Workflow Petri Nets with Time Stamps and Their Using in Project Management

Workflow Petri nets with time stamps (WPNTS) are the newly introduced class of low-level Petri nets, whose definition and the properties are the main topic of this article; they generalize the properties of Petri net processes in the area of design, modeling and verification of generally parallel systems with the discrete time. Property-preserving Petri net process algebras (PPPA) does not need to verify composition of Petri net processes because all their algebraic operators preserve the specified set of the properties. These original PPPA are generalized for the class of the WPNTS in this article. The new JOIN, EBPS, COMP and SYNC algebraic operators are defined for the class of WPNTS and their chosen properties are proved. With the support of these operators the WPNTSs can be extended also to the area of the project management and the determination of the project generalized critical path with the support of the principles of the critical path method (CPM). The new CPWPNTS subclass of WPNTS class is specially designed for the generalization of the CPM activities charts, its properties are proved and then demonstrated on the generalized critical path specification of simple project example in this article.