Modelling and controlling traffic behaviour with continuous Petri nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a compositional formalism to model traffic behaviour. This paper introduces some new features of continuous Petri nets that are useful to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing trac light controllers that minimize the total delay of the vehicles in the system

Semantic Embedding of Petri Nets into Event-B

We present an embedding of Petri nets into B abstract systems. The embedding is achieved by translating both the static structure (modelling aspect) and the evolution semantics of Petri nets. The static structure of a Petri-net is captured within a B abstract system through a graph structure. This abstract system is then included in another abstract system which captures the evolution semantics of Petri-nets. The evolution semantics results in some B events depending on the chosen policies: basic nets or high level Petri nets. The current embedding enables one to use conjointly Petri nets and Event-B in the same system development, but at different steps and for various analysis.Comment: 16 pages, 3 figure

Artifact Lifecycle Discovery

Artifact-centric modeling is a promising approach for modeling business processes based on the so-called business artifacts - key entities driving the company's operations and whose lifecycles define the overall business process. While artifact-centric modeling shows significant advantages, the overwhelming majority of existing process mining methods cannot be applied (directly) as they are tailored to discover monolithic process models. This paper addresses the problem by proposing a chain of methods that can be applied to discover artifact lifecycle models in Guard-Stage-Milestone notation. We decompose the problem in such a way that a wide range of existing (non-artifact-centric) process discovery and analysis methods can be reused in a flexible manner. The methods presented in this paper are implemented as software plug-ins for ProM, a generic open-source framework and architecture for implementing process mining tools

History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps

We show that history-preserving bisimilarity for higher-dimensional automata has a simple characterization directly in terms of higher-dimensional transitions. This implies that it is decidable for finite higher-dimensional automata. To arrive at our characterization, we apply the open-maps framework of Joyal, Nielsen and Winskel in the category of unfoldings of precubical sets.Comment: Minor updates in accordance with reviewer comments. Submitted to MFPS 201

Higher Dimensional Transition Systems

We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures