A combinatorial model for self-organizing networks

In previous works we have proposed to use of self-organization based on emergent design as a model for the programming of very large aggregates of heterogeneous computing resources. In our approach, a large scale computation is divided into small independent units of computation, each provided with its own uniform, autonomous behavior; only local information is used by each unit of computation to take all the decisions needed to carry out the computation. One of the challenges of this novel approach is to provide some theoretical foundation that can assist in the rational design of new systems. In this paper is to demonstrate the use of combinatorial techniques for obtaining quantitative analytical models of the organization pattern emerging from a specific type of self-organizing computation. Specifically, in a previous experiment we have demonstrated a computation in which mobile agents organize themselves around an overlay tree that constantly restructures itself in response to changing node availability and performance levels. In this paper we derive an analytical expression describing how nodes distribute themselves over the tree based on their performance, in a simplified version of the above problem. This result represents an instance of a theoretical tool that can be used to predict global patterns emerging as a result of a self-organizing design, and to establish a direct connection between global features and local behavior parameters.