System of Systems Modeling and Analysis This book provides the reader with motivation, theory, methodology, and ex- amples of modeling and analysis for system of system (SoS) problems. In addition to theory, the text contains history and conceptual definitions, as well as the theo- retical fundamentals of SoS modeling and analysis. It then describes methods for SoS modeling and analysis, including use of existing methodology and original work, specifically oriented to SoS. Providing a bridge between theory and practice for modeling and analysis of SoS, System of Systems Modeling and Analysis includes generalized concepts and Methods, Tools, and Processes (MTP) applicable to SoS across any application domain. Examples of application from various fields will be used to provide a practical demonstration of the use of the methodologies. Features • Offers a modern presentation of SoS principles and guided description of applying a modeling and analysis process to SoS engineering • Provides additional modeling approaches useful for SoS engineering, in- cluding agent-based modeling • Covers the current gap in literature between theory and modeling/ap- plication • Features examples of applications from various fields, such as energy grids and regional transportation • Includes questions, examples, and exercises at the end of each chapter This book is intended for senior undergraduate students in engineering programs studying SoS modeling, SoS analysis, and SoS engineering courses. Professional engineers will also benefit from MTP and examples as a baseline for specific user applications. SYSTEM OF SYSTEMS ENGINEERING Series Editor Mo Jamshidi System of Systems Engineering: Principles and Applications Edited by Mo Jamshidi Discrete-Time Inverse Optimal Control for Nonlinear Systems Edgar N. Sanches, Gernando Ornelas- Tellez Netcentric System of Systems Engineering with DEVS Unified Process Saurabh Mittal, Jose L. Risco Martin Intelligent Control Systems with an Introduction to System of Systems Engineering Thrishantha Nanayakkara, Ferat Sahin, Mo Jamshidi Emergent Behavior in System of Systems Engineering: Real World Applications Larry B. Rainey, Thomas O. Holland System of Systems Modeling and Analysis Daniel A. DeLaurentis, Kushal Moolchandani, Cesare Guariniello For more information about this series, please visit: https://www.routledge.com/System-of-Systems- Engineering/book-series/CRCSYSENGELE System of Systems Modeling and Analysis Daniel A. DeLaurentis Kushal Moolchandani Cesare Guariniello MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. First edition published 2023 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2023 Daniel A. DeLaurentis, Kushal Moolchandani, and Cesare Guariniello Reasonable efforts have been made to publish reliable data and information, but the author and pub- lisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information stor- age or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. ISBN: 978-1-032-13830-5 (hbk) ISBN: 978-1-032-13836-7 (pbk) ISBN: 978-1-003-23101-1 (ebk) DOI: 10.1201/9781003231011 Typeset in Nimbus Roman by KnowledgeWorks Global Ltd. Dedication DD To Prof. Mo Jamshidi, dedicated builder of System of Systems community; to my early mentors: Daniel P. Schrage, Dimitri N. Mavris, and to SoS generational thinkerRobertK.Callaway KM To papa, mummy, and Harsha; and to all others who helpedmereachwhereIamtoday CG To my mom and dad, my sister, and all the friends and relativeswhoneverceasedtosupportmydesiretolearn Contents Preface......................................................................................................................xv Contributors...........................................................................................................xvii Authors....................................................................................................................xix PART I Systems of Systems: Theory and Process for Modeling and Analysis Chapter1 WhatIsaSystemofSystems?.........................................................3 1.1 Motivation:ABetterApproachforGenerational Challenges...............................................................................3 1.2 SystemsandSystemsThinking..............................................5 1.3 DefiningSystems.....................................................................8 1.3.1 ComplexSystems.......................................................9 1.4 BriefHistoryofSystemofSystems.....................................11 1.5 WhatisaSystemofSystems?..............................................13 1.5.1 DistinguishingSoSonAttributes.............................14 1.5.2 ClassifyingSoSonControlAuthority.....................16 1.5.2.1 DirectedSystemofSystems....................16 1.5.2.2 AcknowledgedSystemofSystems..........17 1.5.2.3 CollaborativeSystemofSystems............18 1.5.2.4 VirtualSystemofSystems.......................19 1.6 ChapterSummary.................................................................19 1.7 DiscussionQuestionsandExercises.....................................21 1.7.1 DiscussionQuestions...............................................21 1.7.2 Exercises..................................................................21 Chapter2 WhatIsSystemofSystemsEngineering?.....................................23 2.1 OverviewofSystemsEngineering........................................23 2.2 RoleofModelingandAnalysis............................................26 2.3 SystemofSystemsEngineering...........................................29 2.3.1 WhatisDifferent?....................................................29 2.3.2 SystemsThinking:AKeytoSoSE..........................31 vii viii Contents 2.3.3 DistinctiveFeaturesofSoSE...................................33 2.3.4 SoSE:AnIndustrialSnapshot..................................34 2.3.5 SoSEinAcademia:SmallStart,SteadyGrowth.....35 2.4 Example: Air Transportation System as a System of Systems.................................................................................36 2.5 ChapterSummary.................................................................36 2.6 DiscussionQuestions............................................................37 Chapter3 AFormalProcessofSoSModelingandAnalysis........................39 3.1 SoSRepresentation...............................................................39 3.1.1 SoSRepresentationandHierarchy..........................39 3.1.2 Lexicon....................................................................41 3.1.3 Taxonomy................................................................43 3.2 A3-PhaseMethodforSoSProblems...................................45 3.3 DefinitionPhaseandTools...................................................45 3.3.1 ExampleDefinition:ATS.........................................48 3.4 AbstractionPhaseandTools.................................................49 3.4.1 ExampleAbstraction:ATS......................................52 3.5 ImplementationPhaseandTools..........................................53 3.5.1 VerificationandValidation.......................................54 3.5.2 ExampleImplementation:ATS................................56 3.6 ChapterSummary.................................................................56 3.7 DiscussionQuestionsandExercises.....................................58 3.7.1 DiscussionQuestions...............................................58 3.7.2 Exercises..................................................................59 PART II Methods and Tools for System of Systems Modeling and Analysis Chapter4 BridgingTheoryandPractice........................................................63 4.1 ChoosingtheRightQuestions..............................................63 4.2 ChoosingtheRightTools.....................................................65 4.3 PuttingitAllTogether:TheSoSM&AProject....................76 4.3.1 OverallProjectDescription......................................77 4.3.1.1 Overview.................................................77 4.3.1.2 ProjectLearningObjectives....................77 4.3.1.3 ProjectTechnicalObjective.....................77 4.3.1.4 ProjectDeliverableItems........................78 4.3.2 DefinitionPhaseDeliverable...................................78 4.3.2.1 Format......................................................78 4.3.2.2 Procedure.................................................78 Contents ix 4.3.3 AbstractionPhaseDeliverable.................................79 4.3.3.1 Format......................................................79 4.3.3.2 Procedure.................................................79 4.3.4 ImplementationPhaseDeliverable..........................80 4.3.4.1 DeliverableItemsandExpectations........80 4.3.4.2 ReportSpecifics.......................................81 4.3.4.3 PosterPresentationSpecifics...................81 4.4 Notes on Applications and Selected List of SoS M&A ProjectTopics.......................................................................82 4.5 ChapterSummary.................................................................84 Chapter5 NetworkTheory.............................................................................85 5.1 BasicGraphTheoryandNetworkMeasures........................85 5.1.1 Typesofnetworks....................................................86 5.1.1.1 UndirectedNetwork................................86 5.1.1.2 DirectedNetwork....................................86 5.1.1.3 Hypergraphs.............................................87 5.1.1.4 BipartiteGraphs.......................................87 5.1.1.5 NetworkTypesBasedonTopology.........88 5.1.2 MeasuresinNetworkTheory...................................89 5.1.2.1 Degree,DegreeDistribution,and NetworkDensity......................................90 5.1.2.2 Paths,Cycles,andNetworkDiameter.....92 5.1.2.3 ClusteringCoefficient..............................93 5.1.2.4 NodeCentrality.......................................94 5.1.2.5 Assortativity.............................................95 5.2 ModelingNetworkDynamics...............................................95 5.2.1 GrowthAlgorithms:RandomNetwork....................97 5.2.2 GrowthAlgorithms:Scale-FreeNetwork................97 5.3 UsingNetworksforSoSModelingandAnalysis.................98 5.3.1 ModelingInteractionsandFlowwithinNetworks..99 5.3.2 BehaviorsofComplexNetworks...........................101 5.3.2.1 Example 4: Disease Spread via RandomGeometricGraphs...................101 5.4 Modeling the Air Transportation System Using NetworkTheory..................................................................102 5.5 ChapterSummary...............................................................104 5.6 DiscussionQuestionsandExercises...................................105 5.6.1 DiscussionQuestions.............................................105 5.6.2 Exercises................................................................105 Chapter6 Agent-BasedModeling................................................................107 6.1 ABriefIntroductiontoAgent-BasedModeling.................107 6.1.1 WhatareAgents?...................................................110