pkt.org <- peer.org pkt.org <- 0 pkt.org <- sys.clock
pkt.rec <- peer.rec pkt.rec <- 0 pkt.rec <- sys.clock
pkt.xmt <- sys.clock pkt.xmt <- sys.clock pkt.xmt <- sys.clock
Note that the order of copying should be designed so that the time to
perform the copy operations themselves does not degrade the
measurement accuracy, which implies that the sys.clock values should
be copied last. The reason for the choice of zeros to fill the
pkt.org and pkt.rec packet variables in the symmetric unreachable
case is to avoid the use of old data after a possibly extensive
period of unreachability. The reason for the choice of sys.clock to
fill these variables in the client case is that, if for some reason
the NTP message is returned by the recipient unaltered, as when
testing with an Internet-echo server, this convention still allows at
least the roundtrip time to be accurately determined without special
handling.
3.4.2. Receive Procedure
The receive procedure is executed upon arrival of an NTP message. If
the version number of the message (pkt.version) does not match the
current version number (NTP.VERSION), the message is discarded;
however, exceptions may be advised on a case-by-case basis at times
when the version number is changed.
If the clock of the sender is unsynchronized (pkt.leap = 11), or the
receiver is in server mode or the receiver is in symmetric mode and
the stratum of the sender is greater than the stratum of the receiver
(pkt.stratum > sys.stratum), the message is simply returned to the
sender along with the timestamps. In this case the addresses and
ports are interchanged in the IP and UDP headers:
pkt.srcadr <-> pkt.dstadr pkt.srcport <-> pkt.dstport
The following packet variables are updated from the system variables:
pkt.leap <- sys.leap pkt.distance <- sys.distance
pkt.version <- NTP.VERSION pkt.drift <- sys.drift
pkt.stratum <- sys.stratum pkt.refid <- sys.refid
pkt.precision <- sys.precision pkt.reftime <- sys.reftime
Note that the pkt.poll packet variable is unchanged. The timestamps
are updated in the order shown:
pkt.org <- pkt.xmt
pkt.rec <- sys.clock
pkt.xmt <- sys.clock
Finally, the message is forwarded to the sender and the server
receive procedure terminated at this point.
If the above is not the case, the source and destination Internet
addresses and ports in the IP and UDP headers are matched to the
correct peer. If there is a match, processing continues at the next
step below. If there is no match and symmetric mode is not indicated
(either pkt.srcport or pkt.dstport not equal to NTP.PORT), the
message must be a reply to a previously sent message from a client
which is no longer in operation. In this case the message is dropped
and the receive procedure terminated at this point.
If there is no match and symmetric mode is indicated, (both
pkt.srcport and pkt.dstport equal to NTP.PORT), an implementation-
specific instantiation procedure is called to create and initialize a
new set of peer variables and start the peer timer. The following
peer variables are set from the IP and UDP headers:
peer.srcadr <- pkt.srcadr peer.srcport <- pkt.srcport
peer.dstadr <- pkt.dstadr peer.dstport <- pkt.dstport
The following peer variables are initialized:
peer.state <- symmetric (passive)
peer.timer <- 0 (enabled)
peer.hpoll <- NTP.MINPOLL
peer.disp <- NTP.MAXDISP
The remaining peer variables are undefined and set to zero.
Assuming that instantiation is complete and that match occurs, the
least significant bit of the reachability register (peer.reach) is
set, indicating the peer is now reachable. The following peer
variables are copied (rescaled as necessary) from the NTP packet
variables and system variables:
peer.leap <- pkt.leap peer.distance <- pkt.distance
peer.stratum <- pkt.stratum peer.drift <- pkt.drift
peer.ppoll <- pkt.poll peer.refid <- pkt.refid
peer.precision <- pkt.precision peer.reftime <- pkt.reftime
peer.org <- pkt.xmt peer.rec <- sys.clock
peer.threshold <- max( min( peer.ppoll, peer.hpoll,
NTP.MAXPOLL), NTP.MINPOLL)
If either or both the pkt.org or pkt.rec packet variables are zero,
the sender did not have reliable values for them, so the receive
procedure is terminated at this point. If both of these variables
are nonzero, the roundtrip delay and clock offset relative to the
peer are calculated as follows. Number the times of sending and
receiving NTP messages as shown in Figure 3.1 and let i be an even
integer. Then t(i-3), t(i-2) and t(i-1) and t(i) are the contents of
the pkt.org, pkt.rec, pkt.xmt and peer.rec variables respectively.
| |
t(1) |------------------->| t(2)
| |
t(4) |<-------------------| t(3)
| |
t(5) |------------------->| t(6)
| |
t(8) |<-------------------| t(7)
| |
...
Figure 3.1. Calculating Delay and Offset
The roundtrip delay d and clock offset c of the receiving peer
relative to the sending peer is:
d = (t(i) - t(i-3)) - (t(i-1) - t(i-2))
c = [(t(i-2) - t(i-3)) + (t(i-1) - t(i))]/2 .
This method amounts to a continuously sampled, returnable-time
system, which is used in some digital telephone networks. Among the
advantages are that the order and timing of the messages is
unimportant and that reliable delivery is not required. Obviously,
the accuracies achievable depend upon the statistical properties of
the outbound and inbound net paths. Further analysis and
experimental results bearing on this issue can be found in
Appendix D.
The c and d values are then input to the clock filter algorithm to
produce the delay estimate (peer.delay) and offset estimate
(peer.offset) for the peer involved. If d becomes nonpositive due to
low delays, long polling intervals and high drift rates, it should be
considered invalid; however, even under these conditions it may
still be useful to update the local clock and reduce the drift rate
to the point that d becomes positive again. Specification of the
clock filter algorithm is not an integral part of the NTP
specification; however, one found to work well in the Internet
environment is described in Section 4.
When a primary clock is connected to the host, it is convenient to
incorporate its information into the data base as if the clock were
represented by an ordinary peer. The clocks are usually polled once
or twice a minute and the returned timecheck used to produce a new
update for the logical clock. The update procedure is then called
with the following assumed peer variables:
peer.offset <- timecheck - sys.clock
peer.delay <- as determined
peer.dispersion <- 0
peer.leap <- selected by operator, ordinarily 00
peer.stratum <- 0
peer.distance <- 0
peer.refid <- ASCII identifier
peer.reftime <- timecheck
In this case the peer.delay and peer.refid can be constants
reflecting the type and accuracy of the clock. By convention, the
value for peer.delay is ten times the expected mean error of the
clock, for instance, 10 milliseconds for a WWVB clock and 1000
milliseconds for a less accurate WWV clock, but with a floor of 100
milliseconds. Other peer variables such as the peer timer and
reachability register can be used to control the polling interval and
to confirm the clock is operating correctly. In this way the clock
filter and selection algorithms operate in the usual way and can be
used to mitigate the clock itself, should it appear to be operating
correctly, yet deliver bogus time.
3.4.3. Update Procedure
The update procedure is called when a new delay/offset estimate is
available. First, the clock selection algorithm determines the best
peer on the basis of estimated accuracy and reliability, which may
result in a new clock source (sys.peer). If sys.peer points to the
peer data structure with the just-updated estimates, the state
variables of that peer are used to update the system state variables
as follows:
sys.leap <- peer.leap
sys.stratum <- peer.stratum + 1
sys.distance <- peer.distance + peer.delay
sys.refid <- peer.srcadr
sys.reftime <- peer.rec
Finally, the logical clock procedure is called with peer.offset as
argument to update the logical clock (sys.clock) and recompute the
estimated drift rate (sys.drift). It may happen that the logical
clock may be reset, rather than slewed to its final value. In this
case the peer variables of all reachable peers are are updated as
follows:
peer.hpoll <- NTP.MINPOLL
peer.disp <- NTP.MAXDISP
peer.filter <- 0 (cleared)
peer.org <- 0
peer.rec <- 0
and the clock selection algorithm is called again, which results in a
null clock source (sys.peer = 0). A new selection will occur when
the filters fill up again and the dispersion settles down.
Specification of the clock selection algorithm and logical clock
procedure is not an integral part of the NTP specification. A clock
selection algorithm found to work well in the Internet environment is
described in Section 4, while a logical clock procedure is described
in Section 5. The clock selection algorithm described in Section 4
usually picks the server at the highest stratum and minimum delay
among all those available, unless that server appears to be a
falseticker. The result is that the algorithms all work to build a
minimum-weight spanning tree relative to the primary servers and thus
a hierarchical master-slave system similar to those used by some
digital telephone networks.
3.4.4. Initialization Procedures
Upon reboot the NTP host initializes all system variables as follows:
sys.clock <- best available estimate
sys.leap <- 11 (unsynchronized)
sys.stratum <- 0 (undefined)
sys.precision <- as required
sys.distance <- 0 (undefined)
sys.drift <- as determined
sys.refid <- 0 (undefined)
sys.reftime <- 0 (undefined)
The logical clock sys.clock is presumably undefined at reboot;
however, in some designs such as the Fuzzball an estimate is
available from the reboot environment. The sys.precision variable is
determined by the intrinsic architecture of the local hardware clock.
The sys.drift variable is determined as a side effect of subsequent
logical clock updates, from whatever source.
Next, an implementation-specific instantiation procedure is called
repeatedly to establish the set of client peers or symmetric (active)
peers which will actively probe other servers during regular
operation. The mode and addresses of these peers is determined using
information read during the reboot procedure or as the result of
operator commands.
4. Filtering Algorithms
A very important factor affecting the accuracy and reliability of
time distribution is the complex of algorithms used to deglitch and
smooth the offset estimates and to cast out outlyers due to failure
of the primary reference sources or propagation media. The
algorithms suggested in this section were developed and refined over
several years of operation in the Internet under widely varying net
configurations and utilizations. While these algorithms are believed
the best available at the present time, they are not an integral part
of the NTP specification.
There are two algorithms described in the following, the clock filter
algorithm, which is used to select the best offset samples from a
given clock, and the clock selection algorithm, which is used to
select the best clock among a hierarchical set of clocks.
4.1. Clock Filter Algorithm
The clock filter algorithm is executed upon arrival of each NTP
message that results in new delay/offset sample pairs. New sample
pairs are shifted into the filter register (peer.filter) from the
left end, causing first zeros then old sample pairs to shift off the
right end. Then those sample pairs in peer.filter with nonzero delay
are inserted on a temporary list and sorted in order of increasing
delay. The delay estimate (peer.delay) and offset estimate
(peer.offset) are chosen as the delay/offset values corresponding to
the minimum-delay sample. In case of ties an arbitrary choice is
made.
The dispersion estimate (peer.dispersion) is then computed as the
weighted sum of the offsets in the list. Assume the list has
PEER.SHIFT entries, the first m of which contain valid samples in
order of increasing delay. If X(i) (0 =< i < PEER.SHIFT) is the
offset of the ith sample, then,
d(i) = |X(i) - X(0)| if i < m and |X(i) - X(0)| < 2^15
d(i) = 2^15 - 1 otherwise
peer.dispersion = Sum(d(i)*w^i) ,
(0 =< i < PEER.SHIFT)
where w < 1 is a weighting factor experimentally adjusted to match
typical offset distributions. The peer.dispersion variable is
intended for use as a quality indicator, with increasing values
associated with decreasing quality. The intent is that samples with
a peer.dispersion exceeding a configuration threshold will not be
used in subsequent processing. The prototype implementation uses a
weighting factor w = 0.5, also called PEER.FILTER, and a threshold
PEER.THRESHOLD of 500 ms, which insures that all stages of
peer.filter are filled and contain offsets within a few seconds of
each other.
4.2. Clock Selection Algorithm
The clock selection algorithm uses the values of peer.delay,
peer.offset and peer.dispersion calculated by the clock filter
algorithm and is called when these values change or when the
reachability status changes. It constructs a list of candidate
estimates according to a set of criteria designed to maximize
accuracy and reliability, then sorts the list in order of estimated
precision. Finally, it repeatedly casts out outlyers on the basis of
dispersion until only a single candidate is left.
The selection process operates on each peer in turn and inspects the
various data captured from the last received NTP message header, as
well as the latest clock filter estimates. It selects only those
peers for which the following criteria are satisfied:
1. The peer must be reachable and operating in client or symmetric
modes.
2. The peer logical clock must be synchronized, as indicated by the
Leap Indicator bits being other than 11.
3. If the peer is operating at stratum two or greater, it must not
be synchronized to this host, which means its reference clock
identifier (peer.refid) must not match the Internet address of
this host. This is analogous to the split-horizon rule used in
some variants of the Bellman-Ford routing algorithm.
4. The sum of the peer synchronizing distance (peer.distance) plus
peer.delay must be less than 2^13 (8192) milliseconds. Also, the
peer stratum (peer.stratum) must be less than eight and
peer.dispersion must be less than a configured threshold
PEER.THRESHOLD (currently 500 ms). These range checks were
established through experience with the prototype implementation,
but may be changed in future.
For each peer which satisfies the above criteria, a sixteen-bit
keyword is constructed, with the low-order thirteen bits the sum of
peer.distance plus peer.delay and the high-order three bits the
peer.stratum reduced by one and truncated to three bits (thus mapping
zero to seven). The keyword together with a pointer to the peer data
structure are inserted according to increasing keyword values and
truncated at a maximum of eight entries. The resulting list
represents the order in which peers should be chosen according to the
estimated precision of measurement. If no keywords are found, the
clock source variable (sys.peer) is set to zero and the algorithm
terminates.
The final procedure is designed to detect falsetickers or other
conditions which might result in gross errors. Let m be the number
of samples remaining in the list. For each i (0 =< i < m) compute
the dispersion d(i) of the list relative to i:
d(i) = Sum(|X(j) - X(i)|*w^j) ,
(0 =< j < m)
where w < 1 is a weighting factor experimentally adjusted for the
desired characteristic (see below). Then cast out the entry with
maximum d(i) or, in case of ties, the maximum i, and repeat the
procedure. When only a single entry remains in the list, sys.peer is
set as its peer data structure pointer and the peer.hpoll variable in
that structure is set to NTP.MINPOLL as required by the logical clock
mechanism described in Section 5.
This procedure is designed to favor those peers near the head of the
list, which are at the highest stratum and lowest delay and
presumably can provide the most precise time. With proper selection
of weighting factor w, also called PEER.SELECT, entries will be
trimmed from the tail of the list, unless a few outlyers disagree
significantly with respect to the remaining entries, in which case
the outlyers are discarded first.
In order to see how this procedure works to select outlyers, consider
the case of three entries and assume that one or more of the offsets
are clustered about zero and others are clustered about one. For w =
0.75 as used in the prototype implementations and multiplying by 16
for convenience, the first entry has weight w^0 = 16, the second w^1
= 12 and the third w^2 = 9. Table X shows for all combinations of
peer offsets the calculated dispersion about each of the three
entries, along with the results of the procedure.
Peer 0 1 2 Dispersion Cast Result
Weight 16 12 9 0 1 2 Out
------------------------------------------------------
0 0 0 0 0 0 2 0 0
0 0 1 9 9 28 2 0 0
0 1 0 12 25 12 1 0 0
0 1 1 21 16 16 0 1 1
1 0 0 21 16 16 0 0 0
1 0 1 12 25 12 1 1 1
1 1 0 9 9 28 2 1 1
1 1 1 0 0 0 2 1 1
Table 4.1. Outlyer Selection Procedure
In the four cases where peer 0 and peer 1 disagree, the outcome is
determined by peer 2. Similar outcomes occur in the case of four
peers. While these outcomes depend on judicious choice of w, the
behavior of the algorithm is substantially the same for values of w
between 0.5 and 1.0.
4.3. Variable-Rate Polling
As NTP service matures in the Internet, the resulting network traffic
can become burdensome, especially in the primary service net. In
this expectation, it is useful to explore variable-rate polling, in
which the intervals between NTP messages can be adjusted to fit
prevailing network conditions of delay dispersion and loss rate. The
prototype NTP implementation uses this technique to reduce the
network overheads to one-sixteenth the maximum rate, depending on
observed dispersion and loss.
The prototype implementation adjusts the polling interval peer.hpoll
in response to the reachability register (peer.reach) variable along
with the dispersion (peer.dispersion) variable. So long as the clock
source variable (sys.peer) does not point to the peer data structure,
peer.reach is nonzero (reachable) and peer.dispersion is less than
the PEER.THRESHOLD parameter, the value of peer.hpoll is increased by
one for each call on the update procedure, subject to a maximum of
NTP.MAXPOLL. Following the timeout procedure, if peer.reach
indicates messages have not been received for the preceding two
polling intervals (low-order two bits are zero), the value of
peer.hpoll is decreased by one, subject to a minimum of NTP.MINPOLL.
If peer.reach becomes zero (unreachable), the value of peer.hpoll is
set to NTP.MINPOLL.
The result of the above mechanism is that the polling intervals for
peers not selected for synchronization and in symmetric mode creep
upwards once the filter register (peer.filter) has filled and the
peer.dispersion has settled down, but decrease again in case
peer.dispersion increases or the loss rate increases or the peer
becomes unreachable.
5. Logical Clocks
In order to implement a logical clock, the host must be equipped with
a hardware clock consisting of an oscillator and interface and
capable of the required precision and stability. The logical clock
is adjusted by means of periodic offset corrections computed by NTP
or some other time-synchronization protocol such as Hellospeak [15]
or the Unix 4.3bsd TSP [20]. Following is a description of the
Fuzzball logical clock, which includes provisions for precise time
and frequency adjustment and can maintain time to within a
millisecond and frequency to within a day per millisecond.
The logical clock is implemented using a 48-bit Clock Register, which
increments at 1000-Hz (at the decimal point), a 32-bit Clock-Adjust
Register, which is used to slew the Clock Register in response to
offset corrections, and a Drift-Compensation Register, which is used
to trim the oscillator frequency. In some interface designs such as
the DEC KWV11, an additional hardware register, the Counter Register,
is used as an auxiliary counter. The configuration and decimal point
of these registers are shown in Figure 5.1.
Clock Register
0 16 32
+---------------+---------------+---------------+
| | | |
+---------------+---------------+---------------+
A
decimal point
Clock-Adjust Register
0 16
+---------------+---------------+
| | |
+---------------+---------------+
A
decimal point
Drift-Compensation Register
0 16
+---------------+
| |
+---------------+
A
decimal point
Counter Register
0 16
+---------------+
| |
+---------------+
A
decimal point
Figure 5.1. Clock Registers
The Clock Register, Clock-Adjust Register and Drift-Compensation
Register are implemented in memory. In typical clock interface
designs such as the DEC KWV11, the Counter Register is implemented as
a buffered counter driven by a crystal oscillator. A counter
overflow is signalled by an interrupt, which results in an increment
of the Clock Register at bit 15 and the propagation of carries as
required. The time of day is determined by reading the Counter
Register, which does not disturb the counting process, and adding its
value to that of the Clock Register with decimal points aligned.
In other interface designs such as the LSI-11 event-line mechanism,
each tick of the clock is signalled by an interrupt at intervals of
16-2/3 or 20 ms, depending on interface and mains frequency. When
this occurs the appropriate increment in milliseconds, expressed to
32 bits in precision, is added to the Clock Register with decimal
points aligned.
5.1. Uniform Phase Adjustments
Left uncorrected, the logical clock runs at the rate of its intrinsic
oscillator. A correction is introduced as a signed 32-bit integer in
milliseconds, which is added to the Drift-Compensation Register and
also replaces bits 0-15 of the Clock-Adjust Register, with bits 16-31
set to zero. At adjustment intervals of CLOCK.ADJ a correction
consisting of two components is computed. The first (phase)
component consists of the Clock-Adjust Register shifted right
CLOCK.PHASE bits, which is then subtracted from the Clock-Adjust
Register. The second (frequency) component consists of the Drift-
Compensation Register shifted right CLOCK.FREQ bits. The sum of the
phase and frequency components is the correction, which is then added
to the Clock Register. Operation continues in this way until a new
correction is introduced.
Care is required in the implementation to insure monotonicity of the
Clock Register and to preserve the highest precision while minimizing
the propagation of roundoff errors. This can be done by buffering
the corrections and adding them to the increment at the time the
Clock Register is next updated. Monotonicity is insured with the
parameters shown in Table 5.1, as long as the increment is at least 2
ms. This table shows the above parameters and others discussed below
for both a crystal-stabilized oscillator and a mains-frequency
oscillator.
Parameter Name Crystal Mains
-------------------------------------------------------------------
Update Interval CLOCK.ADJ 4 sec 1 sec
Phase Shift CLOCK.PHASE -8 -9
Frequency Shift CLOCK.FREQ -16 -16
Maximum Aperture CLOCK.MAX +-128 ms +-256 ms
Shift Register Size PEER.SHIFT 8 4
Host Poll Interval peer.hpoll NTP.MINPOLL NTP.MINPOLL
(64 sec) (64 sec)
Table 5.1. Clock Parameters
The above design constitutes a second-order phase-lock loop which
adjusts the logical clock phase and frequency to compensate for the
intrinsic oscillator jitter, wander and drift. Simulation of a loop
with parameters chosen from Table 5.1 for a crystal-stabilized
oscillator and the clock filter described in Section 4 results in the
following transient response: For a phase correction of 100 ms the
loop reaches zero error in 34 minutes, overshoots 7 ms in 76 minutes
and settles to less than 1 ms in about four hours. The maximum
frequency error is about 6 ppm at 40 minutes and returns to less than
1 ppm in about eight hours. For a frequency correction of 10 ppm the
loop settles to within 1 ppm in about nine hours and to within 0.1
ppm in about a day. These characteristics are appropriate for
typical computing equipment using board-mounted crystals without oven
temperature control.
In those cases where mains-frequency oscillators must be used, the
loop parameters must be adapted for the relatively high jitter and
wander characteristics of the national power grid, in which diurnal
peak-to-peak phase excursions can exceed four seconds. Simulation of
a loop with parameters chosen from Table 5.1 for a mains-frequency
oscillator and the clock filter described in Section 4 results in a
transient response similar to the crystal-stabilized case, but with
time constants only one-fourth those in that case. When presented
with actual phase-offset data for typical Summer days when the jitter
and wander are the largest, the loop errors are in the order of a few
tens of milliseconds, but not greater than 150 ms.
The above simulations assume the clock filter algorithm operates to
select the oldest sample in the shift register at each step; that
is, the filter operates as a delay line with delay equal to the
polling interval times the number of stages. This is a worst-case
scenario, since the larger the overall delay the harder it is to
maintain low loop errors together with good transient response. The
parameters in Table 5.1 were experimentally determined with this
scenario and the constraint that the polling interval could not be
reduced below 64 seconds. With these parameters it is not possible
to increase the polling interval above 64 seconds without significant
increase in loop error or degradation of transient response. Thus,
when a clock is selected according to the algorithms of Section 4,
the polling interval peer.hpoll is always set at NTP.MINPOLL.
5.2. Nonuniform Phase Adjustments
When the magnitude of a correction exceeds a maximum aperture
CLOCK.MAX, the possibility exists that the clock is so far out of
synchronization with the reference source that the best action is an
immediate and wholesale replacement of Clock Register contents,
rather than a graduated slewing as described above. In practice the
necessity to do this is rare and occurs when the local host or
reference source is rebooted, for example. This is fortunate, since
step changes in the clock can result in the clock apparently running
backward, as well as incorrect delay and offset measurements of the
synchronization mechanism itself.
Considerable experience with the Internet environment suggests the
values of CLOCK.MAX tabulated in Table 5.1 as appropriate. In
practice, these values are exceeded with a single time-server source
only under conditions of the most extreme congestion or when multiple
failures of nodes or links have occured. The most common case when
the maximum is exceeded is when the time-server source is changed and
the time indicated by the new and old sources exceeds the maximum due
to systematic errors in the primary reference source or large
differences in the synchronizing path delays.
5.3. Maintaining Date and Time
Conversion from NTP format to the common date and time formats used
by application programs is simplified if the internal local-clock
format uses separate date and time registers. The time register is
designed to roll over at 24 hours, give or take a leap second as
determined by the Leap Indicator bits, with its overflows
(underflows) incrementing (decrementing) the date register. The date
and time registers then indicate the number of days and seconds since
some previous reference time, but uncorrected for leap seconds.
On the day prior to the insertion of a leap second the Leap Indicator
bits are set at the primary servers, presumably by manual means.
Subsequently, these bits show up at the local host and are passed to
the logical clock procedure. This causes the modulus of the time
register, which is the length of the current day, to be increased or
decreased by one second as appropriate. On the day following
insertion the bits are turned off at the primary servers. While it
is possible to turn the bits off automatically, the procedure
suggested here insures that all clocks have rolled over and will not
be reset incorrectly to the previous day as the result of possible
corrections near the instant of rollover.
5.4. Estimating Errors
After an NTP message is received and until the next one is received,
the accuracy of the local clock can be expected to degrade somewhat.
The magnitude of this degradation depends on the error at the last
update time together with the drift of the local oscillator with
respect to time. It is possible to estimate both the error and drift
rate from data collected during regular operation. These data can be
used to determine the rate at which NTP neighbors should exchange NTP
messages and thus control net overheads.
NTP messages include the local-clock precision of the sender, as well
as the reference time, estimated drift and a quantity called the
synchronizing distance. The precision of the local clock, together
with its peer clocks, establishes the short-term jitter
characteristics of the offset estimates. The reference time and
estimated drift of the sender provide an error estimate at the time
the latest update was received. The synchronizing distance provides
an estimate of error relative to the primary reference source and is
used by the filtering algorithms to improve the quality and
reliability of the offset estimates.
Estimates of error and drift rate are not essential for the correct
functioning of the clock algorithms, but do improve the accuracy and
adjustment with respect to net overheads. The estimated error allows
the recipient to compute the rate at which independent samples are
required in order to maintain a specified estimated error. The
estimated drift rate allows the recipient to estimate the optimum
polling interval.
It is possible to compute the estimated drift rate of the local clock
to a high degree of precision by simply adding the n offsets received
during an interval T to an accumulator. If X1 and X2 are the values
of the accumulator at the beginning and end of T, then the estimated
drift rate r is:
X2 - X1 n
r = ------- --- .
n T
The intrinsic (uncorrected) drift rate of typical crystal oscillators
under room-temperature conditions is in the order of from a few parts
per million (ppm) to as much as 100 ppm, or up to a few seconds per
day. For most purposes the drift of a particular crystal oscillator
is constant to within perhaps one ppm. Assuming T can be estimated
to within 100 ms, for example, it would take about a day of
accumulation to estimate r to an uncertainty in the order of one ppm.
Some idea of the estimated error of the local clock can be derived
from the variance of the offsets about the mean per unit time. This
can be computed by adding the n offset squares received during T to
an accumulator. If Y1 and Y2 are the values of the accumulator at
the beginning and end of T, then the estimated error s is:
Y2 - Y1 (X2 - X1)^2 n
s = ( ------- - ----------- ) --- .
n n * n T
The quantities r and s have direct utility to the peer as noted
above. However, they also have indirect utility to the recipient of
an NTP message sent by that peer, since they can be used as weights
in such algorithms as described in [22], as well as to improve the
estimates during periods when offsets are not available. It is most
useful if the latest estimate of these quantities are available in
each NTP message sent; however, considerable latitude remains in the
details of computation and storage.
The above formulae for r and s imply equal weighting for offsets
received throughout the accumulation interval T. One way to do this
is using a software shift register implemented as a circular buffer.
A single pointer points to the active entry in the buffer and
advances around one entry as each new offset is stored. There are
two accumulators, one for the offset and the other for its squares.
When a new offset arrives, a quantity equal to the new offset minus
the old (active) entry is added to the first accumulator and the
square of this quantity is added to the second. Finally, the offset
is stored in the circular buffer.
The size of the circular buffer depends on the accumulation interval
T and the rate offsets are produced. In many reachability and
routing algorithms, such as GGP, EGP and local-net control
algorithms, peers exchange messages on the order of once or twice a
minute. If NTP peers exchanged messages at a rate of one per minute
and if T were one day, the circular buffer would have to be 1440
words long; however, a less costly design might aggregate the data
in something like half-hour segments, which would reduce the length
of the buffer to 48 words while not significantly affecting the
quality of the data.
6. References
1. Lamport, L., "Time, Clocks and the Ordering of Events in a
Distributed System", Communications of the ACM, Vol. 21, No. 7,
pgs. 558-565, July 1978.
2. "Time and Frequency Dissemination Services", NBS Special
Publication No. 432, US Department of Commerce, 1979.
3. Lindsay, W., and A. Kantak, "Network Synchronization of Random
Signals", IEEE Trans. Comm., COM-28, No. 8, pgs. 1260-1266,
August 1980.
4. Braun, W., "Short Term Frequency Effects in Networks of Coupled
Oscillators", IEEE Trans. Comm., COM-28, No. 8, pgs. 1269-1275,
August 1980.
5. Mitra, D., "Network Synchronization: Analysis of a Hybrid of
Master-Slave and Mutual Synchronization", IEEE Trans. Comm.
COM-28, No. 8, pgs. 1245-1259, August 1980.
6. Postel, J., "User Datagram Protocol", RFC-768, USC/Information
Sciences Institute, August 1980.
7. Mills, D., "Time Synchronization in DCNET Hosts", IEN-173, COMSAT
Laboratories, February 1981.
8. Mills, D., "DCNET Internet Clock Service", RFC-778, COMSAT
Laboratories, April 1981.
9. Su, Z., "A Specification of the Internet Protocol (IP) Timestamp
Option", RFC-781, SRI International, May 1981.
10. Defense Advanced Research Projects Agency, "Internet Protocol",
RFC-791, USC/Information Sciences Institute, September 1981.
11. Defense Advanced Research Projects Agency, "Internet Control
Message Protocol", RFC-792, USC/Information Sciences Institute,
September 1981.
12. Postel, J., "Daytime Protocol", RFC-867, USC/Information Sciences
Institute, May 1983.
13. Postel, J., "Time Protocol", RFC-868, USC/Information Sciences
Institute, May 1983.
14. Mills, D., "Internet Delay Experiments", RFC-889, M/A-COM
Linkabit, December 1983.
15. Mills, D., "DCN Local-Network Protocols", RFC-891, M/A-COM
Linkabit, December 1983.
16. Gusella, R., and S. Zatti, "TEMPO - A Network Time Controller for
a Distributed Berkeley UNIX System", IEEE Distributed Processing
Technical Committee Newsletter 6, No. SI-2, pgs. 7-15, June 1984.
Also in: Proc. Summer 1984 USENIX, Salt Lake City, June 1984.
17. Halpern, J., Simons, B., Strong, R., and D. Dolly, "Fault-
Tolerant Clock Synchronization", Proc. Third Annual ACM Symposium
on Principles of Distributed Computing, pgs. 89-102, August 1984.
18. Lundelius, J., and N. Lynch, "A New Fault-Tolerant Algorithm for
Clock Synchronization:, Proc. Third Annual ACM Symposium on
Principles of Distributed Computing, pgs. 75-88, August 1984.
19. Lamport, L., and P. Melliar-Smith "Synchronizing Clocks in the
Presence of Faults", JACM 32, No. 1, pgs. 52-78, January 1985.
20. Gusella, R., and S. Zatti, "The Berkeley UNIX 4.3BSD Time
Synchronization Protocol: Protocol Specification", Technical
Report UCB/CSD 85/250, University of California, Berkeley, June
1985.
21. Marzullo, K., and S. Owicki, "Maintaining the Time in a
Distributed System", ACM Operating Systems Review 19, No. 3, pgs.
44-54, July 1985.
22. Mills, D., "Algorithms for Synchronizing Network Clocks", RFC-
956, M/A-COM Linkabit, September 1985.
23. Mills, D., "Experiments in Network Clock Synchronization", RFC-
957, M/A-COM Linkabit, September 1985.
24. Mills, D., "Network Time Protocol (NTP)", RFC-958, M/A-COM
Linkabit, September 1985.
25. Gusella, R., and S. Zatti, "An Election Algorithm for a
Distributed Clock Synchronization Program", Technical Report
UCB/CSD 86/275, University of California, Berkeley, December
1985.
26. Sams, H., "Reference Data for Engineers: Radio, Electronics,
Computer and Communications (Seventh Edition)", Indianapolis,
1985.
27. Schneider, F., "A Paradigm for Reliable Clock Synchronization",
Technical Report TR 86-735, Cornell University, February 1986.
28. Tripathi, S., and S. Chang, "ETempo: A Clock Synchronization
Algorithm for Hierarchical LANs - Implementation and
Measurements", Systems Research Center Technical Report TR-86-48,
University of Maryland, 1986.
29. Bertsekas, D., and R. Gallager, "Data Networks", Prentice-Hall,
Englewood Cliffs, NJ, 1987.
30. Srikanth, T., and S. Toueg. "Optimal Clock Synchronization", JACM
34, No. 3, pgs. 626-645, July 1987.
31. Rickert, N., "Non Byzantine Clock Synchronization - A Programming
Experiment", ACM Operating Systems Review 22, No. 1, pgs. 73-78,
January 1988.
Appendix A. UDP Header Format
An NTP packet consists of the UDP header followed by the NTP data
portion. The format of the UDP header and the interpretation of its
fields are described in [6] and are not part of the NTP
specification. They are shown below for completeness.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Port | Destination Port |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Length | Checksum |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Source Port
UDP source port number. In the case of a client request this
field is assigned by the client host, while for a server reply
it is copied from the Destination Port field of the client
request. In the case of symmetric mode, both the Source Port
and Destination Port fields are assigned the NTP service-port
number 123.
Destination Port
UDP destination port number. In the case of a client request
this field is assigned the NTP service-port number 123, while
for a server reply it is copied from the Source Port field of
the client request. In the case of symmetric mode, both the
Source Port and Destination Port fields are assigned the NTP
service-port number 123.
Length
Length of the request or reply, including UDP header, in
octets
Checksum
Standard UDP checksum
Appendix B. NTP Data Format - Version 1
The format of the NTP data portion, which immediately follows the UDP
header, is shown below along with a description of its fields.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|LI | VN |0 0 0| Stratum | Poll | Precision |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Synchronizing Distance |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Estimated Drift Rate |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Reference Clock Identifier |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| Reference Timestamp (64 bits) |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| Originate Timestamp (64 bits) |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| Receive Timestamp (64 bits) |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| Transmit Timestamp (64 bits) |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Leap Indicator (LI)
Two-bit code warning of impending leap-second to be inserted
at the end of the last day of the current month. Bits are
coded as follows:
00 no warning
01 +1 second (following minute has 61 seconds)
10 -1 second (following minute has 59 seconds)
11 alarm condition (clock not synchronized)
Version Number (VN)
Three-bit code indicating the version number, currently one
(1).
Reserved
Three-bit field consisting of all zeros and reserved for
future use.
Stratum
Integer identifying stratum level of local clock. Values are
defined as follows:
0 unspecified
1 primary reference (e.g., radio clock)
2...n secondary reference (via NTP)
Poll
Signed integer indicating the maximum interval between
successive messages, in seconds to the nearest power of two.
Precision
Signed integer indicating the precision of the local clock, in
seconds to the nearest power of two.
Synchronizing Distance
Fixed-point number indicating the estimated roundtrip delay to
the primary synchronizing source, in seconds with fraction
point between bits 15 and 16.
Estimated Drift Rate
Fixed-point number indicating the estimated drift rate of the
local clock, in dimensionless units with fraction point to the
left of the most significant bit.
Reference Clock Identifier
Code identifying the particular reference clock. In the case
of type 0 (unspecified) or type 1 (primary reference), this is
a left-justified, zero-filled ASCII string, for example:
Type Code Meaning
---------------------------------------------------
0 DCN Determined by DCN routing algorithm
1 WWVB WWVB radio clock (60 kHz)
1 GOES GOES satellite clock (468 MHz)
1 WWV WWV radio clock (5/10/15 MHz)
(and others as necessary)
In the case of type 2 and greater (secondary reference), this
is the 32-bit Internet address of the reference host.
Reference Timestamp
Local time at which the local clock was last set or corrected.
Originate Timestamp
Local time at which the request departed the client host for
the service host.
Receive Timestamp
Local time at which the request arrived at the service host.
Transmit Timestamp
Local time at which the reply departed the service host for
the client host.
Appendix C. Timeteller Experiments
In order to update data collected in June 1985 and reported in RFC-
957, a glorious three-day experiment was carried out in January 1988
with all the hosts and gateways listed in the NIC data base. Four
packets were sent at five-second intervals to each host and gateway
using UDP/NTP, UDP/TIME and ICMP/TIMESTAMP protocols and the clock
offsets (in milliseconds) for each protocol averaged with respect to
local time, which is synchronized via NTP to a radio-clock host.
While the ICMP/TIMESTAMP protocol has much finer granularity
(milliseconds) than UDP/TIME (seconds), it has no provisions for the
date, so is not suitable as a time-synchronization protocol;
however, it was included in the experiments both as a sanity check
and in order to assess the precision of measurement.
In the latest survey of 5498 hosts and 224 gateways, 46 responded to
UDP/NTP requests, 1158 to UDP/TIME and 1963 to ICMP/TIMESTAMP. By
contrast, in the 1985 survey of 1775 hosts and 110 gateways, 163
responded to UDP/TIME requests and 504 to ICMP/TIMESTAMP. At that
time there were no UDP/NTP implementations. There are many more
hosts and gateways listed in the rapidly growing domain-name system,
but not listed in the NIC data base, and therefore not surveyed. The
results of the survey are given in Table C.1, which shows for each of
the three protocols the error X for which the distribution function
P[x =< X] has the value shown.
P[x=<X] UDP/NTP UDP/TIME ICMP/TIMESTAMP
------------------------------------------------------
.1 11 4632 5698
.2 37 18238 27965
.3 66 38842 68596
.4 177 68213 127367
.5 364 126232 201908
.6 567 195950 285092
.7 3466 267119 525509
.8 20149 422129 2.91426E+06
.9 434634 807135 5.02336E+07
1 1.17971E+09 1.59524E+09 2.11591E+09
Table C.1. Distribution Functions
It can be seen that ten percent of the UDP/NTP responses show errors
of 11 milliseconds or less and that ten percent of the UDP/TIME
responses show errors greater than 807135 milliseconds (about 13
minutes). Fifty percent of the UDP/NTP timetellers are within 364
milliseconds, while fifty percent of the UDP/TIME tellers are within
126232 milliseconds (just over two minutes). Surprisingly,
ICMP/TIMESTAMP responses show errors even larger than UDP/TIME.
However, the maximum error shown in all three protocols exceeded the
range that could be recorded, in this case about 12 days. Clearly,
there are good timetellers and bad.
Appendix D. Evaluation of Filtering Algorithms
A number of algorithms for deglitching and filtering time-offset data
were described in RFC-956. These fall in two classes: majority-
subset algorithms, which attempt to separate good subsets from bad by
comparing their means, and clustering algorithms, which attempt to
improve the estimate by repeatedly casting out outlyers. The former
class was suggested as a technique to select the best (i.e. the most
reliable) clocks from a population, while the latter class was
suggested as a technique to improve the offset estimate for a single
clock given a series of observations.
Following publication of RFC-956 and after further development and
experimentation using typical Internet paths, a better algorithm was
found for casting out outlyers from a continuous stream of offset
observations spaced at intervals in the order of minutes. The
algorithm is described as a variant of a median filter, in which a
window consisting of the last n sample offsets is continuously
updated and the median sample selected as the estimate. However, in
the modified algorithm the outlyer (sample furthest from the median)
is then discarded and the entire process repeated until only a single
sample offset is left, which is then selected as the estimate.
The modified algorithm was found to be more resistant to glitches and
to provide a more accurate estimate than the unmodified one. It has
been implemented in the NTP daemons developed for the Fuzzball and