Google Research

Resistance Distance and Control Performance for Google bittide Synchronization

(2021)

Abstract

We discuss control of bittide distributed systems. The bittide mechanism is designed to provide logical synchronization between machines on a network, by observing and controlling data transfer between systems at the physical layer of the network. In this paper we analyze the performance of approximate proportional-integral control of these systems. We develop a simple continuous-time model for the dynamics, and show that the resulting dynamics are stable for any positive choice of gains. We construct explicit formulae for the closed-loop performance of the system, measured using the L2 norm. We show that the performance is a product of two terms, one depending only on the resistance distances in the graph, and the other depending only on the controller gains.

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