Table Of ContentModeling and Managing
Interdependent Complex
Systems ofSystems
Modeling and Managing Interdependent
Complex Systems of Systems
Yacov Y. Haimes
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LibraryofCongressCataloging-in-PublicationData
Names:Haimes,YacovY.,author.
Title:Modelingandmanaginginterdependentcomplexsystemsofsystems/
byYacovY.Haimes.
Description:Hoboken,NJ:JohnWiley&Sons,2018.|Includes
bibliographicalreferencesandindex.|
Identifiers:LCCN2018000550(print)|LCCN2018009974(ebook)|ISBN
9781119173700(pdf)|ISBN9781119173694(epub)|ISBN9781119173656
(cloth)
Subjects:LCSH:Systemsengineering.|Systemanalysis.
Classification:LCCTA168(ebook)|LCCTA168.H282018(print)|
DDC003–dc23
LCrecordavailableathttps://lccn.loc.gov/2018000550
CoverDesign:Wiley
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10 9 8 7 6 5 4 3 2 1
v
Contents
Foreword vii
Acknowledgments xv
1 ModelingandManagingInterdependentComplexSystemsofSystems:
Fundamentals,TheoryandMethodology 1
2 Modeling,Decomposition,andMultilevelCoordinationofComplex
SystemsofSystems 51
3 HierarchicalHolographicModelingandMultilevelCoordination
ofComplexSystemsofSystems 111
4 ModelingComplexSystemsofSystemswithPhantomSystem
Models 141
5 ComplexSystemsofSystems:MultipleGoalsandObjectives 183
6 HierarchicalCoordinatedBayesianModelingofComplexSystems
ofSystems 229
7 HierarchicalMultiobjectiveModelingandDecisionMaking
forComplexSystemsofSystems 279
8 ModelingEconomicInterdependenciesamongComplexSystems
ofSystems 363
9 GuidingPrinciplesforModelingandManagingComplexSystems
ofSystems 411
10 ModelingCyber–PhysicalComplexSystemsofSystems:FourCase
Studies 447
vi Contents
11 GlobalSupplyChainasComplexSystemsofSystems 527
12 UnderstandingandManagingtheOrganizationalDimension
ofComplexSystemsofSystems 559
13 SoftwareEngineering:TheDriverofCyber–PhysicalComplex
SystemsofSystems 607
14 InfrastructurePreparednessforCommunitiesasComplexSystems
ofSystems 647
15 ModelingSafetyofTransportationComplexSystemsofSystems
viaFaultTrees 695
Appendix 739
AuthorIndex 773
SubjectIndex 779
vii
Foreword
Philosophical and Historical Perspectives on
Understanding Commonalities Characterizing
Complexity
Thegrowinginterestbythesystemsmodelingcommunityintheconceptandin
theliteratureoncomplexitydeservesafreshreflectiononitsessenceandonits
evolving definitions and characterizations. For systems modelers, the starting
point begins by focusing on what constitutes complexity and how to under-
stand, model, and manage it. The English language fails to provide a succinct
definitionofthetermcomplexityinoneshortorlongsentence.Thisisbecause
each of the two words – “modeling and managing” – used in the title of this
book has multiple connotations, interpretations, and associations of the term
complexitydependingontheindividualsusingthetermsandthespecificcon-
text inwhich they are used.
Wedefineandmodelcomplexityinthisbookviatheinterdependenciesand
interconnectedness (I-I) characterizing complex systems of systems (SoS)
(Complex SoS). We further model and quantify the I-I by building on the
shared/commonstatesandotheressentialentities(shareddecisions,resources,
functions, policies, decision makers, stakeholders, and organizational setups)
within and among the subsystems that, in their totality, constitute Complex
SoS.Indeed,theabove,alongwithhierarchicaldecompositionandhigher-level
coordination, encompass the essence of the modeling, theory, methodology,
andpracticeespousedinthisbook.Webuildonthefactthatalloutputsfrom
asystemarefunctionsofthestatesofthatsystemandthusalsoofthedecisions
andallotherinputstothesystem.Thisfactisofparticularsignificancetomod-
elingComplexSoS.Forexample,Chen(2012)offersthefollowingsuccinctdef-
initionofstatevariable:“Thestatex(t )ofasystemattimet istheinformation
o o
att thattogetherwiththeinputu(t),fort≥t ,determinesuniquelytheoutput
o o
y(t) forall t≥t .”
o
viii Foreword
Indeed,thestatesofasystemarecommonlyamultidimensionalvectorthat
characterizes the system as a whole and plays a major role in estimating its
future behavior for any given input. Thus, (i) the behavior of the states of the
system as a function of time enables modelers to determine, under certain
conditions,thesystem’sfuturebehaviorforanygiveninput,orinitiatingevent–
and (ii) the shared states and other essential entities within and among the
subsystems and systems constitute the essence of the multifarious attributes
of the I-I characterizing Complex SoS.
Thus, inmodeling Complex SoS, we exploit the I-I characterizing Complex
SoSthataremanifestedviasharedstatesandotheressentialentitiesinmultiple
ways. The following sample of modeling methodologies beyond Chapter 1
includes (i) decomposition and multilevel-hierarchical coordination
(Chapters 2 and 4) with a primer on modeling risk and uncertainty in Part II
of Chapter 2; (ii) hierarchical holographic modeling (HHM) (Chapter 3);
(iii) multiple conflicting, competing, and noncommensurate goals and objec-
tives and the associated tradeoffs (Chapter 5); (iv) hierarchical coordinated
BayesianmodelingofComplexSoS(Chapter6);(v)hierarchical-multiobjective
modelinganddecisionmakingofComplexSoS(Chapter7);(vi)modelingeco-
nomicinterdependenciesamongComplexSoS(Chapter8);(vii)guidingprin-
ciples for modeling and managing Complex SoS (Chapter 9); (viii) modeling
cyber–physicalComplexSoS–fourcasestudies(Chapter10);(ix)globalsupply
chainasComplexSoS(Chapter11);(x)understandingandmanagingtheorgan-
izationaldimensionofComplexSoS(Chapter12);(xi)softwareengineering–
thedriverofcyber–physicalComplexSoS(Chapter13);(xii)infrastructurepre-
paredness for communities as Complex SoS (Chapter 14); and (xiii) modeling
safety of highway Complex SoS via fault trees (Chapter 15).
Throughoutthisbook,weintroducethereader,viaexamplesandcasestudies,
todecomposition,hierarchicalmodeling,multileveldecisionmaking,andopti-
mizationandtomultiobjectivetradeoffanalyses.Decompositionisemployedto
decoupletheI-IcharacterizingComplexSoS.Wepostulatethatdecisionsmade
atthesubsystem’slowerlevelsofthehierarchycanserveasapretextthatthey
are “independent.” The discrepancies and conflicts, fundamental differences,
andtheassociatedtradeoffsareharmonizedatthehighestlevelsofthemodel’s
hierarchical decision-making process.
Startinginthe1960s,manyscholarsaimedatidentifyingthefundamentalcom-
monalitiesthatcharacterizemodelingandmanagingComplexSoS.Mostofthe
theory and methodology that were developed employed decomposition using
pseudo-variablesatthelowerlevelsofthehierarchicalmodelsandwereultimately
harmonizedatahigherlevelofthehierarchy.Overtheyears,wecontinuedto
studyandimproveourmodelingperspectivessupportedbynewtoolsandmeth-
odologiesthatledtoabetterunderstandingandmoreusefulmodelingoftheI-I
that constitute Complex SoS. In the past, modeling the I-I was directed at the
coupled decisions and decision makers that characterized Complex SoS. This
Foreword ix
wasmostlyachievedbythedeploymentofpseudo-variables,whichenabledthe
reliance on decomposition at lower levels of the hierarchy, and a higher-level
hierarchicalcoordinationoftightlyinterdependentandinterconnectedsystems
andsubsystems.
PreviousmethodsdevelopedformodelingComplexSoSwereaimedatadvan-
cingtheoryandmethodologyforuncouplingtheI-Ithatcharacterizethem.In
thisbook,wewillalsostudyandidentifyinterdependenciesandinterconnections
byseekingabettercomprehensionoftheiressenceandtheirdominantcontri-
butionstothecomplexityofSoS.WeaddressthischallengebyidentifyingtheI-I
ofComplexSoSmanifestedviasharedstatesandotheressentialentities.Wealso
embracethefactthatalloutputsfromasystemarefunctionsofthestatesofthat
systemandthelatterarefunctionsofalldecisionsandallinputstothesystem.
ThisnotionisalsoofparticularsignificanceandcentraltomodelingComplex
SoS.Forexample,todeterminethereliabilityandfunctionalityofacar,onemust
knowthestatesofthefuel,oil,tirepressure,andothermechanicalandelectrical
systems.Allsystemsarecharacterizedatanymomentbytheirrespectivestates
andtheconditionsthereof,andtheseconditionsaresubjecttocontinuousvar-
iationandfluctuation.Similarly,thestatesofhealthofahumanaremultifaceted,
includingbloodcompositionandpressure,amongmyriadothers,andtheI-Ithat
existamongthestatesofbiologicalsystems.
Thetimeframehasalwaysbeenrecognizedasamajordriverofwhatweterm
complexity.Thisisduetothefactthatallsystemscontinuetoevolve,emerge,
and thuschange, whilethe capability of ourmodelingtools tokeep pacewith
these changes continues to lag behind. Our inability to model the dynamic
changes that characterize Complex SoS remains an impediment that charac-
terizesandimpairsourmodelingandmanagingtheI-IcharacterizingComplex
SoS. We embrace the fact that complexities cannot, by their essence
and definition, be compounded, packaged, understood, or modeled via one
“straightjacket” modeling schema. Rather, we have to keep building on what
wehavelearnedfrompastcontributionsdevelopedbyotherscholars,research-
ers,andpractitioners,andaugmentthispastknowledgeintoourcurrentthink-
ing, thereby creating new and improved theories and methodologies.
Furthermore,seekingtodiscoverwhatmakestheI-IofComplexSoSsodifficult
tomodelwillultimatelyhelpusbettermanagethem.Thisisnotafatalisticview
ofmodelingcomplexity,ratherasoberunderstandingoftherealitycharacter-
izing Complex SoS.
Complexity, Interdependency, Interconnectedness,
and Reinvention of Fault Trees
Fordecadesengineersandscientistshaveexploredthemodelingpoweroffault
trees in their quest to study and discover connections between two or among
x Foreword
several systems that may lead to catastrophic failure of safety-critical systems.
The fundamental difference characterizing the previous use of fault trees
and our present reinvention stems from the basic characteristics of the two
approaches. In this book we investigate and identify the genesis of the I-I by
exploring the shared/common states and other essential entities within the
systemsandsubsystemsthatcompriseComplexSoS.Bydoingso,wealsodis-
cover and quantify the genesis of potential failure of the entire Complex
SoS, whether the interdependencies and interconnections are manifested by
connections in series and/or in parallel. In this book we also benefit from
decadesofexperiencethatengineersandscientistshavegainedfromtheintrin-
sicpoweroffaulttrees.Furthermore,tomodelandimproveourunderstanding
of the I-I that characterize Complex SoS, we have reinvented the use of
fault trees via an innovative interpretation of the contributions that they
offer systems modelers. We further exploit the I-I characterizing Complex
SoS by tracing (via fault trees) prospective and inevitable failures due to
theirinherentspecificconnectionsviasharedstatesand/orothersharedessen-
tial entities. This process enables us to determine early in the modeling
cycle “what not to do” during planning, design, and future decision making.
By investigating the essence of the I-I characterizing Complex SoS, we can
discover future failures that could be avoided. In the parlance of fault-tree
analysis, the shared states and other essential entities are translated into
systemsconnected inseriesorinparallel,ratherthanbeingseenascompletely
independent.
Thereexistsaninsightfulcorrelationandlessontobelearnedfromthespread
ofdiseaseinthehumanbodyduetotheI-Ithatareenabledbythecontinuous
flow of blood nourishing every cell (subsystem) of every organ (system) and
ultimately of the entire body as Complex SoS. Similarly, all cyber–physical
infrastructuresare,intheiressence,ComplexSoS,andtheirmodeling,under-
standing,andmanagementcanbecharacterizedbyusingtheirsharedstatesand
other essential entities (e.g. communication channels, decisions, decision
makers, resources, and organizational setups). Our ability to observe, study,
andlearnfromthebehavioroftheanimalkingdomasComplexSoSanddevelop
knowledgebasedonlessonslearnedhavebeencentraltotheinsightfromwhich
we benefit today.
Althoughtheaboveobservations,aswellasthetheoreticaldiscoveries,seem
obvioustousnow,theydoshedlighton,andprovideinsightfulunderstanding
of,thegenesisoftheI-Icharacterizingbothlivingentitiesandcyber–physical
ComplexSoS.Thisfindingconstitutesanotherbuildingblockintherepertoire
ofthetheory,methodologies,andtoolsthatenablemodelersofComplexSoSto
gaininvaluableinsightintodecipheringthegenesisoftheI-Ithatcharacterize
Complex SoS.
Consider the nearly two-decade-old perspectives on complexity offered by
scholars inthe 1999 Special Issue of the journal Science:
