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