PhD thesis, pages 1-147. Technical University of Berlin, Berlin, Germany, October 1997.
Abstract: The purpose of this thesis is to propose a ``discrete deterministic and stochastic Petri net'' (DDSPN) formalism with no imposed structural or analytical restrictions.
In a DDSPN, transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. A deterministic firing time is a special case of the geometric distribution. A solution technique for the analysis of DDSPNs is presented where a DDSPN is mapped onto its underlying stochastic process, also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. Conflicts and confusions among transition firings are more likely to appear in discrete than in continuous time. Therefore, the solution method comprises a new state-space-based technique for the automatic detection of conflicts and confusions. Principally, the new detection technique is applicable to all SPN formalisms which need to generate the state space of a given model.
Keywords: discrete time; deterministic and stochastic Petri nets; conflicts; confusions.