Analyzing Resilience Properties of Different Topologies of Collective Adaptive Systems

Modern software systems are often compositions of entities that increasingly use self-adaptive capabilities to improve their behavior to achieve systemic quality goals. Self adaptive managers for each component system attempt to provide locally optimal results, but if they cooperated and potentially coordinated their efforts it might be possible to obtain more globally optimal results. The emergent properties that result from such composition and cooperation of self-adaptive systems are not well understood, difficult to reason about, and present a key challenge in the evolution of modern software systems. For example, the effects of coordination patterns and protocols on emergent properties, such as the resiliency of the collectives, need to be understood when designing these systems. In this paper we propose that probabilistic model checking of stochastic multiplayer games (SMG) provides a promising approach to analyze, understand, and reason about emergent properties in collectives of adaptive systems (CAS). Probabilistic Model Checking of SMGs is a technique particularly suited to analyzing emergent properties in CAS since SMG models capture: (i) the uncertainty and variability intrinsic to a CAS and its execution environment in the form of probabilistic and nondeterministic choices, and (ii) the competitive/cooperative aspects of the interplay among the constituent systems of the CAS. Analysis of SMGs allows us to reason about things like the worst case scenarios, which constitutes a new contribution to understanding emergent properties in CAS. We investigate the use of SMGs to show how they can be useful in analyzing the impact of communication topology for collections of fully cooperative systems defending against an external attack.