## Publica

Hier finden Sie wissenschaftliche Publikationen aus den Fraunhofer-Instituten. # Locally Markovian object nets - the conceptual model

**Abstract**

An object net (ON) can be derived from a (Place- Transition) Petri net (PN) by enhancing the latter with modularization information. The resulting components, called for different reasons objects, have the property that any pair of transitions of the PN which are in a static conflict belong to the same object of any ON derived from that PN. Suppose that there are given probability distributions for the solution of dynamic conflicts in favor to the different sets of concurrently enabled transitions which depend at most upon the current markings of the net but not upon past ones. Given this, usually called memoryless or Markovian, property for a PN, it will be natural to suppose this dependency only on the marking of those places directly connected with the transitions in conflict. According to the definition of objects, the probability distributions for conflict solution will then depend only upon the local markings of the object which the conflict belongs to. For this reason, an ON wit h this property together with the local probability distributions will be called locally Markovian object net (LMON). Based on the local introduction of probabilities, a natural introduction of local "time" becomes possible. In particular, this local time may be qualitatively and quantitative characterized by Phase-Type probability distributions. Consequently, it may be used for an appropriate characterization of the behaviour of the subnets encapsulated by the objects and thus for a qualified abstraction and refinement in "quantified nets". As an important potential application, LMONs promise to be well suited for a distributed probabilistic simulation of models of distributed systems. Particularly, performance measures can be obtained for distributed programs and protocols based on a natural (with respect to the maintenance of the locality principle) "quantitative" extension of a pure "qualitative" model.