Network Synchronization: Analysis of a Hybrid of Master-Slave and Mutual Synchronization

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Abstract
The paper contains a proposal and an analysis of a hybrid method for synchronizing the clocks in a digital switching network to a more select group of "master clocks." The scheme is a hybrid of two well-known techniques, "mutual synchronization" and "masterslave," offering certain unique advantages. It allows different synchronizing disciplines for the masters (such as the toll switching machines) and the remaining subnetwork (composed, for example, of local switches). We begin by considering an idealized model containing only one master with constant clock frequency. The behavior of the controlled frequencies in the subnetwork is described by linear delay-differential equations with the delays determined by distances separating switches. We show that in all cases all clocks in the subnetwork approach in steady state the master clock frequency. Considerable emphasis is placed on the rate of synchronization, as determined by the principal root, the root with largest real part, of the characteristic function of the differential equations. The idealized model is extended in stages. First we consider the effects of many masters with constant but possibly nonidentical frequencies and show that the steady state frequencies in the subnetwork are narrowly bounded. Next, we allow clock drift and the master clocks to fluctuate about nominal centers with given tolerances. An expression for the residual steady-state departures from perfect synchronization shows the tradeoff between transient and stead-state behavior. Finally, two illustrative examples are numerically solved.

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