introduces additional measurement errors. The selection algorithm used
in NTP uses a variant of the Bellman-Ford distributed routing algorithm
[37] to compute the minimum-weight spanning trees rooted on the primary
servers. The distance metric used by the algorithm consists of the
(scaled) stratum plus the synchronization distance, which itself
consists of the dispersion plus one-half the absolute delay. Thus, the
synchronization path will always take the minimum number of servers to
the root, with ties resolved on the basis of maximum error.
As a result of this design, the subnet reconfigures automatically in a
hierarchical-master-slave configuration to produce the most accurate and
reliable time, even when one or more primary or secondary servers or the
network paths between them fail. This includes the case where all normal
primary servers (e.g., highly accurate WWVB radio clock operating at the
lowest synchronization distances) on a possibly partitioned subnet fail,
but one or more backup primary servers (e.g., less accurate WWV radio
clock operating at higher synchronization distances) continue operation.
However, should all primary servers throughout the subnet fail, the
remaining secondary servers will synchronize among themselves while
distances ratchet upwards to a preselected maximum <169>infinity<170>
due to the well-known properties of the Bellman-Ford algorithm. Upon
reaching the maximum on all paths, a server will drop off the subnet and
free-run using its last determined time and frequency. Since these
computations are expected to be very precise, especially in frequency,
even extended outage periods can result in timekeeping errors not
greater than a few milliseconds per day with appropriately stabilized
oscillators (see Section 5).
In the case of multiple primary servers, the spanning-tree computation
will usually select the server at minimum synchronization distance.
However, when these servers are at approximately the same distance, the
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