In this dissertation, the author made a new extension to Petri-Net models. According to its similarity to Non-Deterministic Automata and Colored Nets, the new net model is named NDC-nets, shortly for Non-Deterministic Colored Nets. In comparison to ordinary Petri-net approaches of modeling DED systems, especially for FMS modeling, NDC-nets have the following features: 1. Using ordered sets to model the properties (individualities) of processes. We can differentiate tokens (customers) of a DED system in these two aspects: the resources a token will occupy in time and the sequence in which it takes these resources. In ordinary colored- nets , the individuality of a token is identified with a label : color together with the color-sets associated withplaces and the sequential modeling properties imbedded in the Petri nets. This would in many eases result in the following difficulties : when the paths of a token passing through the DED system become flexible and complex, it is hard to construct the colors set, especially the mapping functions between the multi-sets of colors. In such applications as FMS, the systems must face constant changes in the batches of workpieces they process, and each workpiece can have multi-paths going through the machining shop floor, one colored net model can only describe one batch of workpieces. In a word, color-net models are inflexible to deal with the flexibility of FMS. In order to overcome the difficulties of colored nets , we use ordered-set to describe a token's properties independently of the Petri-net structure. NDC nets essentially separate the modeling procedures for token properties and for system structures, making the DEDS modeling a very uniform, highly- semantic and the most important : small in scale and sufficiently descriptive procedure. 2. Using predicates associated with transitions to cover the individual tokens In Colored Nets, the instance of a transition is by the choice of a color from the colors set associated with the transition, and the result of firing of an enabled transition is a function of the selected color. But in NDC nets, the tokens in the places for firing a transition are selected by predicates, that means that any tokens satisfying the predicates can fire the transition. That is why the name of non-deterministic comes. The selection of predicates for transitions is based upon the physical meanings of the transitions and independent of any concrete token structures. The definitions of predicates can be given upon the data type specified by the ordered-set for token description. That guarantees that the changes in the flow paths of tokens will not affect the net algebraic operations as long as the tokens can be described in the given data type. Here, in order to reduce the complexity of a NDC net model, we usually apply the one-step rule for selection of the predicates, which means that we only observe the fronti~er nodes of token s
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