chapter  14
22 Pages

Attractor Selection as Self-Adaptive Control Mechanism for Communication Networks

WithKENJI LEIBNITZ, MASAYUKI MURATA, TETSUYA YOMO

Contents 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 14.2 Noise and Fluctuations in Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 371

14.2.1 Dynamic Systems under the Influence of Noise. . . . . . . . . . . . . . . . 374 14.2.2 Relationship between Fluctuation and Its Response . . . . . . . . . . . 375

14.3 Mathematical Models of Attractor Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 14.3.1 Mutually Inhibitory Operon Regulatory Network . . . . . . . . . . . . . 376 14.3.2 Sigmoid Gene Activation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 14.3.3 Gaussian Mixture Attractor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

14.4 Application to Self-Adaptive Network Control . . . . . . . . . . . . . . . . . . . . . . . . . 382 14.4.1 Differences between Biological Networks and

Communication Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 14.4.1.1 Mapping of Growth Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 14.4.1.2 Fluctuations: Ambient or Controllable? . . . . . . . . . . . . . 383 14.4.1.3 Centralized vs. Distributed Control . . . . . . . . . . . . . . . . . 383

14.4.2 Applications to Self-Adaptive Network Control . . . . . . . . . . . . . . . 383 14.4.2.1 Self-Adaptive Overlay Path Selection. . . . . . . . . . . . . . . . 384 14.4.2.2 Next Hop Selection in Ad Hoc Network Routing . . . 386

14.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

In this chapter, we discuss a self-adaptive control mechanism inspired by cell biology and provide examples of its application to communication networks. The model originates from the dynamic behavior observed in the gene expression of operons in Escherichia coli cells as a reaction to the lack of nutrients in the cells’ environment and it is driven by system-inherent fluctuations. We will begin this chapter by describing the influence of noise in biological systems, then illustrate the background of the model and provide an overview of alternative mathematical formulations. Based on this dynamic model, we then show two case studies on how to apply attractor selection as a robust and self-adaptive control mechanism in information and communication networks.