In this paper we first give an overview of the dierent approaches to time in Petri nets. If time is considered for performance analysis then we need also probability distributions for choices. So then we have Petri nets with time and stochastics. In literature most attention is paid to models where the time is connected to the transitions and for the stochastic case to continuous time models with exponential enabling distributions, none by its software tools as GSPN. Here we focuss on discrete models where the time is discrete and the probability distributions are discrete, because we believe that this model class has some advantages. We study the expressive power of dierent discrete models and we show how several approaches can be unified by transformations from one into the other, which is also useful for the application of software tools. We also consider timed automata and compare them with the Petri net models. We show how model checking methods can be applied for the non-stochastic case. We show when the tools for timed automata, UPPAAL, can be used for this purpose. For the stochastic case we show how Markov techniques can be used. We also consider structural analysis techniques, that do not need the state space, for the class of workflownets and we show how these techniques can be applied to reduce the computational eort.

ing Common Business Rules to Petri

In this paper we propose a framework for SOA covering such important features as proper termination (soundness) and correct correlation of tasks. Within this framework, we define a method for the calculation of the price of services. Our framework is compositional in the sense that composing a system from subsystems that meet our correctness requirements we obtain a system that still meets these requirements.

This paper describes a system for automated rail scheduling currently being developed at Dutch Rail (NS). This system will be used initially to base infrastructure decisions upon. Rail infrastructure poses constraints upon the rail schedules that can be made within it, because of the large extent in which trains share it. Good infrastructure is the one that allows good schedules. The Petri net based ExSpect editor is used to model infrastructure variants and to help converting them into schedule constraints. With OR techniques, schedules are then made generated. ExSpect is then used to simulate the execution of these schedules within their infrastructure.

A framework to design component based software architectures is presented. The framework incorporates concepts from workflow management and object orientation. The notation for defining architectures is based on the Unified Modelling Language. For semantics we use coloured Petri nets with time.

A formal framework for the specification of discrete event systems is introduced. The precise description of such a system, either for analysis or design, is a major problem in systems engineering. The underlying theoretical model is based on automata theory, and subsumes the Petri net approach. For modeling real systems one has to consider a network of interacting components and therefore three aspects of a system have to be specified: the structure of the state spaces of the components, the state transformations of the components and the interaction structure. Within the framework a tool has been developed with a language for an integrated specification of those three aspects of a system. After the introduction of the language an example illustrates our approach. IThis research is partly supported by IBM Nederland N.V.

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The best practice in information system development is to model the business processes that have to be supported and the database of the information system separately. This is inefficient because they are closely related. Therefore we present a framework in which it is possible to derive one from the other. To this end we introduce a special class of Petri nets, called Jackson nets, to model the business processes, and a document type, called Jackson types, to model the database. We show that there is a one-to-one correspondence between Jackson nets and Jackson types. We illustrate the use of the framework by an example.