Introduction

The omnipresence of networks in economic and social organization makes the very concept of networks a paradigm of the contemporary world. The needs for various services (transport, energy, consumption of manufactured goods, healthcare, information and communication, etc.) involve users in an interlinking of networks, which are themselves made up of so many interlinks of both tangible and intangible flows, within which the consumer-citizen is sometimes the recipient of goods and services from industries, and sometimes are themselves a component of the organization (social networks). In this work, the authors questioned the invariants which unify networks in their diversity, as well as the specificities which differentiate them. This book aims to produce, to a certain extent, a unifying vision of networks and the related analysis, modeling and optimization problems, by proposing a reading grid that distinguishes a generic level, where these systems find a common interpretation, and a specific level, where appropriate study methods are mobilized. The presentation of case studies, deliberately drawn from distant fields, aims to exemplify the rationale behind this book through concrete studies.

This book is written in three parts. Part 1, "Network Variety and Modeling", offers a comparative analysis of the networks that surround us, and presents the general modeling aspects that prevail in an engineering context. The reader will find in Chapter 1 a review of the diversity of networks through a functional approach, that is, by the services provided to the user, with the overarching aim of characterizing and classifying the networks available to us today. We then explore the engineering contexts that arise in connection with networks, as well as the performance issues that accompany them in terms of quality of service, productivity and even environmental impact. Modern engineering is based on models. Before analysis and optimization, the modeling of a system, here a network, uses standardized representation formalisms (IDEF, SADT, GRAI, state machines, Petri networks, queueing networks, UML, etc.), as shared by a smaller number of experts, de facto making each formalism a technical language that facilitates exchanges within a community of specialists. However, this modeling exercise is by no means an objective in itself, nor a method for solving problems, but instead is a simplified representation of a real system, before the engineering logic pertaining to it. In this regard, let us quote the definition given, in the IT field, by OMG (Object Management Group): "A model represents some concrete or abstract thing of interest, with a specific purpose in mind". Getting into the specifics, the emphasis of Chapter 2 is on the phenomena which govern the flows, whether material or not, that form within a network. We have focused the chapter on the case of discrete flows (of vehicles, material batches, computer data packets, etc.), the kinematics of which turn out to be considerably richer than that of continuous flows (fluid and energy distribution networks). In fact, the separable entities that constitute discrete flows can be the subject of individualized processing and routing within the network, in turn making modeling these flows more complex. We present the main phenomena (resource-flow synchronization, congestion) which determine the kinematics of discrete flows in a network, as well as the diffusion process, which applies more specifically to intangible discrete flows (information and communication networks, digital social networks). Unfortunately, a review of the main discrete flow modeling formalisms shows that none of these formalisms manages, on its own, to cover all of the modeling needs as they emerge from the above, which makes a heterogeneous and multi-scale modeling approach necessary. Chapter 2 presents the general aspects of discrete flow modeling in the most diverse networks. The technical level of this chapter is limited to a basic knowledge of graphs and Petri nets, DEVS, alongside a fundamental familiarity of statistics and probability.

On the basis of a model deemed as representative of the real phenomena implemented in a network, an analyst will have at their disposal state-of-the-art performance evaluation and enhancement methods. As with most scientific domains, we will proceed here with exact methods, heuristic or digital simulation techniques; or even a combination of these different approaches. These exact methods respond to a scientific ideal by pre-establishing a parametric solution, and are thus valid for a class of cases. On the one hand, the strengths of exact methods are multiple:

• - The speed of performance evaluation by the simple instantiation of parameter values for pre-established solutions.
• - The facilitation of reverse engineering logic that consists, for a given performance objective, of determining the values of the parameters that lead to the desired performance.
• - More broadly, by providing a deep understanding of the link between system configuration and resulting performance.

On the other hand, the weak point of exact methods and, to a lesser extent, of approximate (heuristic) methods of resolution, is the requisite that the case in question respect the hypotheses required by the theoretical pre-resolution of a general problem, in turn reserving this approach either for systems of low complexity, or else those belonging to strongly typical case classes. A contrario, complex networks require the use of a simulation technique, the advantages and limitations of which are opposite to those of exact methods. Indeed, the strong point of simulation is its applicability to the evaluation of any network, provided that it has previously modeled the main mechanisms of its operation. However, the weak point of simulation is the lack of an inverse model, which deprives the analyst of a deeper understanding of the connections between the network configuration and the resulting performance. Exploring this link requires empirical iterative simulation campaigns, which may encounter computational, time and cost constraints.

Part 2, "Network Analysis Methods and Applications", illustrates the alternative mentioned above. Chapter 3 brings together the main theoretical methods of evaluating, and even optimizing, the kinematics of discrete flows and the performances associated with them, within uncomplicated networks of a particular type. These are, on the one hand, networks with additive flows responding to Kirchhoff's current law, and, on the other hand, networks with synchronized flows, examples of which can be found in flow-shop organizations of manufacturing production. We will thus deal with a workshop sizing problem by expressing the production rate as a function of the operating times of the machines and the number of containers in circulation. A contrario, Chapter 4 presents the general simulation techniques that can be used for network analysis, as well as a specific application for an analysis of the propagation process in social network flows. The technical nature of Chapters 3 and 4 may require some external reading (see Table I.1).

Part 3, "Case Studies", illustrates, through examples from projects, the similarity and specificities of network engineering in various fields: Smart Grid, forestry logistics, information dissemination within a social network.

For each case, we will first present a project description sheet summarizing:

• - the function or nature of the service offered by the network;
• - the type of network: topological (the nodes represent fixed places) versus sociological (the nodes represent mobile individuals);
• - the mode of user inclusion: are they circulating entities, are they associated with network nodes, if so which ones (source nodes, intermediaries, terminals)?
• - whether or not the network infrastructure is dedicated;
• - the possible intermediation of operators;
• - the nature of the flows (physical versus intangible, continuous versus discrete) and the unit of flow;
• - the mode of transport ensuring the flows (ambient vs. routing);
• - the command mode (centralized, on-board, distributed);
• - the engineering context relating to the project presented (design, redesign, management) and the issue motivating the study (evaluation, optimization);
• - the analysis tools used (formal resolution, optimization, numerical simulation).

Table I.1 seeks to assist the reader in identifying key areas of knowledge ahead of reading certain chapters.

Table I.1. Required reading

Part 1

Part 2

Simulation Techniques

Applied to the Analysis of Sociological Networks

State machines

Agent...