Foreword

Philosophical and Historical Perspectives on Understanding Commonalities Characterizing Complexity

The growing interest by the systems modeling community in the concept and in the literature on complexity deserves a fresh reflection on its essence and on its evolving definitions and characterizations. For systems modelers, the starting point begins by focusing on what constitutes complexity and how to understand, model, and manage it. The English language fails to provide a succinct definition of the term complexity in one short or long sentence. This is because each of the two words - "modeling and managing" - used in the title of this book has multiple connotations, interpretations, and associations of the term complexity depending on the individuals using the terms and the specific context in which they are used.

We define and model complexity in this book via the interdependencies and interconnectedness (I-I) characterizing complex systems of systems (SoS) (Complex SoS). We further model and quantify the I-I by building on the shared/common states and other essential entities (shared decisions, resources, functions, policies, decision makers, stakeholders, and organizational setups) within and among the subsystems that, in their totality, constitute Complex SoS. Indeed, the above, along with hierarchical decomposition and higher-level coordination, encompass the essence of the modeling, theory, methodology, and practice espoused in this book. We build on the fact that all outputs from a system are functions of the states of that system and thus also of the decisions and all other inputs to the system. This fact is of particular significance to modeling Complex SoS. For example, Chen (2012) offers the following succinct definition of state variable: "The state x(to) of a system at time to is the information at to that together with the input u(t), for t = to, determines uniquely the output y(t) for all t = to."

Indeed, the states of a system are commonly a multidimensional vector that 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, the system's future behavior for any given input, or initiating event - 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, in modeling Complex SoS, we exploit the I-I characterizing Complex SoS that are manifested via shared states and other essential entities in multiple 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 objectives and the associated tradeoffs (Chapter 5); (iv) hierarchical coordinated Bayesian modeling of Complex SoS (Chapter 6); (v) hierarchical-multiobjective modeling and decision making of Complex SoS (Chapter 7); (vi) modeling economic interdependencies among Complex SoS (Chapter 8); (vii) guiding principles for modeling and managing Complex SoS (Chapter 9); (viii) modeling cyber-physical Complex SoS - four case studies (Chapter 10); (ix) global supply chain as Complex SoS (Chapter 11); (x) understanding and managing the organizational dimension of Complex SoS (Chapter 12); (xi) software engineering - the driver of cyber-physical Complex SoS (Chapter 13); (xii) infrastructure preparedness for communities as Complex SoS (Chapter 14); and (xiii) modeling safety of highway Complex SoS via fault trees (Chapter 15).

Throughout this book, we introduce the reader, via examples and case studies, to decomposition, hierarchical modeling, multilevel decision making, and optimization and to multiobjective tradeoff analyses. Decomposition is employed to decouple the I-I characterizing Complex SoS. We postulate that decisions made at the subsystem's lower levels of the hierarchy can serve as a pretext that they are "independent." The discrepancies and conflicts, fundamental differences, and the associated tradeoffs are harmonized at the highest levels of the model's hierarchical decision-making process.

Starting in the 1960s, many scholars aimed at identifying the fundamental commonalities that characterize modeling and managing Complex SoS. Most of the theory and methodology that were developed employed decomposition using pseudo-variables at the lower levels of the hierarchical models and were ultimately harmonized at a higher level of the hierarchy. Over the years, we continued to study and improve our modeling perspectives supported by new tools and methodologies that led to a better understanding and more useful modeling of the I-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 was mostly achieved by the deployment of pseudo-variables, which enabled the reliance on decomposition at lower levels of the hierarchy, and a higher-level hierarchical coordination of tightly interdependent and interconnected systems and subsystems.

Previous methods developed for modeling Complex SoS were aimed at advancing theory and methodology for uncoupling the I-I that characterize them. In this book, we will also study and identify interdependencies and interconnections by seeking a better comprehension of their essence and their dominant contributions to the complexity of SoS. We address this challenge by identifying the I-I of Complex SoS manifested via shared states and other essential entities. We also embrace the fact that all outputs from a system are functions of the states of that system and the latter are functions of all decisions and all inputs to the system. This notion is also of particular significance and central to modeling Complex SoS. For example, to determine the reliability and functionality of a car, one must know the states of the fuel, oil, tire pressure, and other mechanical and electrical systems. All systems are characterized at any moment by their respective states and the conditions thereof, and these conditions are subject to continuous variation and fluctuation. Similarly, the states of health of a human are multifaceted, including blood composition and pressure, among myriad others, and the I-I that exist among the states of biological systems.

The time frame has always been recognized as a major driver of what we term complexity. This is due to the fact that all systems continue to evolve, emerge, and thus change, while the capability of our modeling tools to keep pace with these changes continues to lag behind. Our inability to model the dynamic changes that characterize Complex SoS remains an impediment that characterizes and impairs our modeling and managing the I-I characterizing Complex 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 we have learned from past contributions developed by other scholars, researchers, and practitioners, and augment this past knowledge into our current thinking, thereby creating new and improved theories and methodologies. Furthermore, seeking to discover what makes the I-I of Complex SoS so difficult to model will ultimately help us better manage them. This is not a fatalistic view of modeling complexity, rather a sober understanding of the reality characterizing Complex SoS.

Complexity, Interdependency, Interconnectedness, and Reinvention of Fault Trees

For decades engineers and scientists have explored the modeling power of fault trees in their quest to study and discover connections between two or among 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 systems and subsystems that comprise Complex SoS. By doing so, we also discover 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 decades of experience that engineers and scientists have gained from the intrinsic power of fault trees. Furthermore, to model and improve our understanding 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 their inherent specific connections via shared states and/or other shared essential entities. This...