Petri net representation of decision models

Bibliography: p. 24-25."June 1984""N00014-83-K-0185" "AFOSR-80-0229"Daniel Tabak, Alexander H. Levis

Fuzzy-Petri-Net Reasoning Supervisory Controller and Estimating States of Markov Chain Models

Markov chain models are efficient tools for representing stochastic discrete event processes with wide applications in decision and control. A novel approach to fuzzy-Petri-net reasoning generated solution to initial or another state in Markov-chain models is proposed. Reasoning is performed by a fuzzy-Petri-net supervisory controller employing a fuzzy-rule production system design and a fuzzy-Petri-net reasoning algorithm, which has been developed and implemented in C++. The reasoning algorithm implements calculation of the degrees of fulfilment for all the rules and their appropriate assignment to places of Petri net representation structure. The reasoning process involves firing active transitions and calculating degrees of fulfilment for the output places, which represent propositions in the knowledge base, and determining of fuzzy-distributions for output variables as well as their defuzzified values. Finally, these values are transferred to assign the state of Markov-chain decision model in terms of transition probabilities

Study of decentralised decision models in distributed environments

Many of today's complex systems require effective decision making within uncertain distributed environments. The central theme of the thesis considers the systematic analysis for the representation of decision making organisations. The basic concept of stochastic learning automata provides a framework for modelling decision making in complex systems. Models of interactive decision making are discussed, which result from interconnecting decision makers in both synchronous and sequential configurations. The concepts and viewpoints from learning theory and game theory are used to explain the behaviour of these structures. This work is then extended by presenting a quantitative framework based on Petri Net theory. This formalism provides a powerful means for capturing the information flow in the decision-making process and demonstrating the explicit interactions between decision makers. Additionally, it is also used for the description and analysis of systems that axe characterised as being concurrent, asynchronous, distributed, parallel and/ or stochastic activities. The thesis discusses the limitations of each modelling framework. The thesis proposes an extension to the existing methodologies by presenting a new class of Petri Nets. This extension has resulted in a novel structure which has the additional feature of an embedded stochastic learning automata. An application of this approach to a realistic decision problem demonstrates the impact that the use of an artificial intelligence technique embedded within Petri Nets can have on the performance of decision models

Distributed product development approaches and system for achieving optimal design.

The research in this dissertation attempts to provide theoretic approaches and design systems to support engineers who are located in different places and belong to different teams or companies to work collaboratively to perform product development.The second challenge is addressed by developing a collaborative design process modeling technique based on Petri-net. Petri-net is used to describe complex design processes and to construct different design process alternatives. These alternative Petri-net models are then analyzed to evaluate design process alternatives and to select the appropriate process.In this dissertation, three major challenges are identified in realization of a collaborative design paradigm: (i) development of design method that supports multidisciplinary xi design teams to collaboratively solve coupled design problems, (ii) development of process modeling techniques to support representation and improve complex collaborative design process, and (iii) implementation of a testbed system that demonstrates the feasibility of enhancing current design system to satisfy with the needs of organizing collaborative design process for collaborative decision making and associated design activities.New paradigms, along with accompanying approaches and software systems are necessary to support collaborative design work, in a distributed design environment, of multidisciplinary engineering teams who have different knowledge, experience, and skills. Current research generally focuses on the development of online collaborative tools, and software frameworks that integrate and coordinate these tools. However, a gap exists between the needs of a distributed collaborative design paradigm and current collaborative design tools. On one side, design methodologies facilitating engineering teams' decision making is not well developed. In a distributed collaborative design paradigm, each team holds its own perspective towards the product realization problem, and each team seeks design decisions that can maximize the design performance in its own discipline. Design methodologies that coordinate the separate design decisions are essential to achieve successful collaboration. On the other side, design of products is becoming more complex. Organizing a complex design process is a major obstacle in the application of a distributed collaborative design paradigm in practice. Therefore, the principal research goal in this dissertation is to develop a collaborative multidisciplinary decision making methodology and design process modeling technique that bridges the gap between a collaborative design paradigm and current collaborative design systems.To overcome the first challenge, decision templates are constructed to exchange design information among interacting disciplines. Three game protocols from game theory are utilized to categorize the collaboration in decision makings. Design formulations are used to capture the design freedom among coupled design activities.The third challenge, implementation of collaborative design testbed, is addressed by integration of existing Petri-net modeling tools into the design system. The testbed incorporates optimization software, collaborative design tools, and management software for product and process design to support group design activities.Two product realization examples are presented to demonstrate the applicability of the research and collaborative testbed. A simplified manipulator design example is used for explanation of collaborative decision making and design process organization. And a reverse engineering design example is introduced to verify the application of collaborative design paradigm with design support systems in practice

Representing Conversations for Scalable Overhearing

Open distributed multi-agent systems are gaining interest in the academic community and in industry. In such open settings, agents are often coordinated using standardized agent conversation protocols. The representation of such protocols (for analysis, validation, monitoring, etc) is an important aspect of multi-agent applications. Recently, Petri nets have been shown to be an interesting approach to such representation, and radically different approaches using Petri nets have been proposed. However, their relative strengths and weaknesses have not been examined. Moreover, their scalability and suitability for different tasks have not been addressed. This paper addresses both these challenges. First, we analyze existing Petri net representations in terms of their scalability and appropriateness for overhearing, an important task in monitoring open multi-agent systems. Then, building on the insights gained, we introduce a novel representation using Colored Petri nets that explicitly represent legal joint conversation states and messages. This representation approach offers significant improvements in scalability and is particularly suitable for overhearing. Furthermore, we show that this new representation offers a comprehensive coverage of all conversation features of FIPA conversation standards. We also present a procedure for transforming AUML conversation protocol diagrams (a standard human-readable representation), to our Colored Petri net representation

A Process Modelling Framework Based on Point Interval Temporal Logic with an Application to Modelling Patient Flows

This thesis considers an application of a temporal theory to describe and model the patient journey in the hospital accident and emergency (A&E) department. The aim is to introduce a generic but dynamic method applied to any setting, including healthcare. Constructing a consistent process model can be instrumental in streamlining healthcare issues. Current process modelling techniques used in healthcare such as flowcharts, unified modelling language activity diagram (UML AD), and business process modelling notation (BPMN) are intuitive and imprecise. They cannot fully capture the complexities of the types of activities and the full extent of temporal constraints to an extent where one could reason about the flows. Formal approaches such as Petri have also been reviewed to investigate their applicability to the healthcare domain to model processes. Additionally, to schedule patient flows, current modelling standards do not offer any formal mechanism, so healthcare relies on critical path method (CPM) and program evaluation review technique (PERT), that also have limitations, i.e. finish-start barrier. It is imperative to specify the temporal constraints between the start and/or end of a process, e.g., the beginning of a process A precedes the start (or end) of a process B. However, these approaches failed to provide us with a mechanism for handling these temporal situations. If provided, a formal representation can assist in effective knowledge representation and quality enhancement concerning a process. Also, it would help in uncovering complexities of a system and assist in modelling it in a consistent way which is not possible with the existing modelling techniques. The above issues are addressed in this thesis by proposing a framework that would provide a knowledge base to model patient flows for accurate representation based on point interval temporal logic (PITL) that treats point and interval as primitives. These objects would constitute the knowledge base for the formal description of a system. With the aid of the inference mechanism of the temporal theory presented here, exhaustive temporal constraints derived from the proposed axiomatic system’ components serves as a knowledge base. The proposed methodological framework would adopt a model-theoretic approach in which a theory is developed and considered as a model while the corresponding instance is considered as its application. Using this approach would assist in identifying core components of the system and their precise operation representing a real-life domain deemed suitable to the process modelling issues specified in this thesis. Thus, I have evaluated the modelling standards for their most-used terminologies and constructs to identify their key components. It will also assist in the generalisation of the critical terms (of process modelling standards) based on their ontology. A set of generalised terms proposed would serve as an enumeration of the theory and subsume the core modelling elements of the process modelling standards. The catalogue presents a knowledge base for the business and healthcare domains, and its components are formally defined (semantics). Furthermore, a resolution theorem-proof is used to show the structural features of the theory (model) to establish it is sound and complete. After establishing that the theory is sound and complete, the next step is to provide the instantiation of the theory. This is achieved by mapping the core components of the theory to their corresponding instances. Additionally, a formal graphical tool termed as point graph (PG) is used to visualise the cases of the proposed axiomatic system. PG facilitates in modelling, and scheduling patient flows and enables analysing existing models for possible inaccuracies and inconsistencies supported by a reasoning mechanism based on PITL. Following that, a transformation is developed to map the core modelling components of the standards into the extended PG (PG*) based on the semantics presented by the axiomatic system. A real-life case (from the King’s College hospital accident and emergency (A&E) department’s trauma patient pathway) is considered to validate the framework. It is divided into three patient flows to depict the journey of a patient with significant trauma, arriving at A&E, undergoing a procedure and subsequently discharged. Their staff relied upon the UML-AD and BPMN to model the patient flows. An evaluation of their representation is presented to show the shortfalls of the modelling standards to model patient flows. The last step is to model these patient flows using the developed approach, which is supported by enhanced reasoning and scheduling

A comparative analysis of business process modelling techniques

Business process modelling is an increasingly popular research area for both organisations and academia due to its usefulness in facilitating human understanding and communication. Several modelling techniques have been proposed and used to capture the characteristics of business processes. However, available techniques view business processes from different perspectives and have different features and capabilities. Furthermore, to date limited guidelines exist for selecting appropriate modelling techniques based on the characteristics of the problem and its requirements. This paper presents a comparative analysis of some popular business process modelling techniques. The comparative framework is based on five criteria: flexibility, ease of use, understandability, simulation support and scope. The study highlights some of the major paradigmatic differences between the techniques. The proposed framework can serve as the basis for evaluating further modelling techniques and generating selection procedures

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Computational models for inferring biochemical networks

Biochemical networks are of great practical importance. The interaction of biological compounds in cells has been enforced to a proper understanding by the numerous bioinformatics projects, which contributed to a vast amount of biological information. The construction of biochemical systems (systems of chemical reactions), which include both topology and kinetic constants of the chemical reactions, is NP-hard and is a well-studied system biology problem. In this paper, we propose a hybrid architecture, which combines genetic programming and simulated annealing in order to generate and optimize both the topology (the network) and the reaction rates of a biochemical system. Simulations and analysis of an artificial model and three real models (two models and the noisy version of one of them) show promising results for the proposed method.The Romanian National Authority for Scientific Research, CNDI–UEFISCDI, Project No. PN-II-PT-PCCA-2011-3.2-0917