Timely Coordination in a Multi-Agent System

In a distributed algorithm, multiple processes, or agents, work toward a common goal. More often than not, the actions of some agents are dependent on the previous execution (if not also on the outcome) of the actions of other agents. The resulting interdependencies between the timings of the actions of the various agents give rise to the study of methods for timely coordination of these actions. In this work, we formulate and mathematically analyze a novel multi-agent coordination problem, which we call “Timely-Coordinated Response”, and in which the time difference between each pair of actions may be constrained by upper and/or lower bounds. This problem generalizes some classic coordination problems formulated and studied by Halpern and Moses, and some coordination problems recently formulated and studied by Ben-Zvi and Moses. We optimally solve (i.e. provide an optimal protocol for solving) the timelycoordinated response problem in two ways: one using a generalization of the fixedpoint approach of Halpern and Moses, and one using a generalization of the synchronous causality (“syncausality”) approach of Ben-Zvi and Moses. Furthermore, we constructively show the equivalence of the solutions yielded by both approaches, despite the vast conceptual differences between them. By combining both approaches, we derive strengthened versions of known results for some previouslydefined special cases of this problem. Our analysis is conducted under minimal assumptions: we work in a continuoustime model with possibly infinitely many agents. The general results we obtain for this model reduce to stronger results for discrete-time models with only finitely many agents. In order to distill the properties of such models that are significant to this reduction, we define several novel classes of naturally-occurring models, all generalizing discrete-time models with finitely many agents, which in a sense separate the different results. We investigate the timely-coordinated response problem in these models, and present both a more practical optimal solution for the problem, as well as a surprisingly simple condition for solvability thereof, for these models. To conclude this work, we show how our results for the timely-coordinated response problem generalize the results known for previously-studied special cases of this problem, and present some open questions and further research directions.