Cooperative networked systems: Multiple graphs, coalitional games, new probabilistics models

The consideration of cooperative networked systems has raised fundamental new questions and challenges. We consider networked systems from various domains including control, communications, sensing, sociology, economics, and biology. We first describe a general model for modeling such systems that involve several interacting dynamic multigraphs. These multigraphs evolve in at least three planes. At the higher plane (layer) we have the network of cognitive agents, where decisions are made and executed. At the intermediate plane (layer) we have the information network, where data, models, observations and signaling are represented. At the lower plane (layer) we have the communication network that supports the information and agent networks. There are several ways to capture these ideas and principles, and the one presented here is one of the simpler possible representations. The lower layer is more connected to the physical layer, while the middle and higher layer is more logical. The networks involve have links and nodes that are annotated by weights that can be scalar, vector or even policies and rules. Furthermore, the networks are dynamic. The resulting dynamic models are very complex and require a combination of methods from analysis, algebra, logic and optimization. The simplest possible model involves two interacting multigraphs: (a) the collaboration multigraph, which describes the time varying relation of collaboration between the agents; and (b) the communication multigraph, which describes the time-varying communications that occur between the agents. We link these concepts to ideas from distributed computing, distributed programs, and distributed computer hardware. We also link this representation to the behavior and structure models used in modern model-based-systems engineering. We describe a novel path-oriented characterization of these activities in networked dynamic systems. Next, we introduce three fundamental problems and challenges emerging from this framework. The first addresses the joint analysis of the collaboration and communication multigraphs and their impact on the performance of the networked system. The second fundamental problem addresses the development of a taxonomy of collaboration and communication multigraphs, from the perspective of system performance. The third fundamental problem addresses the need for different probability models for such cooperative networked systems. We relate the new framework, emerging from the results of the first and second problems, and its basic constructs, to information and control patterns, generalized information theory and entropy, and to distributed computing with local states. This new framework indicates the need for a new kind of probability over dynamical logical structures that is reminiscent of the axiomatic framework of quantum physics.