On the concept of 'stability' in asynchronous, distributed, decision-making systems

This work investigates the fundamental property of stability in Asynchronous Distributed Decision-Making (ADDM) systems. ADDM systems are large, complex, real-world systems wherein the principal elements are the geographically-dispersed entities that communicate between themselves asynchronously through message passing and are permitted autonomy in local decision-making. Given their real-world use, ADDM systems are subject to unexpected changes in their operating conditions which necessitates a thorough understanding of their behavior under representative perturbations to their environments. This is referred to as stability in this paper. While a comprehensive study of all possible perturbations is too complex and time consuming, this paper focuses on a subset of perturbations, relative to each problem domain, that are important and are likely to occur with greater frequency.; Definition of Stability: A stable ADDM system is one that returns to a steady-state in finite time, following perturbation, provided that it begins in a steady-state.; For an ADDM system, equilibrium or steady-state is defined based on placing bounds on the measured error in the system. Where the final steady-state is equivalent to the initial one, we refer to the system as "strongly stable." If the final steady-state is potentially worse than the initial one, the system is deemed "marginally stable." The perturbations are classified as either changes in the input pattern or changes in one or more characteristics of the system such as hardware failures.; To facilitate the understanding of stability in representative, real-world systems, this paper presents in-depth stability analysis for two very different ADDM systems: a distributed railway network management system and a decentralized military command and control system, both proposed in the literature.; Our results of the stability analysis of both of these ADDM systems accurately highlights key stable and unstable conditions. For the former, it gives us a reassurance that the system will perform well under adverse conditions, and for the latter it identifies areas which must be given more consideration before constructing the real system. This illustrates that a thorough stability analysis is a necessary and critical step in the development of any ADDM system.