. With bounded activity time variation considered, this paper addresses their real-time scheduling issues and conducts their schedulability analysis. With Petri net (PN) model and a real-time control policy, this paper derives closed form schedulability conditions. If schedulable, an algorithm is developed to obtain an off-line periodic schedule. This schedule together with a real-time control policy forms a real-time schedule. It is optimal in terms of cycle time and can be analytically computed with closed form expressions.