On the Use of Sequences, Phase Changes, and HoneyBees For Designing Adaptive Distributed Systems

The invention of distributed protocols is an extremely challenging ac-tivity. Today however, few design paradigms are available for the cre-ative task of designing scalable and reliable protocols for the Grid, peer to peer systems, etc. This paper first presents adesign method-ology to translate sequence equations, that are extensions of the form xm+1 = f(xm, xm-_{1,..., xm-k), into distributed protocols that are provably equivalent, i. e., exhibit the same equilibrium points and trajectories. These novel sequence protocols are decentralized, sim-ple, scalable, and highly fault-tolerant. We then demonstrate how phase changes in sequence protocols can be used to detect certain global predicates in a decentralized manner. Two such new proto-cols called the Multiplicative protocol and the Logistic protocol are presented, rigorously analyzed, and experimentally studied. Fi-nally, we present HoneySort, a novel sequence protocol for adaptive Grid computing. HoneySort is derived from sequence equations rep-resenting coordination among honeybees in nature. Through rigorous analysis and experiments with a real deployment on a 30-node PC cluster, we show that HoneySort outperforms well-known distributed sorting algorithms such as Quicksort and Insertion sort. Keywords: Science of Protocol Design, Distributed Proto-cols, Sequence Protocols, Scalability, Reliability.}