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Resistance Distance and Control Performance for bittide Synchronization


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.