Colored ACD and its application

The classical ACD invented by KD Tocher about 60 years ago was recently enhanced to the extended ACD by allowing each edge to have a guard and multiplicity, and then to the parameterized ACD (P-ACD) by adding parameters and variables. This paper presents a colored ACD (C-ACD) formalism which extends the P-ACD formalism by (1) introducing colors to increase model tractability and (2) adding hierarchical modeling features to reduce model complexity. As a result, C-ACD models are easier to construct and validate and is suitable for online simulation. In order to quantify the tractability of ACD models, two kinds of measures are introduced: model tractability index (MTI) and initialization tractability index (ITI). Also presented is a systematic method of initializing C-ACD models required for online simulation. It is shown that the C-ACD formalism provides more tractable models in terms of both MTI and ITI. The applicability of the C-ACD formalism is demonstrated via an illustrative simulation example for a hypothetical electronics Fab.