RECONFIGURABLE OPEN AHL SYSTEMS - user.tu OPEN AHL SYSTEMS ... Real-life systems are frequently characterized by complexity and ... urable AHL system consists of an AHL

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  • Conny Ullrich

    RECONFIGURABLE

    OPEN AHL SYSTEMS

    Supervisor: PD Dr.habil. Julia Padberg

    Diploma Thesis

    19th May 2008

    Institut fur Softwaretechnik und

    Theoretische Informatik

    Technische Universitat Berlin

  • Eidesstattliche Erklarung

    Hiermit erklare ich, dass ich diese Arbeit selbststandig verfasst und keine anderen alsdie angegebenen Quellen und Hilfsmittel benutzt habe, und die Arbeit in gleicher oderahnlicher Fassung noch nicht Bestandteil einer Studien- oder Prufungsleistung war.

    Berlin, 19.05.2008

    Conny Ullrich

  • Abstract

    In this thesis reconfigurable open AHL systems are introduced.

    Open AHL systems are an extension of AHL systems introduced in [PER95] with openplaces and communicating transitions. In addition to the modelling of concurrent sys-tems with complex data they allow to model open systems which communicate withtheir environment.

    OAHLSystems, the category of open AHL systems and morphisms, is defined, and itis shown that OAHLSystems is a weak adhesive HLR category. This result allows todefine reconfigurable open AHL systems as an instance of weak adhesive HLR systemswhich are introduced in [EP06] to model dynamic systems.

    Finally, a case study is presented that demonstrate the practical application of reconfig-urable open AHL systems. This case study point out an enhancement of clarity, whenmodelling and simulating a large-scale system by decomposing it into simple subsystems.

    Zusammenfassung

    In dieser Diplomarbeit werden rekonfigurierbare offene AHL Systeme eingefuhrt.

    Offene AHL Systeme stellen eine Erweiterung der in [PER95] eingefuhrten AHL Sys-teme um offene Stellen und Kommunikationstransitionen dar. Neben der Modellierungnebenlaufiger Systeme mit komplexen Daten ermoglichen sie die Modellierung offenerSysteme, die sich in Kommunikation mit ihrer Umwelt befinden.

    Es wird OAHLSystems, die Kategorie der offenen AHL Systeme und Morphismen,definiert und gezeigt, dass diese eine weak adhesive HLR Kategorie ist. Dieses Ergebnisermoglicht die Definition der rekonfigurierbaren offenen AHL Systeme als eine Instanzder weak adhesive HLR Systeme, die in [EP06] zur Modellierung dynamischer Systemeeingefuhrte wurden.

    Den Abschluss bildet eine Fallstudie, die die praktische Anwendung der rekonfig-urierbaren offenen AHL Systeme aufzeigt. Sie verdeutlicht eine Steigerung derUbersichtlichkeit bei der Modellierung und Simulation eines komplexen Systems durchDekomposition in einfache Subsysteme.

  • Contents

    1. Introduction 71.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2. Goal and Structure of this Work . . . . . . . . . . . . . . . . . . . . . . . 91.3. Informal Introduction of Open AHL Systems . . . . . . . . . . . . . . . . 11

    1.3.1. Place/Transition Systems . . . . . . . . . . . . . . . . . . . . . . . 111.3.2. Algebraic High Level Systems . . . . . . . . . . . . . . . . . . . . . 111.3.3. Open Algebraic High-Level Systems . . . . . . . . . . . . . . . . . 12

    1.4. Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.1. Reactive/Modular Systems with Petri Nets . . . . . . . . . . . . . 131.4.2. Dynamic Changes of Systems . . . . . . . . . . . . . . . . . . . . . 14

    2. Open Algebraic High Level Systems 172.1. Open Algebraic High Level Nets . . . . . . . . . . . . . . . . . . . . . . . 17

    2.1.1. Disjoint Union as Functor . . . . . . . . . . . . . . . . . . . . . . . 172.1.2. Formal Definition and Operational Behaviour of Open AHL Nets . 212.1.3. Generalised Open AHL Net Morphisms . . . . . . . . . . . . . . . 272.1.4. Structuring of Open AHL Nets . . . . . . . . . . . . . . . . . . . . 32

    2.2. Open Algebraic High Level Systems . . . . . . . . . . . . . . . . . . . . . 41

    3. Open AHL Systems as Weak Adhesive HLR Category 433.1. Overview of Weak Adhesive HLR Categories . . . . . . . . . . . . . . . . 433.2. Open AHL Schemas as weak adhesive HLR Category . . . . . . . . . . . . 453.3. Open AHL Nets as weak adhesive HLR Category . . . . . . . . . . . . . . 523.4. From Open AHL Nets to Open AHL Systems . . . . . . . . . . . . . . . . 523.5. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

    4. Reconfigurable Open AHL Systems 554.1. Overview of Weak Adhesive HLR Systems . . . . . . . . . . . . . . . . . . 554.2. Reconfigurable Open AHL Systems . . . . . . . . . . . . . . . . . . . . . . 57

    4.2.1. Communication Rules . . . . . . . . . . . . . . . . . . . . . . . . . 574.2.2. Application of Rules . . . . . . . . . . . . . . . . . . . . . . . . . . 60

    5. Case Study 63

  • 6 Contents

    5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2. Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

    5.2.1. Algebraic Specification . . . . . . . . . . . . . . . . . . . . . . . . . 655.2.2. Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.2.3. Workflows and Rules . . . . . . . . . . . . . . . . . . . . . . . . . . 67

    5.3. Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.3.1. Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.3.2. Initial Open AHL System . . . . . . . . . . . . . . . . . . . . . . . 795.3.3. The Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    6. Conclusion 876.1. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876.2. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    A. Categorical Background 89A.1. Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89A.2. Universal and General Colimit Constructions . . . . . . . . . . . . . . . . 90

    B. Categories and Specifications 95B.1. Basic Weak Adhesive HLR Categories . . . . . . . . . . . . . . . . . . . . 95B.2. Basic Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

    C. Case Study - Simulation 101C.1. Construction of the Case Study Specification . . . . . . . . . . . . . . . . 101C.2. Scenario Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    C.2.1. Simulation of the Security Group . . . . . . . . . . . . . . . . . . . 104C.2.2. Simulation of the Central Exchange Officer . . . . . . . . . . . . . 149C.2.3. Simulation of the Nursing Staff . . . . . . . . . . . . . . . . . . . . 162

  • 1. Introduction

    1.1. Motivation

    Real-life systems are frequently characterized by complexity and dynamic, and consistof interacting subsystems. In order to examine and optimise such complex, dynamicsystems an adequate modelling is a sine qua non (condition precedent).

    To model dynamic systems and process flows the framework of weak adhesive high-levelreplacement (HLR) systems have been introduced in [EP06]. Weak adhesive HLR sys-tems, based on weak adhesive HLR categories, are a categorical generalisation of graphgrammars with double pushout approach ([Ehr79]) from graphs to high-level structures.This framework gives a categorical description of a rule based, abstract rewriting tech-nique. Since their introduction weak adhesive HLR systems have been instantiated withvarious kinds of graphs, Petri nets, Petri systems and algebraic specifications.

    One of these instances are reconfigurable algebraic high-level (AHL) systems, based onAHLSystems, the category of AHL systems and AHL system morphisms. A reconfig-urable AHL system consists of an AHL system, i.e. an AHL net with an actual marking,and a set of rules whose application modify the AHL systems structure at runtime.AHL Nets themself are an extension of the categorical P/T Nets and combine P/T netswith algebraic specifications. Categorical P/T Nets are based on the monoid struc-ture of the classical formulation of Petri nets (see [MM90]) and have been introducedin [EM96] to put the Petri nets into the mathematical context of category theory andto use categorical methods.

    Just like all kinds of Petri nets and Petri systems reconfigurable AHL systems are par-ticularly suitable for modelling a system, that is characterised to be concurrent, asyn-chronous, distributed, parallel or nondeterministic. Additionally, reconfigurable AHLsystems are very useful to model complex data and systems, whose structure can changedynamically. However, reconfigurable AHL systems force us to take a global view whenmodelling the behaviour of an open system, e.g. a subsystem. Since the complexity ofreal-life systems become larger and more complex, the AHL system, that models such areal-life system, become very large and unclear.

    We point out this problem with the following example.

  • 8 1. Introduction

    Example 1.1. A typical application field of reconfigurable systems is the modelling ofdynamic workflows, e.g. emergency scenarios (see [HEP07]) where several organisationscan be involved. Figure 1.1 illustrates a workflow of an emergency scenario in a hospitalwhere two organisations are involved: the Fire Department and the hospital personnelwhich consists of three groups. The different groups are marked by blue squares. Eachline represents the workflow of one person. Hence, the group Nurses contains of twoNurses (N1, N2), Security contains of three persons (SCO, S1, EO), Fire Departmentcontains of four persons (FDO, F1, F2, F3) and CEO represent one person. For the sakeof clarity we dispense with the naming of the places and transitions and with the arcinscriptions.

    Nurses CEO SecurityN2 N1 SCO S1 EO

    Fire DepartmentFDO F1 F3F2

    Figure 1.1: Emergency Scenario modelled with an AHL System

    The net in Figure 1.1 describes the workflow from a global perspective