On the concept of “stability” in asynchronous distributed decision-making systems

Asynchronous distributed, decision-making (ADDM) systems constitute a special class of distributed problems and are characterized as large, complex, real-world systems wherein the principal elements are the geographically-dispersed entities that communicate among themselves, asynchronously, through message passing and are permitted autonomy in local decision-making. Such systems generally offer significant advantages over the traditional, centralized algorithms in the form of concurrency, scalability, high throughput, efficiency, low vulnerability to catastrophic failures, and robustness. A fundamental property of ADDM systems is stability that refers to their behavior under representative perturbations to their operating environments, given that such systems are intended to be real, complex, and to some extent, mission critical systems, and are subject to unexpected changes in their operating conditions. This paper introduces the concept of stability in ADDM systems and proposes, for the first time, an intuitive definition that reflects those used in Control Systems and Physics. A comprehensive stability analysis on an accurate simulation model will provide the necessary assurance, with a high level of confidence, that the system will perform adequately. An ADDM system is defined as a stable system if it returns to a steady-state in finite time, following perturbation, provided that it is initiated in a steady-state. Equilibrium or steady-state is defined through placing bounds on the measured error in the system. Where the final steady-state is equivalent to the initial one, the system is referred to as strongly stable. If the final steady-state is potentially worse then the initial one, the system is deemed marginally stable. When the system fails to return to steady-state following the perturbation, it is unstable. The perturbations are classified as either changes in the input pattern or changes in one or more environmental characteristics of the system such as hardware failures. To facilitate the understanding of stability in representative real-world systems, this paper reports the in-depth analysis of a basic manifestation of ADDM systems-a decentralized military command and control problem, MFAD. The entities in MFAD lack temporal external inputs and their interactions are subject to their initial conditions. Stability analysis of MFAD accurately highlights key stable and unstable conditions. Performance analysis reveals that MFAD is strongly stable to perturbations of short durations, it is inherently marginally stable, the sensor degradation bears a greater impact on sensor error than movement error, and the impact of communication failure is higher on movement error as opposed to sensor error