Petri net

About: Petri net is a research topic. Over the lifetime, 25039 publications have been published within this topic receiving 406994 citations.

Modular Analysis of Petri Nets

Abstract: This paper shows how two of the most important analysis methods for Petri nets can be performed in a modular way. We illustrate our techniques by means of modular Place/Transitions nets (modular PT-nets) in which the individual modules interact via shared places and shared transitions. For place invariants we show that it is possible to construct invariants of the total modular PT-net from invariants of the individual modules. For state spaces, we show that it is possible to decide behavioural properties of the modular PT-net from state spaces of the individual modules plus a synchronization graph, without unfolding to the ordinary state space. The generalization of our techniques to high-level Petri nets is rather straightforward.

User-guided discovery of declarative process models

Abstract: Process mining techniques can be used to effectively discover process models from logs with example behaviour. Cross-correlating a discovered model with information in the log can be used to improve the underlying process. However, existing process discovery techniques have two important drawbacks. The produced models tend to be large and complex, especially in flexible environments where process executions involve multiple alternatives. This “overload” of information is caused by the fact that traditional discovery techniques construct procedural models explicitly showing all possible behaviours. Moreover, existing techniques offer limited possibilities to guide the mining process towards specific properties of interest. These problems can be solved by discovering declarative models. Using a declarative model, the discovered process behaviour is described as a (compact) set of rules. Moreover, the discovery of such models can easily be guided in terms of rule templates. This paper uses DECLARE, a declarative language that provides more flexibility than conventional procedural notations such as BPMN, Petri nets, UML ADs, EPCs and BPEL. We present an approach to automatically discover DECLARE models. This has been implemented in the process mining tool ProM. Our approach and toolset have been applied to a case study provided by the company Thales in the domain of maritime safety and security.

Verification of EPCs: using reduction rules and petri nets

Abstract: Designing business models is a complicated and error prone task. On the one hand, business models need to be intuitive and easy to understand. On the other hand, ambiguities may lead to different interpretations and false consensus. Moreover, to configure process-aware information systems (e.g., a workflow system), the business model needs to be transformed into an executable model. Event-driven Process Chains (EPCs), but also other informal languages, are intended as a language to support the transition from a business model to an executable model. Many researchers have assigned formal semantics to EPCs and are using these semantics for execution and verification. In this paper, we use a different tactic. We propose a two-step approach where first the informal model is reduced and then verified in an interactive manner. This approach acknowledges that some constructs are correct or incorrect no matter what interpretation is used and that the remaining constructs require human judgment to assess correctness. This paper presents a software tool that supports this two-step approach and thus allows for the verification of real-life EPCs as illustrated by two case studies.

State equation, controllability, and maximal matchings of petri nets

Abstract: Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.

A formal modeling approach for supply chain event management

Abstract: As supply chains become more dynamic, there is a need for a sense-and-respond capability to react to events in a real-time manner In this paper, we propose Petri nets extended with time and color (to represent case data) as a formalism for managing events We designed seven basic patterns to capture modeling concepts that arise commonly in supply chains These basic patterns may be used by themselves and also combined to create new patterns We also show how to combine the patterns to build a complete Petri net and analyze it using dependency graphs and simulation Dependency graphs can be used to analyze the various events and their causes Simulation was, in addition, used to analyze various performance indicators (eg, fill rates, replenishment times, and lead times) under different strategies We showed it is possible to perform sensitivity analysis to study the effect of changing parameter values on the performance indicators This approach thus makes a very complex problem tractable