Stepwise refinements of net models and their place invariants

Abstract

Schedules for manufacturing cells can be systematically derived by simple stepwise refinements which, in consecutive steps, increase the complexity of the cell by introducing its components one after another. Timed Petri net models of schedules derived in this way have some convenient structural properties-net models are covered by conflict-free subnets, determined by place invariants of the model. These place invariant implied subnets can be used for evaluation of the basic performance characteristics of the model. The paper shows that place invariants of net models of schedules can be obtained by the same stepwise refinements that are used for model derivation. Simple examples of performance evaluation are included as an illustration of the use of place invariants in the analysis of schedules.