Measuring Adaptability and Reliability of Large Scale Systems

In this paper we propose a metric approach to the analysis and verification of large scale self-organising collective systems. Typically, these systems consist of a large number of agents that have to interact to coordinate their activities and, at the same time, have to adapt their behaviour to the dynamic surrounding environment. It is then natural to apply a probabilistic modelling to these systems and, thus, to use a metric for the comparison of their behaviours. In detail, we introduce the population metric, namely a pseudometric measuring the differences in the probabilistic evolution of two systems with respect to some given requirements. We also use this metric to express the properties of adaptability and reliability of a system, which allow us to identify potential critical issues with respect to perturbations in its initial conditions. Then we show how we can combine our metric with statistical inference techniques to obtain a mathematically tractable analysis of large scale systems. Finally, we exploit mean-field approximations to measure the adaptability and reliability of large scale systems.