Username / Password : Request For Comments

RFC Number : 957

Title : Experiments in network clock synchronization.

Network Working Group D.L. Mills
Request for Comments: 957 M/A-COM Linkabit
September 1985

Experiments in Network Clock Synchronization

Status of this Memo

This RFC discusses some experiments in clock synchronization in the
ARPA-Internet community, and requests discussion and suggestions for
improvements. Distribution of this memo is unlimited.

Table of Contents

1. Introduction
2. Design of the Synchronization Algorithm
2.1. The Logical Clock
2.2. Linear Phase Adjustments
2.3. Nonlinear Phase Adjustments
3. Synchronizing Network Clocks
3.1. Reference Clocks and Reference Hosts
3.2. Distribution of Timing Information
4. Experimental Validation of the Design
4.1. Experiment Design
4.2. Experiment Execution
4.3. Discussion of Results
4.3.1. On Power-Grid Clocks
4.3.2. On Clocks Synchronized via Network Links
4.3.3. On the Accuracy of Radio Clocks The Spectracom 8170 WWVB Radio Clock The True Time 468-DC GOES Radio Clock The Heath GC-1000 WWV Radio Clock
4.3.4. On Handling Disruptions
4.4. Additional Experiments
5. Summary and Conclusions
6. References

List of Figures

Figure 1. Clock Registers
Figure 2. Network Configuration

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List of Tables

Table 1. Experiment Hosts
Table 2. Link Measurements
Table 3. First Derivative of Delay
Table 4. GOES Radio Clock Offsets
Table 5. WWV Radio Clock Offsets
Table 6. ISI-MCON-GW Clock Statistics
Table 7. LL-GW Clock Statistics
Table 8. LL-GW Clock Statistics

1. Introduction

One of the services frequently neglected in computer network design
is a high-quality, time-of-day clock capable of generating accurate
timestamps with small residual errors compared to intrinsic one-way
network delays. Such a service would be useful for tracing the
progress of complex transactions, synchronizing cached data bases,
monitoring network performance and isolating problems.

Several mechanisms have been specified in the Internet protocol suite
to record and transmit the time at which an event takes place,
including the ICMP Timestamp message [6], Time Protocol [7], Daytime
protocol [8] and IP Timestamp option [9]. A new Network Time
Protocol [12] has been proposed as well. Additional information on
network time synchronization can be found in the References at the
end of this document. Synchronization protocols are described in [3]
and [12] and synchronization algorithms in [2], [5], [10] and [11].
Experimental results on measured roundtrip delays in the Internet are
discussed in [4]. A comprehensive mathematical treatment of clock
synchronization can be found in [1].

Several mechanisms have been specified in the Internet protocol suite
to record and transmit the time at which an event takes place,
including the ICMP Timestamp message [6], Time protocol [7], Daytime
protocol [8] and IP Timestamp option [9]. Issues on time
synchronization are discussed in [4] and synchronization algorithms
in [2] and [5]. Experimental results on measured roundtrip delays in
the Internet are discussed in [2]. A comprehensive mathematical
treatment of the subject can be found in [1], while an interesting
discussion on mutual-synchonization techniques can be found in [10].

There are several ways accurate timestamps can be generated. One is
to provide at every service point an accurate, machine-readable clock
synchronized to a central reference, such as the National Bureau of
Standards (NBS). Such clocks are readily available in several models
ranging in accuracies of a few hundred milliseconds to less than a

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millisecond and are typically synchronized to special ground-based or
satellite-based radio broadcasts. While the expense of the clocks
themselves, currently in the range $300 to $3000, can often be
justified, all require carefully sited antennas well away from
computer-generated electromagnetic noise, as well as shielded
connections to the clocks. In addition, these clocks can require a
lengthy synchonization period upon power-up, so that a battery-backup
power supply is required for reliable service in the event of power

If the propagation delays in the network are stable or can be
predicted accurately, timestamps can be generated by a central
server, equipped with a clock such as described above, in response to
requests from remote service points. However, there are many
instances where the trans-network delay to obtain a timestamp would
be intolerable, such as when timestamping a message before
transmission. In addition, propagation delays are usually not
predictable with precisions in the order required, due to
probabilistic queuing and channel-contention delays.

In principle, a clock of sufficient accuracy can be provided at each
service point using a stable, crystal-controlled clock which is
corrected from time to time by messages from a central server.
Suitable inexpensive, crystal-controlled clock interfaces are
available for virtually any computer. The interesting problem
remaining is the design of the synchronization algorithm and protocol
used to transmit the corrections. In this document one such design
will be described and its performance assessed. This design has been
incorprated as an integral part of the network routing and control
protocols of the Distributed Computer Network (DCnet) architecture
[5], clones of which have been established at several sites in the US
and Europe. These protocols have been in use since 1979 and been
continuously tested and refined since then.

2. Design of the Synchronization Algorithm

The synchronization algorithm is distributed in nature, with protocol
peers maintained in every host on the network. Peers communicate
with each other on a pairwise basis using special control messages,
called Hello messages, exchanged periodically over the ordinary data
links between them. The Hello messages contain information necessary
for each host to calculate the delay and offset between the local
clock of the host and the clock of every other host on the network
and are also used to drive the routing algorithm.

The synchronization algorithm includes several features to improve
the accuracy and stability of the local clock in the case of host or

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link failures. In following sections the design of the algorithm is
summarized. Full design details are given in [5] along with a formal
description of the Hello protocol.

2.1. The Logical Clock

In the DCnet model each service point, or host, is equipped with a
hardware clock, usually in the form of an off-the-shelf interface.
Using this and software registers, a logical clock is constructed
including a 48-bit Clock Register, which increments at a 1000 Hz
rate, a 32-bit Clock-Adjust Register, which is used to slew the Clock
Register in response to raw corrections received over the net, and a
Counter Register, which is used in some interface designs as an
auxilliary counter. The configuration and decimal point of these
registers are shown in Figure 1.

Clock Register

0 16 32
| | | |
decimal point

Clock-Adjust Register

0 16
| | |
decimal point

Counter Register

0 16
| |
decimal point

Figure 1. Clock Registers

The Clock Register and Clock-Adjust Register are implemented in
memory. In typical clock interface designs such as the DEC KMV11-A

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the Counter Register is implemented in the interface 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 its counting process, and adding its value to that of the
Clock Register with decimal points aligned.

In other interface designs such as the simple LSI-11 event-line
mechanism, each tick of the clock is signalled by an interrupt at
intervals of 10, 16-2/3 or 20 ms, depending on interface and clock
source. When this occurs the appropriate number of milliseconds,
expressed to 32 bits in precision, is added to the Clock Register
with decimal points aligned.

It should be noted at this point that great care in operating system
design is necessary in order to preserve the full accuracy of
timestamps with respect to the application program, which must be
protected from pre-emption, excessive device latencies and so forth.
In addition, the execution times of all sequences operating with the
interrupt system disabled must be strictly limited. Since the PDP11
operating system most often used in the DCnet (the 'Fuzzball'
operating system) has been constructed with these considerations
foremost in mind, it has been especially useful for detailed network
performance testing and evaluation. Other systems, in particular the
various Unix systems, have not been found sufficiently accurate for
this purpose.

Left uncorrected, the host logical clock runs at the rate of its
intrinsic oscillator, whether derived from a crystal or the power
frequency. The correction mechanism uses the Clock-Adjust Register,
which is updated from time to time as raw corrections are received.
The corrections are computed using roundtrip delays and offsets
derived from the routing algorithm, described later in this document,
which are relatively noisy compared to the precision of the logical
clock. A carefully designed smoothing mechansim insures stability,
as well as isolation from large transients that occur due to link
retransmissions, host reboots and similar disruptions.

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2.2. Linear Phase Adjustments

The correction is introduced as a signed 32-bit integer in
milliseconds. If the magnitude of the correction is less than 128
ms, the low-order 16 bits replaces bits 0-15 in the Clock-Adjust
register. At suitable intervals, depending on the jitter of the
intrinsic oscillator, the value of this register is divided by a
fixed value, forming a quotient which is first added to the Clock
Register, then subtracted from the Clock-Adjust Register. This
technique has several advantages:

1. The clock never runs backwards; that is, successive
timestamps always increase monotonically.

2. In the event of loss of correction information, the clock
slews to the last correction received.

3. The rate of slew is proportional to the magnitude of the last
correction. This allows rapid settling in case of large
corrections, but provides high stability in case of small

4. The sequence of computations preserves the highest precision
and minimizes the propagation of round-off errors.

Experience has indicated the choice of 256 as appropriate for the
dividend above, which yields a maximum slew-rate magnitude less than
0.5 ms per adjustment interval and a granularity of about 2.0
microseconds, which is of the same order as the intrinsic tolerance
of the crystal oscillators used in typical clock interfaces. In the
case of crystal-derived clocks, an adjustment interval of four
seconds has worked well, which yields a maximum slew-rate magnitude
of 125 microseconds per second. In the case of power-frequency
clocks or especially noisy links, the greatly increased jitter
requires shorter adjustment intervals in the range of 0.5 second,
which yields a maximum slew-rate magnitude of 1.0 ms per second.

In most cases, independent corrections are generated over each link
at intervals of 30 seconds or less. Using the above choices a single
sample error of 128 ms causes an error at the next sample interval no
greater than about 7.5 ms with the longer adjustment interval and 30
ms with the shorter. The number of adjustment intervals to reduce
the residual error by half is about 177, or about 12 minutes with the
longer interval and about 1.5 minutes with the shorter. This
completely characterizes the linear dynamics of the mechanism.

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2.3. Nonlinear Phase Adjustments

When the magnitude of the correction exceeds 128 ms, the possiblity
exists that the clock is so far out of synchronization with the
reference host 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 host 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

However, it sometimes happens that, due to link retransmissions or
occasional host glitches, a single correction sample will be computed
with magnitude exceeding 128 ms. In practice this happens often
enough that a special procedure has been incorporated into the
design. If a sample exceeding the limit is received, its value is
saved temporarily and does not affect the Clock-Adjust Register. In
addition, a timer is initialized, if not already running, to count
down to zero in a specified time, currently 30 seconds.

If the timer is already running when a new correction sample with
magnitude exceeeding 128 ms arrives, its value and the saved sample
value are averaged with equal weights to form a new saved sample
value. If a new correction sample arrives with magnitude less than
128 ms, the timer is stopped and the saved sample value discarded.
If the timer counts down to zero, the saved sample value replaces the
contents of the Clock Register and the Clock-Adjust Register is set
to zero. This procedure has the effect that occasional spikes in
correction values are discarded, but legitimate step changes are
prefiltered and then used to reset the clock after no more than a
30-second delay.

3. Synchronizing Network Clocks

The algorithms described in the previous section are designed to
achieve a high degree of accuracy and stability of the logical clocks
in each participating host. In this section algorithms will be
described which synchronize these logical clocks to each other and to
standard time derived from NBS broadcasts. These algorithms are
designed to minimize the cumulative errors using linear synchronizing
techniques. See [10] for a discussion of algorithms using nonlinear

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3.1. Reference Clocks and Reference Hosts

The accuracy of the entire network of logical clocks depends on the
accuracy of the device used as the reference clock. In the DCnet
clones the reference clock takes the form of a precision crystal
oscillator which is synchronized via radio or satellite with the NBS
standard clocks in Boulder, CO. The date and time derived from the
oscillator can be sent continuously or read upon command via a serial
asynchronous line. Stand-alone units containing the oscillator,
synchronizing receiver and controlling microprocessor are available
from a number of manufacturers.

The device driver responsible for the reference clock uses its
serial-line protocol to derive both an 'on-time' timestamp relative
to the logical clock of the reference host and an absolute time
encoded in messages sent by the clock. About once every 30 seconds
the difference between these two quantities is calculated and used to
correct the logical clock according to the mechanisms described
previously. The corrected logical clock is then used to correct all
other logical clocks in the network. Note the different
nomenclature: The term 'reference clock' applies to the physical
clock itself, while the term 'reference host' applies to the logical
clock of the host to which it is connected. Each has an individual
address, delay and offset in synchronizing messages.

There are three different commercial units used as reference clocks
in DCnet clones. One of these uses the LF radio broadcasts on 60 KHz
from NBS radio WWVB, another the HF radio broadcasts on 5, 10 and 15
MHz from NBS radio WWV or WWVH and the third the UHF broadcasts from
a GOES satellite. The WWVB and GOES clocks claim accuracies in the
one-millisecond range. The WWV clock claims accuracies in the 100-ms
range, although actual accuracies have been measured somewhat better
than that.

All three clocks include some kind of quality indication in their
messages, although of widely varying detail. At present this
indication is used only to establish whether the clock is
synchronized to the NBS clocks and convey this information to the
network routing algorithm as described later. All clocks include
some provision to set the local-time offset and propagation delay,
although for DCnet use all clocks are set at zero offset relative to
Universal Time (UT). Due to various uncertaincies in propagation
delay, serial-line speed and interrupt latencies, the absolute
accuracy of timestamps derived from a reference host equipped with a
WWVB or GOES reference clock is probably no better than a couple of

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3.2. Distribution of Timing Information

The timekeeping accuracy at the various hosts in the network depends
critically on the precision whith which corrections can be
distributed throughout the network. In the DCnet design a
distributed routing algorithm is used to determine minimum-delay
routes between any two hosts in the net. The algorithms used, which
are described in detail in [5] and only in outline form here, provide
reachability and delay information, as well as clock offsets, between
neighboring hosts by means of periodic exchanges of routing packets
called Hello messages. This information is then incorporated into a
set of routing tables maintained by each host and spread throughout
the network by means of the Hello messages.

The detailed mechanisms to accomplish these functions have been
carefully designed to minimize timing uncertaincies. For instance,
all timestamping is done in the drivers themselves, which are given
the highest priority for resource access. The mechanism to measure
roundtrip delays on the individual links is insensitive to the delays
inherent in the processing of the Hello message itself, as well as
the intervals between transmissions. Finally, care is taken to
isolate and discard transient timing errors that occur when a host is
rebooted or a link is restarted.

The routing algorithm uses a table called the Host Table, which
contains for each host in the network the computed roundtrip delay
and clock offset, in milliseconds. In order to separately identify
each reference clock, if there is more than one in the network, a
separate entry is used for each clock, as well as each host. The
delay and offset fields of the host itself are set to zero, as is the
delay field of each attached reference clock. The offset field of
each attached reference clock is recomputed periodically as described

Hello messages containing a copy of the Host Table are sent
periodically to each neighbor host via the individual links
connecting them. In the case of broadcast networks the Hello message
is broadcast to all hosts sharing the same cable. The Hello message
also contains a timestamp inserted at the time of transmission, as
well as information used to accurately compute the roundtrip delay on
point-to-point links.

A host receiving a Hello message processes the message for each host
in turn, including those corresponding to the reference clocks. It
adds the delay field in the message to the previously determined
roundtrip link delay and compares this with the entry already in its
Host Table. If the sum is greater than the delay field in the Host

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Table, nothing further is done. If the sum is less, an update
procedure is executed. The update procedure, described in detail in
[5], causes the new delay to replace the old and the routing to be
amended accordingly.

The update procedure also causes a new correction sample to be
computed as the difference between the timestamp in the Hello message
and the local clock, which is used to correct the local clock as
described above. In addition, the sum of this correction sample plus
the offset field in the Hello message replaces the offset field in
the Hello Table. The effect of these procedures is that the local
clock is corrected relative to the neighbor clock only if the
neighbor is on the path of least delay relative to the selected
reference clock. If there is no route to the reference clock, as
determined by the routing algorithm, no corrections are computable
and the local clock free-runs relative to the last received

As the result of the operation of the routing algorithm, all local
clocks in the network will eventually stabilize at a constant offset
relative to the reference clock, depending upon the drift rates of
the individual oscillators. For most applications the offset is
small and can be neglected. For the most precise measurements the
computed offset in the Host Table entry associated with any host,
including the reference clock, can be used to adjust the apparent
time relative to the local clock of that host. However, since the
computed offsets are relatively noisy, it is necessary to smooth them
using some algorithm depending upon application. For this reason,
the computed offsets are provided separately from the local time.

4. Experimental Validation of the Design

The original DCnet was established as a 'port expander' net connected
to an ARPAnet IMP in 1978. It was and is intended as an experimental
testbed for the development of protocols and measurement of network
performance. Since then the DCnet network-layer protocols have
evolved to include multi-level routing, logical addressing,
multicasting and time synchronization. Several DCnet clones have
been established in the US and Europe and connected to the DARPA
Internet system. The experiments described below were performed
using the DCnet clone at Linkabit East, near Washington, DC, and
another at Ford Motor Division, near Detroit, MI. Other clones at
Ford Aerospace and the Universities of Maryland and Michigan were
used for calibration and test, while clones at various sites in
Norway and Germany were used for occasional tests. Additional

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ARPANET gateways of the WIDEBAND/EISN satellite system were also
included in the experiments in order to determine the feasability of
synchronizing clocks across the ARPANET.

There were four principal issues of interest in the experiments:

1. What are the factors affecting accuracy of a network of clocks
using the power grid as the basic timing source, together with
corrections broadcast from a central point?

2. What are the factors affecting accuracy of a network of clocks
synchronized via links used also to carry ordinary data.

3. How does the accuracy of the various radio clocks - WWVB, GOES
and WWV compare?

4. What is the best way to handle disruptions, such as a leap

These issues will be discussed in turn after presentation of the
experiment design and execution.

4.1. Experiment Design

Figure 2 shows the configuration used in a series of tests conducted
during late June and early July of 1985. The tests involved six
hosts, three reference clocks and several types of communication
links. The tests were designed to coincide with the insertion of a
leap second in the standard time broadcast by NBS, providing an
interesting test of system stability in the face of such disruptions.
The test was also designed to test the feasability of using the power
grid as a reference clock, with corrections broadcast as described
above, but not used to adjust the local clock.

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ARPAnet |
- - - - - - - - - - - - - - - - - - | - - - - - - - - - -
56K |
+---------+ +---------+ +----+----+ 1.2 +---------+
| WWV | 1.2 | | 4.8 | +-----+ WWVB |
| radio +-----+ DCN6 +-----+ DCN1 |async| radio |
| clock |async| |DDCMP| +--+ | clock |
+---------+ +---------+ +----+----+ | +---------+
Ethernet | |
DCnet ===o===============o=======o=== | 1822/DH
| | |
+----+----+ +----+----+ +----+----+
power | | | | | | power
freq <--+ DCN3 | | DCN5 | | DCN7 +--> freq
60 Hz | | | | | | 60 Hz
+---------+ +----+----+ +---------+
9.6 |
- - - - - - - - - - - - - - | - - - - - - - - - - - - - -
+----+----+ +---------+
| | 1.2 | GOES |
FORDnet | FORD1 +-----+satellite|
| |async| clock |
+---------+ +---------+

Figure 2. Network Configuration

Only those hosts and links directly participating in the tests are
shown in Figure 2. All hosts shown operate using the DCnet protocols
and timekeeping algorithms summarized in this document and detailed
in [5]. The DCnet hosts operate as one self-contained net of the
Internet systems, while the FORDnet hosts operate as another with
distinct net numbers. The gateway functions connecting the two nets
are distributed in the DCN5 and FORD1 hosts and the link connecting
them. This means that, although the clock offsets of individual
DCnet hosts are visible to other DCnet hosts and the clock offsets of
individual FORDnet hosts are visible to other FORDnet hosts, only the
clock offset of the gateway host on one net is visible to hosts on
the other net.

In Figure 2 the links are labelled with both the intrinsic speed, in
kilobits per second, as well as the link protocol type. The DDCMP
links use microprocessor-based DMA interfaces that retransmit in case
of message failure. The 1822/DH link connecting DCN1 and DCN7
operates at DMA speeds over a short cable. The Ethernet link uses

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DMA interfaces that retransmit only in case of collisions. The
asynchronous links are used only to connect the reference clocks to
the hosts over a short cable.

While all hosts and links were carrying normal traffic throughout the
test period, the incidence of retransmissions was very low, perhaps
no more than a few times per day on any link. However, the DDCMP
link protocol includes the use of short control messages exhanged
between the microprocessors about once per second in the absence of
link traffic. These messages, together with retransmissions when they
occur, cause small uncertaincies in Hello message delays that
contribute to the total measurement error. An additional uncertaincy
(less than 0.5 per-cent on average) in Hello message length can be
introduced when the link protocol makes use of character-stuffing or
bit-stuffing techniques to achieve code transparency, such as with
the LAPB link-level protocol of X.25. However, the particular links
used in the tests use a count field in the header, so that no
stuffing is required.

Although the timekeeping algorithms have been carefully designed to
be insensitive to traffic levels, it sometimes happens that an
intense burst of traffic results in a shortage of memory buffers in
the various hosts. In the case of the Ethernet interfaces, which
have internal buffers, this can result in additional delays while the
message is held in the interface pending delivery to the host.
Conditions where these delays become significant occur perhaps once
or twice a day in the present system and were observed occasionally
during the tests. As described above, the correction-sample
processing incorporates a filtering procedure that discards the vast
majority of glitches due to this and other causes.

4.2. Experiment Execution

The series of experiments conducted in late June and early July of
1985 involved collecting data on the delays and offsets of the six
hosts and three reference clocks shown in Figure 2. In order to
accomplish this, a special program was installed in a Unix 4.2bsd
system connected to the Ethernet link but not shown in Figure 2. The
program collected each 128-octet Hello message broadcast from DCN1
every 16 seconds and appended it bit-for-bit to the data base. The
total volume of raw data collected amounted to almost 0.7 megabyte
per day.

The raw Hello-message data were processed to extract only the
timestamp and measured clock offsets for the hosts shown in Table 1
and then reformatted as an ASCII file, one line per Hello message.

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Host Clock Drift Experiment Use
Name ID (ppm)
DCN1 WWVB -2.5 WWVB reference host
DCN3 - 60-Hz power-grid (unlocked)
DCN5 DCN1 6.8 Ethernet host
DCN6 DCN1 -1.7 DDCMP host, WWV reference host
DCN7 DCN1 60-Hz power-grid (locked)
FORD1 GOES 17.9 GOES reference host
WWV - - WWV reference clock
WWVB - - WWVB reference clock

Table 1. Experiment Hosts

In Table 1 the Clock ID column shows the reference host selected as
the master clock for each host shown. In this particular
configuration host DCN1 was locked to host WWVB, while hosts DCN5,
DCN6 and DCN7 were locked to DCN1. Although the offset of GOES can
not be directly determined from the Hello messages exchanged between
DCnet and FORDnet hosts, the offset of FORD1 relative to GOES was
determined by observation to be in the order of a millisecond, so for
all practical purposes the offset of FORD1 represents the offset of
GOES. In addition, since the WWVB clock was considered by experience
the most accurate and reliable and the offset of DCN1 relative to
WWVB was negligible, DCN1 was considered the reference clock with
offset zero relative to the NBS clocks.

During the setup phase of the experiments the intrinsic drift rates
of the crystal oscillators in the four hosts DCN1, DCN5, DCN6 and
FORD1 equipped with them was measured as shown in the 'Drift' column
in Table 1. The two hosts DCN3 and DCN7 are equipped with
line-frequency clocks. For experimental purposes DCN3 was unlocked
and allowed to free-run at the line-frequency rate, while DCN7
remained locked.

An ASCII file consisting of about 0.2 megabyte of reformatted data,
was collected for each Universal-Time (UT) day of observation
beginning on 28 June and continuing through 8 July. Each file was
processed by a program that produces an eight-color display of
measured offsets as a function of time of observation. Since the
display technique uses a bit-map display and each observation
overwrites the bit-map in an inclusive-OR fashion, the sample
dispersion is immediately apparent. Over eight samples per pixel on
the time axis are available in a 24-hour collection period. On the
other hand, the fine granularity of almost four samples per minute
allows zooming the display to focus on interesting short-term
fluctuations, such as in the case of the WWV clock.

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4.3. Discussion of Results

Each of the four previously mentioned issues of interest will be
discussed in following subsections.

4.3.1. On Power-Grid Clocks

Telephone interviews with operators and supervisors of the Potomac
Electric Power Company (PEPCO), the electric utility serving the
Washington, DC, area, indicate that there are three major operating
regions or grids, one east of the Rockies, a second west of the
Rockies and a third in parts of Texas. The member electric utilities
in each grid operate on a synchronous basis, so that clocks anywhere
within the grid should keep identical time. However, in the rare
case when a utility drops off the grid, no attempt is made to
re-establish correct time upon rejoining the grrd. In the much more
common case when areas within the grid are isolated due to local
thunderstorms, for example, clock synchronization is also disrupted.

The experiments provided an opportunity to measure with exquisite
precision the offset between a clock connected to the eastern grid
(DCN3) and the NBS clocks. The results, confirmed by the telephone
interviews, show a gradual gain in time of between four and six
seconds during the interval from about 1700 local time to 0800 the
next morning, followed by a more rapid loss in time between 0800 and
1700. If the time was slewed uniformly throughout these extremes,
the rate would be about 100 ppm.

The actual slewing rates depend on the demand, which itself is a
function of weather, day of the week and season of the year. Similar
effects occur in the western and Texas grids, with more extreme
variations in the Texas grid due to the smaller inertia of the
system, and less extreme variations in the western grid, due to
smaller extremes in temperature, less total industrial demand and a
larger fraction of hydro-electric generation.

The uilities consider timekeeping a non-tariffed service provided as
a convenience to the customer. In the eastern grid a control station
in Ohio manually establishes the baseline system output, which
indirectly affects the clock offset and slewing rate. The local time
is determined at the control station with respect to a WWVB radio
clock. The maximum slewing rate is specified as .025 Hz (about 400
ppm), which is consistent with the maximum rates observed. In the
western grid the baseline system output is adjusted automatically
using a servomechanism driven by measured offsets from the NBS

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RFC 957 September 1985
Experiments in Network Clock Synchronization

Given the considerations above, it would seem feasable for hosts to
synchronize logical clocks to a particular power grid, but only if
corrections were transmitted often enough to maintain the required
accuracy and these corrections were delivered to the hosts
essentially at the same time. Assuming a worst-case 400-ppm slewing
rate and one minute between correction broadcasts, for example, it
would in principle be possible to achieve accuracies in the 20-ms
range. There are a number of prediction and smoothing techniques
that could be used to inhance accuracy and reduce the overhead of the

Host DCN3, which uses a line-frequency clock interface, was unlocked
during the experiment period so that the offset between the PEPCO
clock, which is locked to the eastern power grid, could be measured
with respect to the reference host DCN1. Host DCN7, which uses the
same interface, remained locked to DCN1. In spite of the previously
noted instability of the power grid, DCN7 remained typically within
30 ms of DCN1 and only infrequently exceeded 100 ms in the vicinity
of large changes in system load that occured near 0800 and 1700 local
time. Over the seven-day period from 2 July through 8 July the mean
offset was less than a millisecond with standard deviation about 24
ms, while the maximum was 79 ms and minimum -116 ms.

Experiments were also carried out using ICMP Timestamp messages with
hosts known to use line-frequency clock interfaces in California,
Norway and Germany. The results indicated that the western power
grid is rather more stable than the eastern grid and that the
overseas grids are rather less stable. In the Oslo, Munich and
Stuttgart areas, for example, the diurnal variation was observed to
exceed ten seconds.

4.3.2. On Clocks Synchronized via Network Links

As mentioned previously, all network links used to synchronize the
clocks were carrying normal data traffic throughout the experiment
period. It would therefore be of interest to investigate how this
affects the accuracy of the individual clocks.

Table 2 summarizes the mean and standard deviation of the measured
offsets between the WWVB radio clock and various hosts as shown in
Figure 2. Measurements were made over the 24-hour period for each of
several days during the experimental period. Each entry shown in
Table 2 includes the mean of the statistic over these days, together
with the maximum variation.

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RFC 957 September 1985
Experiments in Network Clock Synchronization

Host Mean Deviation Link Type and Speed
DCN1 .08/.02 0.53/.02 WWVB radio clock (1200 bps)
DCN5 -13.61/.04 1.1/0.4 Ethernet (10 Mbps)
DCN6 0.27/.18 5.8/1.0 DDCMP (4800 bps)
FORD1 38.5/1.6 2.5/0.5 DDCMP (9600 bps)

Table 2. Link Measurements

The departure of the mean shown in Table 2 from zero is related to
the drift of the crystal oscillator used in the hardware interface
(see Table 1). As described previously, FORD1 was synchonized to the
GOES radio clock with neglible offset, so that the mean and standard
deviation shown can be accurately interpreted to apply to the GOES
radio clock as well.

The results show that the uncertaincies inherent in the
synchronization algorithm and protocols is in the same order as that
of the reference clocks and is related to the speed of the links
connected the reference hosts to the other hosts in the network.
Further discussion on the FORD1/GOES statistics can be found in the
next section.

Further insight into the error process can be seen in Table 3, which
shows the first derivative of delay.

Host Dev Max Min Error
DCN3 2.3 12 -17 10
DCN5 1.5 45 -45 5
DCN6 9 94 -54 40
DCN7 1.4 6 -7 5
FORD1 3.4 68 -51 15

Table 3. First Derivative of Delay

The mean and standard deviation of delay were computed for all hosts
on a typical day during the experimental period. In all cases the
magnitude of the mean was less than one. The standard deviation,
maximum and minimum for each link is summarized by host in Table 3.
A common characteristic of the distribution in most cases was that
only a handful of samples approached the maximum or minimum extrema,
while the vast majority of samples were much less than this. The
'Error' colum in Table 3 indicates the magnitude of the estimated
error when these extrema are discarded.

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RFC 957 September 1985
Experiments in Network Clock Synchronization

A very interesting feature of the observations was the unexpectedly
low standard deviation of DCN3, which was locked to the power grid
and thus would be expected to show wide variations. Upon analysis,
this turned out to be a natural consequence of the fact that the
Hello messages are generated as the result of interrupts based on the
line frequency when the local clock had just been incremented by
1/60th of a second.

The synchronizing protocol and implementation were carefully
constructed to minimize the loss of accuracy due to sharing of the
network links between data and control traffic, as long as sufficient
resources (in particular, packet buffers) are available. Since the
various network links shown in Figure 2 operate over a wide range of
rates, it is possible that undisciplined bursts of traffic can swamp
a host or gateway and precipitate a condition of buffer starvation.

While most hosts using paths through the experimental configuration
were relatively well-disciplined in their packetization and
retransmission policies, some Unix 4.2bsd systems were notorious
exceptions. On occasion these hosts were observed sending floods of
packets, with only a small amount of data per packet, together with
excessive retransmissions. As expected, this caused massive
congestion, unpredictable link delays and occasional clock
synchronizing errors.

The synchronizing algorithms described above successfully cope with
almost all instances of congestion as described, since delay-induced
errors tend to be isolated, while inherent anti-spike and smoothing
properties of the synchronizing algorithm help to preserve accuracies
in any case. Only one case was found during the ten-day experiment
period where a host was mistakenly synchronized outside the
linear-tracking window due to congestion. Even in this case the host
was quickly resynchronized to the correct time when the congestion
was cleared.

4.3.3. On the Accuracy of Radio Clocks

One of the more potent motivations for the experiments was to assess
the accuracy of the various radio clocks and to determine whether the
WWV radio clock was an appropriate replacement for the expensive WWVB
or GOES clocks. A secondary consideration, discussed further in the
next section, was how the various clocks handled disruptions due to
power interruptions, leap seconds and so forth.

Mills [Page 18]

RFC 957 September 1985
Experiments in Network Clock Synchronization The Spectracom 8170 WWVB Radio Clock

As the result of several years of experience with the WWVB radio
clock, which is manufactured by Spectracom Corporation as Model 8170,
it was chosen as the reference for comparison for the GOES and WWV
radio clocks. Washington, DC, is near the 100-microvolt/meter
countour of the WWVB transmitter at Boulder, CO, well in excess of
the 25-microvolt/meter sensitivity of the receiver. The antenna is
located in a favorable location on the roof of a four-storey building
in an urban area.

Using the data from the instruction manual, the propagation delay for
the path from Boulder to Washington is about 8 ms, while the
intrinsic receiver delay is about 17 ms. The clock is read via a
1200-bps asynchronous line, which introduces an additional delay of
about 7 ms between the on-time transition of the first character and
the interrupt at the middle of the first stop bit. Thus, the WWVB
radio clock indications should be late by 8 + 17 + 7 = 32 ms relative
to NBS standard time. While it is possible to include this delay
directly in the clock indication, this was not done in the
experiments. In order to account for this, 32 ms should be
subtracted from all indications derived from this clock. The
uncertaincy in the indication due to all causes is estimated to be a
couple of milliseconds. The True Time 468-DC GOES Radio Clock

The GOES radio clock is manufactured by True Time Division of
Kinemetrics, Incorporated, as Model 468-DC. It uses the
Geosynchronous Orbiting Environmental Satellite (GOES), which
includes an NBS-derived clock channel. Early in the experiment
period there was some ambiguity as to the exact longitude of the
satellite and also whether the antenna was correctly positioned.
This was reflected in the rather low quality-of-signal indications
and occasional signal loss reported by the clock and also its
apparent offset compared with the other radio clocks.

Table 4 shows a summary of offset statistics for the GOES radio clock
by day (all day numbers refer to July, 1985).

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RFC 957 September 1985
Experiments in Network Clock Synchronization

Day Mean Dev Max Min
2 31.6 9.4 53 -76
3 19.8 22.1 53 -64
4 42.8 17.1 >150 19
5 39.3 2.2 54 -45
6 37.8 2.7 53 19
7 62.2 13.0 89 22
8 38.2 2.8 90 -7

Table 4. GOES Radio Clock Offsets

On all days except days 5, 6 and 8 long periods of poor-quality
signal reception were evident. Since the antenna and satellite
configuration are known to be marginal, these conditions are not
considered representative of the capabilities of the clock. When the
data from these days are discarded, the mean offset is 38.4 ms with
standard deviation in the range 2.2 to 2.8. The maximum offset is 90
ms and the minimum is -45 ms; however, only a very small number of
samples are this large - most excursions are limited to 10 ms of the

In order to compute the discrepancy between the GOES and WWVB clocks,
it is necessary to subtract the WWVB clock delay from the mean
offsets computed above. Thus, the GOES clock indications are 38.4 -
32 = 6.4 ms late with respect to the WWVB clock indications. which
is probably within the bounds of experiment error. The Heath GC-1000 WWV Radio Clock

The WWV radio clock is manufactured by Heath Company as Model
GC-1000. It uses a three-channel scanning WWV/WWVH receiver on 5, 10
and 15 MHz together with a microprocessor-based controller. The
receiver is connected to an 80-meter dipole up about 15 meters and
located in a quiet suburban location. Signal reception from the Fort
Collins transmitters was average to poor during the experiment period
due to low sunspot activity together with a moderate level of
geomagnetic disturbances, but was best during periods of darkness
over the path. The clock locked at one of the frequencies for
varying periods up to an hour from two to several times a day.

The propagation delay on the path between Fort Collins and Washington
is estimated at about 10 ms and can vary up to a couple of
milliseconds over the day and night. While it is possible to include
this delay in the clock indications, which are already corrected for

Mills [Page 20]

RFC 957 September 1985
Experiments in Network Clock Synchronization

the intrinsic receiver delay, this was not done in the experiments.
During periods of lock, the clock indications are claimed to be
accurate to within 100 ms.

Table 5 shows a summary of offset statistics for the WWV radio clock
by day (all day numbers refer to July, 1985).

Day Mean Dev Max Min
2 -31 36 110 -119
3 -42 38 184 -141
4 -21 38 61 -133
5 -31 37 114 -136
6 -48 42 53 -160
7 -100 80 86 -315
8 -71 70 115 -339

Table 5. WWV Radio Clock Offsets

On inspection of the detailed plots of offsets versus time the data
reveal an interesting sawtooth variation with period about 25 cycles
per hour and amplitude about 90 ms. Once the clock has locked for
some time the variation decreases in frequency and sometimes
disappears. This behavior is precisely what would be expected of a
phase-locked oscillator and accounts for the rather large standard
deviations in Table 5.

On inspection of the plots of offsets versus time, it is apparent
that by far the best accuracies are obtained at or in the periods of
lock, which is most frequent during periods of darkness over the
propagation path, which occured roughly between 0800 UT and 1100 UT
during the experiment period. Excluding all data except that
collected during this period, the mean offset is -21.3 ms with
standard deviation in the range 29-31. The maximum offset is 59 ms
and the minimum is -118 ms.

In order to compute the discrepancy between the WWV and WWVB clocks,
it is necessary to subtract the total of the propagation delay plus
WWVB clock delay from the mean offsets computed above. Thus, the WWV
clock indications are -21.3 - 10 - 32 = -72.3 ms late (72.3 ms early)
with respect to the WWVB clock indications. Considering the large
standard deviations noted above, it is probably not worthwhile to
include this correction in the WWV clock indications.

On exceptional occasions excursions in offset over 300 ms relative to
the WWVB clock were observed. Close inspection of the data showed
that this was due to an extended period (a day or more) in which lock

Mills [Page 21]

RFC 957 September 1985
Experiments in Network Clock Synchronization

was not achieved on any frequency. The master oscillator uses a
3.6-MHz crystal oscillator trimmed by a digital/analog converter and
register which is loaded by the microprocessor. The occasional
excursions in offset were apparently due to incorrect register values
as the result of noisy reception conditions and excessive intervals
between lock. On occasion the oscillator frequency was observed in
error over 4 ppm due to this cause, which could result in a
cumulative error of almost 400 ms per day if uncorrected.

4.3.4. On Handling Disruptions

The experiment period was intentionally selected to coincide with the
insertion of a leap second in the worldwide time broadcasts. The
intent was to examine the resulting behavior of the various radio
clocks and the synchronization algorithm when an additional second
was introduced at 2400 UT on 30 June.

As it turned out, radio reception conditions at the time of insertion
were quite poor on all WWV frequencies, the WWVB frequency and the
GOES frequency. Thus, all three clocks took varying periods up to
several hours to resynchonize and correct the indicated time. In
fact, the only time signals heard around the time of interest were
those from Canadian radio CHU, but the time code of the Canadian
broadcasts is incompatible with the of the US broadcasts.

As mentioned above, the WWVB clock was used as the master during the
experiment period. About two hours after insertion of the leap
second the clock resynchronized and all hosts in the experimental
network were corrected shortly afterwards. Since the magnitude of
the correction exceeded 128 ms, the correction was of a step nature,
but was not performed simultaneously in all hosts due to the
individual timing of the Hello messages. Thus, if timing-critical
network operations happened to take place during the correction
process, inconsistent timestamps could result.

The lesson drawn from this experience is quite clear. Accurate time
synchronization requires by its very nature long integration times,
so that epochal events which disrupt the process must be predicted in
advance and applied in all hosts independently. In principle, this
would not be hard to do and could even be integrated into the
operation of the step-correction procedure described earlier, perhaps
in the form of bits included in Hello messages which trigger a
one-second correction at the next rollover from 2400 to 0000 hours.

In order for such an out-of-band correction to be effective, advance
notice of the leap second must be available. At present, this
information is not available in the broadcast format and must be

Mills [Page 22]

RFC 957 September 1985
Experiments in Network Clock Synchronization

obtained via the news media. In fact, there are spare bits in the
broadcast format that could be adapted for this purpose, but this
would require reprogramming both the transmitting and receiving
equipment. Nevertheless, this feature should be considered for future

4.4. Additional Experiments

A set of experiments was performed using two WIDEBAND/EISN gateways
equipped with WWVB radio clocks and connected to the ARPANET. These
experiments were designed to determine the limits of accuracy when
comparing these clocks via ARPANET paths. One of the gateways
(ISI-MCON-GW) is located at the Information Sciences Institute near
Los Angeles, while the other (LL-GW) is located at Lincoln
Laboratories near Boston. Both gateways consist of PDP11/44
computers running the EPOS operating system and clock-interface
boards with oscillators phase-locked to the WWVB clock.

The clock indications of the WIDEBAND/EISN gateways were compared
with the DCNet WWVB reference clock using ICMP Timestamp messages
[6], which record the individual timestamps with a precision of a
millisecond. This technique is not as accurate as the one described
in Section 3, since the protocol implementation involves the
user-process level, which can be subject to minor delays due to
process scheduling and interprocess-message queueing. However,
calibration measurements made over several of the links shown in
Figure 2 indicate that the measurement errors are dominated by the
individual link variations and not by the characteristics of the
measurement technique itself.

Measurements were made separately with each gateway by sending an
ICMP Timestamp Request message from the ARPANET address of DCN1 to
the ARPANET address of the gateway and computing the round-trip delay
and clock offset from the ICMP Timestamp Reply message. This process
was continued for 1000 message exchanges, which took about seven
minutes. Table 6 shows the statistics obtained with ISI-MCON-GW and
Table 7 those with LL-GW (all numbers are milliseconds).

Mills [Page 23]

RFC 957 September 1985
Experiments in Network Clock Synchronization

ISI-MCON-GW Mean Dev Max Min
Offset -16 40 126 -908
Delay 347 59 902 264

Table 6. ISI-MCON-GW Clock Statistics

LL-GW (a) Mean Dev Max Min
Offset -23 15 32 -143
Delay 310 25 536 252

Table 7. LL-GW Clock Statistics

The smaller values of standard deviation and extreme for LL-GW are
probably due to the shorter ARPANET path involved. The confidence in
the mean offset can be estimated by dividing the standard deviation
by the square root of the number of samples (1000), which suggests
that the mean offsets are accurate to within a couple of miliseconds.
The mean offsets of the WIDEBAND/EISN clocks as a group relative to
the DCN1 clock may thus indicate a minor discrepancy in the setting
of the delay-compensation switches.

It is well known that ARPANET paths exhibit wide variations in
delays, with occasional delays reaching surprising values up to many
seconds. In order to improve the estimates a few samples were
removed from both the offset and delay data, including all those with
magnitude greater than one second.

The above experiments involve a burst of activity over a relatively
short time during which the ratio of the measurement traffic to other
network traffic may be nontrivial. Another experiment with LL-GW was
designed with intervals of ten seconds between ICMP messages and
operated over a period of about three hours. The results are shown
in Table 8.

LL-GW (b) Mean Dev Max Min
Offset -16 93 990 -874
Delay 371 108 977 240

Table 8. LL-GW Clock Statistics

Mills [Page 24]

RFC 957 September 1985
Experiments in Network Clock Synchronization

Note that the standard deviations and extrema are higher than in the
previous experiments, but the mean offset is about the same.

The results of these experiments suggest that time synchronization
via ARPANET paths can yield accuracies to the order of a few
milliseconds, but only if relatively large numbers of samples are
available. The number of samples can be reduced and the accuracy
improved by using the techniques of Section 3 modified for ICMP
Timestamp messages and the longer, more noisy paths involved.

5. Summary and Conclusions

The experiments described above were designed to verify the correct
operation of the DCnet time-synchronization algorithms and protocols
under a variety of scenarios, including the use of line-frequency
clocks, three types of radio clocks and various types of
interprocessor links. They involved the collection and processing of
many megabytes of data collected over a ten-day period that included
the insertion of a leap second in the standard NBS time scale. Among
the lessons learned were the following:

1. The algorithms and protocols operate as designed, yielding
accuracies throughout the experimental net in the order of a
few milliseconds to a few tens of milliseconds, depending on
the topology and link type.

2. Glitches due to congestion, rebooted hosts and link failures
are acceptably low, even in the face of massive congestion
resulting from inappropriate host implementations elsewhere in
the Internet.

3. A synchronization scenario where the clocks in all hosts are
locked to the line frequency and corrections are broadcast
from a central time standard will work only if all hosts are
on the same power grid, which is unlikely in the present
Internet configuration, but may be appropriate for some

4. In spite of the eastern power grid wandering over as much as
six seconds in a day, it is possible to achieve accuracies in
the 30-ms range using line-frequency interface clocks and
corrections broadcast on the local net.

5. Radio clocks can vary widely in accuracy depending on signal
reception conditions. Absolute time can be determined to
within a couple of milliseconds using WWVB and GOES radio
clocks, but only if they are calibrated using an independent

Mills [Page 25]

RFC 957 September 1985
Experiments in Network Clock Synchronization

standard such as a portable clock. The inexpensive WWV clocks
perform surprisingly well most of the time, but can be in
error up to a significant fraction of a second under some

6. Adjustments in the time scale due to leap seconds must be
anticipated before they occur. The synchronization protocol
must include a mechanism to broadcast an adjustment in advance
of its occurance, so that it can be incorporated in each host
simultaneously. There is a need to incorporate advance notice
of leap seconds in the broadcast time code.

7. Time synchronization via ARPANET paths can yield accuracies in
the order of a few milliseconds, but only if relatively large
numbers of samples are available. Further work is needed to
develop efficient protocols capable of similar accuracies but
using smaller numbers of samples.

6. References

1. Lindsay, W.C., and A.V. Kantak. Network Synchronization of
Random Signals. IEEE Trans. Comm. COM-28, 8 (August 1980),

2. Mills, D.L. Time Synchronization in DCNET Hosts. DARPA Internet
Project Report IEN-173, COMSAT Laboratories, February 1981.

3. Mills, D.L. DCNET Internet Clock Service. DARPA Network Working
Group Report RFC-778, COMSAT Laboratories, April 1981.

4. Mills, D.L. Internet Delay Experiments. DARPA Network Working
Group Report RFC-889, M/A-COM Linkabit, December 1983.

5. Mills, D.L. DCN Local-Network Protocols. DARPA Network Working
Group Report RFC-891, M/A-COM Linkabit, December 1983.

6. Postel, J. Internet Control Message Protocol. DARPA Network
Working Group Report RFC-792, USC Information Sciences Institute,
September 1981.

7. Postel, J. Time Protocol. DARPA Network Working Group Report
RFC-868, USC Information Sciences Institute, May 1983.

8. Postel, J. Daytime Protocol. DARPA Network Working Group Report
RFC-867, USC Information Sciences Institute, May 1983.

Mills [Page 26]

RFC 957 September 1985
Experiments in Network Clock Synchronization

9. Su, Z. A Specification of the Internet Protocol (IP) Timestamp
Option. DARPA Network Working Group Report RFC-781. SRI
International, May 1981.

10. Marzullo, K., and S. Owicki. Maintaining the Time in a
Distributed System. ACM Operating Systems Review 19, 3 (July
1985), 44-54.

11. Mills, D.L. Algorithms for Synchronizing Network Clocks. DARPA
Network Working Group Report RFC-956, M/A-COM Linkabit, September

12. Mills, D.L. Network Time Protocol (NTP). DARPA Network Working
Group Report RFC-958, M/A-COM Linkabit, September 1985.

Mills [Page 27]

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