Using Equation-Free Macroscopic Analysis for Studying Self-Organising Emergent Solutions

When engineering distributed software systems based on self-organizing emergent solutions, assessing and understanding the relation between the microscopic dynamics and the resulting macroscopic behavior is a fundamental issue. In our research, we investigate a systematic approach for understanding the link between microscopic and macroscopic behavior, based on a numerical analysis technique called equation-free macroscopic analysis. Instead of deriving a (simplified) macroscopic model, equation-free methods only assume that such a model exists, and mimic a macroscopic simulation using only appropriately initialized simulations with the complete system.There are two crucial issues in this technique. The first issue is defining a complete set of macroscopic variables that would uniquely characterize the self-organizing emergent behavior in the solution. The second issue is the definition of a suitable initialization operator, that can create a good initial condition for the complete system, given only the values of the macroscopic variables. In this paper, we propose a bottom-up approach for the selection of macroscopic variables and the related initialization operator. We show how the equation-free approach can guide simulations to systematically increase understanding of the studied system. To illustrate the approach, we use a data clustering system inspired by termite nest building algorithms.