Timed Petri nets and performance evaluation of systems

Several simple applications of timed Petri nets to modeling and performance analysis of concurrent systems are presented as an illustration of a uniform approach to analysis of a wide class of discrete-event systems. Such a unified approach is used in a graduate course on performance evaluation of systems at Memorial University

Improving The Service Design Process: Process Integration, Conflict Reduction And Customer Involvement

Service design is the science of creating service experiences based on the customer’s perspective, to make it useful, enjoyable and cost-effective for the customer. Although the field of service design is relatively new, it has been rapidly expanding in research and practice. Most researchers focus on the usefulness of the service, cost efficiency, meeting customers’ needs, or service strategy. However, all service elements can benefit from improving the service design process. Current service design processes are suffering a lack of integration of activities, conflicts in decision-making processes, and exclusion of practitioners’ methods. In prior research, information models were created to integrate the service design process across the enterprise. As an extension, this dissertation introduces Petri Nets to improve the service design process. Petri Nets provide a uniform environment for modeling, analysis, and design of discrete event systems. Petri Nets are used to develop a new service design process that enhances the multidisciplinary approach and includes the practitioner methods. Additionally, this dissertation uses the Lens Model to improve the decision-making mechanism. The Lens Model is to characterize decision-making policy in service design. Research shows that there is a conflict between the designer and the manager in service design decision-making. Single Lens Model systems are designed to capture the decision policy for the service designer and the service manager. A double Lens Model system is used to compare the perspectives. Finally, this research suggests a new role for the customer in the design by applying an Asset-Based approach. Asset-based System Engineering (ABSE) is a recently introduced concept that attempts to synthesize systems around their key assets and strengths. ABSE is developed with as an innovative approach that views customers as a primary asset. Customer integration in the design process is achieved through several new service design tools

A Comparison of Petri Net Semantics under the Collective Token Philosophy

In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. We use the notion of adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic

A new approach for diagnosability analysis of Petri nets using Verifier Nets

In this paper, we analyze the diagnosability properties of labeled Petri nets. We consider the standard notion of diagnosability of languages, requiring that every occurrence of an unobservable fault event be eventually detected, as well as the stronger notion of diagnosability in K steps, where the detection must occur within a fixed bound of K event occurrences after the fault. We give necessary and sufficient conditions for these two notions of diagnosability for both bounded and unbounded Petri nets and then present an algorithmic technique for testing the conditions based on linear programming. Our approach is novel and based on the analysis of the reachability/coverability graph of a special Petri net, called Verifier Net, that is built from the Petri net model of the given system. In the case of systems that are diagnosable in K steps, we give a procedure to compute the bound K. To the best of our knowledge, this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented

About Dynamical Systems Appearing in the Microscopic Traffic Modeling

Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The dynamics of these Petri nets are well-defined and may be described by a generalized matrix with a submatrix in the standard algebra with possibly negative entries, and another submatrix in the minplus algebra. When the dynamics is additively homogeneous, a generalized additive eigenvalue may be introduced, and the ergodic theory may be used to define a growth rate under additional technical assumptions. In the traffic example of two roads with one junction, we compute explicitly the eigenvalue and we show, by numerical simulations, that these two quantities (the additive eigenvalue and the growth rate) are not equal, but are close to each other. With this result, we are able to extend the well-studied notion of fundamental traffic diagram (the average flow as a function of the car density on a road) to the case of two roads with one junction and give a very simple analytic approximation of this diagram where four phases appear with clear traffic interpretations. Simulations show that the fundamental diagram shape obtained is also valid for systems with many junctions. To simulate these systems, we have to compute their dynamics, which are not quite simple. For building them in a modular way, we introduce generalized parallel, series and feedback compositions of piecewise linear concave dynamics.Comment: PDF 38 page

Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA), EPTCS 20m 201