Scheduling and control of extended event graphs with negative places and tokens for time constrained discrete event systems

Abstract

Many discrete event systems are subject to time constraints. For instance, in a cluster tool for semiconductor manufacturing, a wafer processed at a processing chamber should leave the chamber within a time limit. Otherwise, the wafer undergoes a severe quality problem due to residual gases or heat in the processing chamber. Hoist-based processing systems for printed circuit board manufacturing, microcircuits like digital signal processing, and real-time software systems also have similar time constraints. Such time constraints make scheduling decisions complicated. The critical scheduling issues include how the system with time constraints is modeled, whether there exists a feasible schedule that satisfies all time constraints, how a feasible schedule is identified or computed, and how the timings of the activities are controlled. There have been attempts for addressing some of the scheduling issues, including p-time Petri nets, PERT-like graph models, and linear programming models. Petri nets are known to be useful for modeling and analyzing discrete event dynamic systems. An interesting question is whether or how the Petri nets can be extended for addressing the time constraints. While p-time Petri nets or PERT-like graphs propose some extension, we still need a more unified Petri net theory that can model and analyze time constrained systems more systematically. To do this, places and tokens that are essential for representing the conditions and states of discrete event systems should be extended. In this thesis, we propose an extended event graph that can model and analyze decision-free discrete event systems with general time window constraints. To do this, we introduce places with negative holding times and tokens with negative token counts into a timed event graph. Such an extended graph is called a negative event graph(NEG). We define enabling and firing rules for NEGs and develop the theory for analyzing NEGs. We first examine the liveness of an NEG, ...