The design of novel distributed protocols from differential equations

Abstract

This paper proposes a framework to translate certain subclasses of differential equation systems into practical protocols for distributed systems. The generated protocols are intended for large-scale distributed systems that contain several hundreds to thousands of processes. The synthesized protocols are state machines containing probabilistic transitions and actions, and they are proved to show equivalent stochastic behavior to the original equations. The protocols are probabilistically scalable and reliable, and have practical applications in large-scale distributed systems, e.g., peer to peer systems. In order to illustrate the usefulness of the framework, it is used to generate new solutions for the problems of (a) responsibility migration (giving rise to a novel model of dynamic replication), and (b) majority selection. We present mathematical analysis of these two protocols, and experimental results from our implementations. These two protocols are derived from natural analogies that are represented as differential equations-endemics and the LotkaVolterra model of competition, respectively. We believe the design framework could be effectively used in transforming, in a very systematic manner, well-known natural phenomena into protocols for distributed systems.

A Survey on Analog Models of Computation

“…A framework to translate certain subclasses of differential equations into protocols for distributed systems has been proposed [195]. This is illustrated on several examples either taken from distributed problematics (responsibility migration, majority selection) or from classical models of populations such as Lotka-Volterra model of competition.…”

Computing with Large Populations Using Interactions

“…A few papers addressed the asymptotic behavior of population protocols, when the population size grows to infinity. In [24], a framework for translating certain subclasses of differential equation systems into practical protocols for distributed systems, assuming a large population, is described. In [17], the authors study the dynamics and the stability of (probabilistic) population protocols via ordinary differential equations.…”