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RFC 1305

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Network Time Protocol (Version 3) Specification, Implementation and Analysis

Part 1 of 4, p. 1 to 34
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Obsoleted by:    5905
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Network Working Group                           David L. Mills
Request for Comments: 1305                      University of Delaware
Obsoletes RFC-1119, RFC-1059, RFC-958           March 1992

                   Network Time Protocol (Version 3)
               Specification, Implementation and Analysis

Note: This document consists of an approximate rendering in ASCII of the
PostScript document of the same name. It is provided for convenience and
for use in searches, etc. However, most tables, figures, equations and
captions have not been rendered and the pagination and section headings
are not available.


This document describes the Network Time Protocol (NTP), specifies its
formal structure and summarizes information useful for its
implementation. NTP provides the mechanisms to synchronize time and
coordinate time distribution in a large, diverse internet operating at
rates from mundane to lightwave. It uses a returnable-time design in
which a distributed subnet of time servers operating in a self-
organizing, hierarchical-master-slave configuration synchronizes local
clocks within the subnet and to national time standards via wire or
radio. The servers can also redistribute reference time via local
routing algorithms and time daemons.

Status of this Memo

This RFC specifies an IAB standards track protocol for the Internet
community and requests discussion and suggestions for improvements.
Please refer to the current edition of the <169>IAB Official Protocol
Standards<170> for the standardization state and status of this
protocol. Distribution of this memo is unlimited.

Keywords: network clock synchronization, standard time distribution,
fault-tolerant architecture, maximum-likelihood estimation, disciplined
oscillator, internet protocol, high-speed networks, formal


This document describes Version 3 of the Network Time Protocol (NTP). It
supersedes Version 2 of the protocol described in RFC-1119 dated
September 1989. However, it neither changes the protocol in any
significant way nor obsoletes previous versions or existing
implementations. The main motivation for the new version is to refine

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the analysis and implementation models for new applications at much
higher network speeds to the gigabit-per-second regime and to provide
for the enhanced stability, accuracy and precision required at such
speeds. In particular, the sources of time and frequency errors have
been rigorously examined and error bounds established in order to
improve performance, provide a model for correctness assertions and
indicate timekeeping quality to the user. The revision also incorporates
two new optional features, (1) an algorithm to combine the offsets of a
number of peer time servers in order to enhance accuracy and (2)
improved local-clock algorithms which allow the poll intervals on all
synchronization paths to be substantially increased in order to reduce
network overhead. An overview of the changes, which are described in
detail in Appendix D, follows:

In Version 3 The local-clock algorithm has been overhauled to improve
stability and accuracy. Appendix G presents a detailed mathematical
model and design example which has been refined with the aid of
feedback-control analysis and extensive simulation using data collected
over ordinary Internet paths. Section 5 of RFC-1119 on the NTP local
clock has been completely rewritten to describe the new algorithm. Since
the new algorithm can result in message rates far below the old ones, it
is highly recommended that they be used in new implementations. Note
that use of the new algorithm does not affect interoperability with
previous versions or existing implementations.


In Version 3 a new algorithm to combine the offsets of a number of peer
time servers is presented in Appendix F. This algorithm is modelled on
those used by national standards laboratories to combine the weighted
offsets from a number of standard clocks to construct a synthetic
laboratory timescale more accurate than that of any clock separately. It
can be used in an NTP implementation to improve accuracy and stability
and reduce errors due to asymmetric paths in the Internet. The new
algorithm has been simulated using data collected over ordinary Internet
paths and, along with the new local-clock algorithm, implemented and
tested in the Fuzzball time servers now running in the Internet. Note
that use of the new algorithm does not affect interoperability with
previous versions or existing implementations.


Several inconsistencies and minor errors in previous versions have been
corrected in Version 3. The description of the procedures has been
rewritten in pseudo-code augmented by English commentary for clarity and
to avoid ambiguity. Appendix I has been added to illustrate C-language
implementations of the various filtering and selection algorithms
suggested for NTP. Additional information is included in Section 5 and
in Appendix E, which includes the tutorial material formerly included in

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Section 2 of RFC-1119, as well as much new material clarifying the
interpretation of timescales and leap seconds.


Minor changes have been made in the Version-3 local-clock algorithms to
avoid problems observed when leap seconds are introduced in the UTC
timescale and also to support an auxiliary precision oscillator, such as
a cesium clock or timing receiver, as a precision timebase. In addition,
changes were made to some procedures described in Section 3 and in the
clock-filter and clock-selection procedures described in Section 4.
While these changes were made to correct minor bugs found as the result
of experience and are recommended for new implementations, they do not
affect interoperability with previous versions or existing
implementations in other than minor ways (at least until the next leap


In Version 3 changes were made to the way delay, offset and dispersion
are defined, calculated and processed in order to reliably bound the
errors inherent in the time-transfer procedures. In particular, the
error accumulations were moved from the delay computation to the
dispersion computation and both included in the clock filter and
selection procedures. The clock-selection procedure was modified to
remove the first of the two sorting/discarding steps and replace with an
algorithm first proposed by Marzullo and later incorporated in the
Digital Time Service. These changes do not significantly affect the
ordinary operation of or compatibility with various versions of NTP, but
they do provide the basis for formal statements of correctness as
described in Appendix H.
Table of Contents

1.       Introduction   1

1.1.     Related Technology     2

2.       System Architecture    4

2.1.     Implementation Model   6

2.2.     Network Configurations 7

3.       Network Time Protocol  8

3.1.     Data Formats   8

3.2.     State Variables and Parameters 9

3.2.1.   Common Variables       9

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3.2.2.   System Variables       12

3.2.3.   Peer Variables 12

3.2.4.   Packet Variables       14

3.2.5.   Clock-Filter Variables 14

3.2.6.   Authentication Variables       15

3.2.7.   Parameters     15

3.3.     Modes of Operation     17

3.4.     Event Processing       19

3.4.1.   Notation Conventions   19

3.4.2.   Transmit Procedure     20

3.4.3.   Receive Procedure      22

3.4.4.   Packet Procedure       24

3.4.5.   Clock-Update Procedure 27

3.4.6.   Primary-Clock Procedure        28

3.4.7.   Initialization Procedures      28         Initialization Procedure       29         Initialization-Instantiation Procedure 29         Receive-Instantiation Procedure        30         Primary Clock-Instantiation Procedure  31

3.4.8.   Clear Procedure        31

3.4.9.   Poll-Update Procedure  32

3.5.     Synchronization Distance Procedure     32

3.6.     Access Control Issues  33

4.       Filtering and Selection Algorithms     34

4.1.     Clock-Filter Procedure 35

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4.2.     Clock-Selection Procedure      36

4.2.1.   Intersection Algorithm 36

5.       Local Clocks   40

5.1.     Fuzzball Implementation        41

5.2.     Gradual Phase Adjustments      42

5.3.     Step Phase Adjustments 43

5.4.     Implementation Issues  44

6.       Acknowledgments        45

7.       References     46

A.       Appendix A. NTP Data Format - Version 3        50

B.       Appendix B. NTP Control Messages       53

B.1.     NTP Control Message Format     54

B.2.     Status Words   56

B.2.1.   System Status Word     56

B.2.2.   Peer Status Word       57

B.2.3.   Clock Status Word      58

B.2.4.   Error Status Word      58

B.3.     Commands       59

C.       Appendix C. Authentication Issues      61

C.1.     NTP Authentication Mechanism   62

C.2.     NTP Authentication Procedures  63

C.2.1.   Encrypt Procedure      63

4.2.2.   Clustering Algorithm   38

C.2.2.   Decrypt Procedure      64

C.2.3.   Control-Message Procedures     65

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D.       Appendix D. Differences from Previous Versions.        66

E.       Appendix E. The NTP Timescale and its Chronometry      70

E.1.     Introduction   70

E.2.     Primary Frequency and Time Standards   70

E.3.     Time and Frequency Dissemination       72

E.4.     Calendar Systems       74

E.5.     The Modified Julian Day System 75

E.6.     Determination of Frequency     76

E.7.     Determination of Time and Leap Seconds 76

E.8.     The NTP Timescale and Reckoning with UTC       78

F.       Appendix F. The NTP Clock-Combining Algorithm  80

F.1.     Introduction   80

F.2.     Determining Time and Frequency 80

F.3.     Clock Modelling        81

F.4.     Development of a Composite Timescale   81

F.5.     Application to NTP     84

F.6.     Clock-Combining Procedure      84

G.       Appendix G. Computer Clock Modelling and Analysis      86

G.1.     Computer Clock Models  86

G.1.1.   The Fuzzball Clock Model       88

G.1.2.   The Unix Clock Model   89

G.2.     Mathematical Model of the NTP Logical Clock    91

G.3.     Parameter Management   93

G.4.     Adjusting VCO Gain (<$Ebold alpha>)    94

G.5.     Adjusting PLL Bandwidth (<$Ebold tau>) 94

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G.6.     The NTP Clock Model    95

H.       Appendix H. Analysis of Errors and Correctness Principles


H.1.     Introduction   98

H.2.     Timestamp Errors       98

H.3.     Measurement Errors     100

H.4.     Network Errors 101

H.5.     Inherited Errors       102

H.6.     Correctness Principles 104

I.       Appendix I. Selected C-Language Program Listings       107

I.1.     Common Definitions and Variables       107

I.2.     Clock<196>Filter Algorithm     108

I.3.     Interval Intersection Algorithm        109

I.4.     Clock<196>Selection Algorithm  110

I.5.     Clock<196>Combining Procedure  111

I.6.     Subroutine to Compute Synchronization Distance 112

List of Figures

Figure 1. Implementation Model  6

Figure 2. Calculating Delay and Offset  25

Figure 3. Clock Registers       39

Figure 4. NTP Message Header    50

Figure 5. NTP Control Message Header    54

Figure 6. Status Word Formats   55

Figure 7. Authenticator Format  63

Figure 8. Comparison of UTC and NTP Timescales at Leap  79

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Figure 9. Network Time Protocol 80

Figure 10. Hardware Clock Models        86

Figure 11. Clock Adjustment Process     90

Figure 12. NTP Phase-Lock Loop (PLL) Model      91

Figure 13. Timing Intervals     96

Figure 14. Measuring Delay and Offset   100

Figure 15. Error Accumulations  103

Figure 16. Confidence Intervals and Intersections       105

List of Tables

Table 1. System Variables       12

Table 2. Peer Variables 13

Table 3. Packet Variables       14

Table 4. Parameters     16

Table 5. Modes and Actions      22

Table 6. Clock Parameters       40

Table 7. Characteristics of Standard Oscillators        71

Table 8. Table of Leap-Second Insertions        77

Table 9. Notation Used in PLL Analysis  91

Table 10. PLL Parameters        91

Table 11. Notation Used in PLL Analysis 95

Table 12. Notation Used in Error Analysis       98

This document constitutes a formal specification of the Network Time
Protocol (NTP) Version 3, which is used to synchronize timekeeping among
a set of distributed time servers and clients. It defines the
architectures, algorithms, entities and protocols used by NTP and is
intended primarily for implementors. A companion document [MIL91a]
summarizes the requirements, analytical models, algorithmic analysis and

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performance under typical Internet conditions. Another document [MIL91b]
describes the NTP timescale and its relationship to other standard
timescales now in use. NTP was first described in RFC-958 [MIL85c], but
has since evolved in significant ways, culminating in the most recent
NTP Version 2 described in RFC-1119 [MIL89]. It is built on the Internet
Protocol (IP) [DAR81a] and User Datagram Protocol (UDP) [POS80], which
provide a connectionless transport mechanism; however, it is readily
adaptable to other protocol suites. NTP is evolved from the Time
Protocol [POS83b] and the ICMP Timestamp message [DAR81b], but is
specifically designed to maintain accuracy and robustness, even when
used over typical Internet paths involving multiple gateways, highly
dispersive delays and unreliable nets.

The service environment consists of the implementation model and service
model described in Section 2. The implementation model is based on a
multiple-process operating system architecture, although other
architectures could be used as well. The service model is based on a
returnable-time design which depends only on measured clock offsets, but
does not require reliable message delivery. The synchronization subnet
uses a self-organizing, hierarchical-master-slave configuration, with
synchronization paths determined by a minimum-weight spanning tree.
While multiple masters (primary servers) may exist, there is no
requirement for an election protocol.

NTP itself is described in Section 3. It provides the protocol
mechanisms to synchronize time in principle to precisions in the order
of nanoseconds while preserving a non-ambiguous date well into the next
century. The protocol includes provisions to specify the characteristics
and estimate the error of the local clock and the time server to which
it may be synchronized. It also includes provisions for operation with a
number of mutually suspicious, hierarchically distributed primary
reference sources such as radio-synchronized clocks.

Section 4 describes algorithms useful for deglitching and smoothing
clock-offset samples collected on a continuous basis. These algorithms
evolved from those suggested in [MIL85a], were refined as the results of
experiments described in [MIL85b] and further evolved under typical
operating conditions over the last three years. In addition, as the
result of experience in operating multiple-server subnets including
radio clocks at several sites in the U.S. and with clients in the U.S.
and Europe, reliable algorithms for selecting good clocks from a
population possibly including broken ones have been developed [DEC89],
[MIL91a] and are described in Section 4.

The accuracies achievable by NTP depend strongly on the precision of the
local-clock hardware and stringent control of device and process
latencies. Provisions must be included to adjust the software logical-
clock time and frequency in response to corrections produced by NTP.
Section 5 describes a local-clock design evolved from the Fuzzball
implementation described in [MIL83b] and [MIL88b]. This design includes

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offset-slewing, frequency compensation and deglitching mechanisms
capable of accuracies in the order of a millisecond, even after extended
periods when synchronization to primary reference sources has been lost.

Details specific to NTP packet formats used with the Internet Protocol
(IP) and User Datagram Protocol (UDP) are presented in Appendix A, while
details of a suggested auxiliary NTP Control Message, which may be used
when comprehensive network-monitoring facilities are not available, are
presented in Appendix B. Appendix C contains specification and
implementation details of an optional authentication mechanism which can
be used to control access and prevent unauthorized data modification,
while Appendix D contains a listing of differences between Version 3 of
NTP and previous versions. Appendix E expands on issues involved with
precision timescales and calendar dating peculiar to computer networks
and NTP. Appendix F describes an optional algorithm to improve accuracy
by combining the time offsets of a number of clocks. Appendix G presents
a detailed mathematical model and analysis of the NTP local-clock
algorithms. Appendix H analyzes the sources and propagation of errors
and presents correctness principles relating to the time-transfer
service. Appendix I illustrates C-language code segments for the clock-
filter, clock-selection and related algorithms described in Section 4.

Related Technology

Other mechanisms have been specified in the Internet protocol suite to
record and transmit the time at which an event takes place, including
the Daytime protocol [POS83a], Time Protocol [POS83b], ICMP Timestamp
message [DAR81b] and IP Timestamp option [SU81]. Experimental results on
measured clock offsets and roundtrip delays in the Internet are
discussed in [MIL83a], [MIL85b], [COL88] and [MIL88a]. Other
synchronization algorithms are discussed in [LAM78], [GUS84], [HAL84],
[LUN84], [LAM85], [MAR85], [MIL85a], [MIL85b], [MIL85c], [GUS85b],
[SCH86], [TRI86], [RIC88], [MIL88a], [DEC89] and [MIL91a], while
protocols based on them are described in [MIL81a], [MIL81b], [MIL83b],
[GUS85a], [MIL85c], [TRI86], [MIL88a], [DEC89] and [MIL91a]. NTP uses
techniques evolved from them and both linear-systems and agreement
methodologies. Linear methods for digital telephone network
synchronization are summarized in [LIN80], while agreement methods for
clock synchronization are summarized in [LAM85].

The Digital Time Service (DTS) [DEC89] has many of the same service
objectives as NTP. The DTS design places heavy emphasis on configuration
management and correctness principles when operated in a managed LAN or
LAN-cluster environment, while NTP places heavy emphasis on the accuracy
and stability of the service operated in an unmanaged, global-internet
environment. In DTS a synchronization subnet consists of clerks,
servers, couriers and time providers. With respect to the NTP
nomenclature, a time provider is a primary reference source, a courier
is a secondary server intended to import time from one or more distant
primary servers for local redistribution and a server is intended to

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provide time for possibly many end nodes or clerks. Unlike NTP, DTS does
not need or use mode or stratum information in clock selection and does
not include provisions to filter timing noise, select the most accurate
from a set of presumed correct clocks or compensate for inherent
frequency errors.

In fact, the latest revisions in NTP have adopted certain features of
DTS in order to support correctness principles. These include mechanisms
to bound the maximum errors inherent in the time-transfer procedures and
the use of a provably correct (subject to stated assumptions) mechanism
to reject inappropriate peers in the clock-selection procedures. These
features are described in Section 4 and Appendix H of this document.

The Fuzzball routing protocol [MIL83b], sometimes called Hellospeak,
incorporates time synchronization directly into the routing-protocol
design. One or more processes synchronize to an external reference
source, such as a radio clock or NTP daemon, and the routing algorithm
constructs a minimum-weight spanning tree rooted on these processes. The
clock offsets are then distributed along the arcs of the spanning tree
to all processes in the system and the various process clocks corrected
using the procedure described in Section 5 of this document. While it
can be seen that the design of Hellospeak strongly influenced the design
of NTP, Hellospeak itself is not an Internet protocol and is unsuited
for use outside its local-net environment.

The Unix 4.3bsd time daemon timed [GUS85a] uses a single master-time
daemon to measure offsets of a number of slave hosts and send periodic
corrections to them. In this model the master is determined using an
election algorithm [GUS85b] designed to avoid situations where either no
master is elected or more than one master is elected. The election
process requires a broadcast capability, which is not a ubiquitous
feature of the Internet. While this model has been extended to support
hierarchical configurations in which a slave on one network serves as a
master on the other [TRI86], the model requires handcrafted
configuration tables in order to establish the hierarchy and avoid
loops. In addition to the burdensome, but presumably infrequent,
overheads of the election process, the offset measurement/correction
process requires twice as many messages as NTP per update.

A scheme with features similar to NTP is described in [KOP87]. This
scheme is intended for multi-server LANs where each of a set of possibly
many time servers determines its local-time offset relative to each of
the other servers in the set using periodic timestamped messages, then
determines the local-clock correction using the Fault-Tolerant Average
(FTA) algorithm of [LUN84]. The FTA algorithm, which is useful where up
to k servers may be faulty, sorts the offsets, discards the k highest
and lowest ones and averages the rest. The scheme, as described in
[SCH86], is most suitable to LAN environments which support broadcast
and would result in unacceptable overhead in an internet environment. In
addition, for reasons given in Section 4 of this paper, the statistical

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properties of the FTA algorithm are not likely to be optimal in an
internet environment with highly dispersive delays.

A good deal of research has gone into the issue of maintaining accurate
time in a community where some clocks cannot be trusted. A truechimer is
a clock that maintains timekeeping accuracy to a previously published
(and trusted) standard, while a falseticker is a clock that does not.
Determining whether a particular clock is a truechimer or falseticker is
an interesting abstract problem which can be attacked using agreement
methods summarized in [LAM85] and [SRI87].

A convergence function operates upon the offsets between the clocks in a
system to increase the accuracy by reducing or eliminating errors caused
by falsetickers. There are two classes of convergence functions, those
involving interactive-convergence algorithms and those involving
interactive-consistency algorithms. Interactive-convergence algorithms
use statistical clustering techniques such as the fault-tolerant average
algorithm of [HAL84], the CNV algorithm of [LUN84], the majority-subset
algorithm of [MIL85a], the non-Byzantine algorithm of [RIC88], the
egocentric algorithm of [SCH86], the intersection algorithm of [MAR85]
and [DEC89] and the algorithms in Section 4 of this document.

Interactive-consistency algorithms are designed to detect faulty clock
processes which might indicate grossly inconsistent offsets in
successive readings or to different readers. These algorithms use an
agreement protocol involving successive rounds of readings, possibly
relayed and possibly augmented by digital signatures. Examples include
the fireworks algorithm of [HAL84] and the optimum algorithm of [SRI87].
However, these algorithms require large numbers of messages, especially
when large numbers of clocks are involved, and are designed to detect
faults that have rarely been found in the Internet experience. For these
reasons they are not considered further in this document.

In practice it is not possible to determine the truechimers from the
falsetickers on other than a statistical basis, especially with
hierarchical configurations and a statistically noisy Internet. While it
is possible to bound the maximum errors in the time-transfer procedures,
assuming sufficiently generous tolerances are adopted for the hardware
components, this generally results in rather poor accuracies and
stabilities. The approach taken in the NTP design and its predecessors
involves mutually coupled oscillators and maximum-likelihood estimation
and clock-selection procedures, together with a design that allows
provable assertions on error bounds to be made relative to stated
assumptions on the correctness of the primary reference sources. From
the analytical point of view, the system of distributed NTP peers
operates as a set of coupled phase-locked oscillators, with the update
algorithm functioning as a phase detector and the local clock as a
disciplined oscillator, but with deterministic error bounds calculated
at each step in the time-transfer process.

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The particular choice of offset measurement and computation procedure
described in Section 3 is a variant of the returnable-time system used
in some digital telephone networks [LIN80]. The clock filter and
selection algorithms are designed so that the clock synchronization
subnet self-organizes into a hierarchical-master-slave configuration
[MIT80]. With respect to timekeeping accuracy and stability, the
similarity of NTP to digital telephone systems is not accidental, since
systems like this have been studied extensively [LIN80], [BRA80]. What
makes the NTP model unique is the adaptive configuration, polling,
filtering, selection and correctness mechanisms which tailor the
dynamics of the system to fit the ubiquitous Internet environment.

System Architecture

In the NTP model a number of primary reference sources, synchronized by
wire or radio to national standards, are connected to widely accessible
resources, such as backbone gateways, and operated as primary time
servers. The purpose of NTP is to convey timekeeping information from
these servers to other time servers via the Internet and also to cross-
check clocks and mitigate errors due to equipment or propagation
failures. Some number of local-net hosts or gateways, acting as
secondary time servers, run NTP with one or more of the primary servers.
In order to reduce the protocol overhead, the secondary servers
distribute time via NTP to the remaining local-net hosts. In the
interest of reliability, selected hosts can be equipped with less
accurate but less expensive radio clocks and used for backup in case of
failure of the primary and/or secondary servers or communication paths
between them.

Throughout this document a standard nomenclature has been adopted: the
stability of a clock is how well it can maintain a constant frequency,
the accuracy is how well its frequency and time compare with national
standards and the precision is how precisely these quantities can be
maintained within a particular timekeeping system. Unless indicated
otherwise, the offset of two clocks is the time difference between them,
while the skew is the frequency difference (first derivative of offset
with time) between them. Real clocks exhibit some variation in skew
(second derivative of offset with time), which is called drift; however,
in this version of the specification the drift is assumed zero.

NTP is designed to produce three products: clock offset, roundtrip delay
and dispersion, all of which are relative to a selected reference clock.
Clock offset represents the amount to adjust the local clock to bring it
into correspondence with the reference clock. Roundtrip delay provides
the capability to launch a message to arrive at the reference clock at a
specified time. Dispersion represents the maximum error of the local
clock relative to the reference clock. Since most host time servers will
synchronize via another peer time server, there are two components in
each of these three products, those determined by the peer relative to
the primary reference source of standard time and those measured by the

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host relative to the peer. Each of these components are maintained
separately in the protocol in order to facilitate error control and
management of the subnet itself. They provide not only precision
measurements of offset and delay, but also definitive maximum error
bounds, so that the user interface can determine not only the time, but
the quality of the time as well.

There is no provision for peer discovery or virtual-circuit management
in NTP. Data integrity is provided by the IP and UDP checksums. No flow-
control or retransmission facilities are provided or necessary.
Duplicate detection is inherent in the processing algorithms. The
service can operate in a symmetric mode, in which servers and clients
are indistinguishable, yet maintain a small amount of state information,
or in client/server mode, in which servers need maintain no state other
than that contained in the client request. A lightweight association-
management capability, including dynamic reachability and variable poll-
rate mechanisms, is included only to manage the state information and
reduce resource requirements. Since only a single NTP message format is
used, the protocol is easily implemented and can be used in a variety of
solicited or unsolicited polling mechanisms.

It should be recognized that clock synchronization requires by its
nature long periods and multiple comparisons in order to maintain
accurate timekeeping. While only a few measurements are usually adequate
to reliably determine local time to within a second or so, periods of
many hours and dozens of measurements are required to resolve oscillator
skew and maintain local time to the order of a millisecond. Thus, the
accuracy achieved is directly dependent on the time taken to achieve it.
Fortunately, the frequency of measurements can be quite low and almost
always non-intrusive to normal net operations.

Implementation Model

In what may be the most common client/server model a client sends an NTP
message to one or more servers and processes the replies as received.
The server interchanges addresses and ports, overwrites certain fields
in the message, recalculates the checksum and returns the message
immediately. Information included in the NTP message allows the client
to determine the server time with respect to local time and adjust the
local clock accordingly. In addition, the message includes information
to calculate the expected timekeeping accuracy and reliability, as well
as select the best from possibly several servers.

While the client/server model may suffice for use on local nets
involving a public server and perhaps many workstation clients, the full
generality of NTP requires distributed participation of a number of
client/servers or peers arranged in a dynamically reconfigurable,
hierarchically distributed configuration. It also requires sophisticated
algorithms for association management, data manipulation and local-clock
control. Throughout the remainder of this document the term host refers

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to an instantiation of the protocol on a local processor, while the term
peer refers to the instantiation of the protocol on a remote processor
connected by a network path.

Figure 1<$&fig1> shows an implementation model for a host including
three processes sharing a partitioned data base, with a partition
dedicated to each peer, and interconnected by a message-passing system.
The transmit process, driven by independent timers for each peer,
collects information in the data base and sends NTP messages to the
peers. Each message contains the local timestamp when the message is
sent, together with previously received timestamps and other information
necessary to determine the hierarchy and manage the association. The
message transmission rate is determined by the accuracy required of the
local clock, as well as the accuracies of its peers.

The receive process receives NTP messages and perhaps messages in other
protocols, as well as information from directly connected radio clocks.
When an NTP message is received, the offset between the peer clock and
the local clock is computed and incorporated into the data base along
with other information useful for error determination and peer
selection. A filtering algorithm described in Section 4 improves the
accuracy by discarding inferior data.

The update procedure is initiated upon receipt of a message and at other
times. It processes the offset data from each peer and selects the best
one using the algorithms of Section 4. This may involve many
observations of a few peers or a few observations of many peers,
depending on the accuracies required.

The local-clock process operates upon the offset data produced by the
update procedure and adjusts the phase and frequency of the local clock
using the mechanisms described in Section 5. This may result in either a
step-change or a gradual phase adjustment of the local clock to reduce
the offset to zero. The local clock provides a stable source of time
information to other users of the system and for subsequent reference by
NTP itself.

Network Configurations

The synchronization subnet is a connected network of primary and
secondary time servers, clients and interconnecting transmission paths.
A primary time server is directly synchronized to a primary reference
source, usually a radio clock. A secondary time server derives
synchronization, possibly via other secondary servers, from a primary
server over network paths possibly shared with other services. Under
normal circumstances it is intended that the synchronization subnet of
primary and secondary servers assumes a hierarchical-master-slave
configuration with the primary servers at the root and secondary servers
of decreasing accuracy at successive levels toward the leaves.

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Following conventions established by the telephone industry [BEL86], the
accuracy of each server is defined by a number called the stratum, with
the topmost level (primary servers) assigned as one and each level
downwards (secondary servers) in the hierarchy assigned as one greater
than the preceding level. With current technology and available radio
clocks, single-sample accuracies in the order of a millisecond can be
achieved at the network interface of a primary server. Accuracies of
this order require special care in the design and implementation of the
operating system and the local-clock mechanism, such as described in
Section 5.

As the stratum increases from one, the single-sample accuracies
achievable will degrade depending on the network paths and local-clock
stabilities. In order to avoid the tedious calculations [BRA80]
necessary to estimate errors in each specific configuration, it is
useful to assume the mean measurement errors accumulate approximately in
proportion to the measured delay and dispersion relative to the root of
the synchronization subnet. Appendix H contains an analysis of errors,
including a derivation of maximum error as a function of delay and
dispersion, where the latter quantity depends on the precision of the
timekeeping system, frequency tolerance of the local clock and various
residuals. Assuming the primary servers are synchronized to standard
time within known accuracies, this provides a reliable, determistic
specification on timekeeping accuracies throughout the synchronization

Again drawing from the experience of the telephone industry, which
learned such lessons at considerable cost [ABA89], the synchronization
subnet topology should be organized to produce the highest accuracy, but
must never be allowed to form a loop. An additional factor is that each
increment in stratum involves a potentially unreliable time server which
introduces additional measurement errors. The selection algorithm used
in NTP uses a variant of the Bellman-Ford distributed routing algorithm
[37] to compute the minimum-weight spanning trees rooted on the primary
servers. The distance metric used by the algorithm consists of the
(scaled) stratum plus the synchronization distance, which itself
consists of the dispersion plus one-half the absolute delay. Thus, the
synchronization path will always take the minimum number of servers to
the root, with ties resolved on the basis of maximum error.

As a result of this design, the subnet reconfigures automatically in a
hierarchical-master-slave configuration to produce the most accurate and
reliable time, even when one or more primary or secondary servers or the
network paths between them fail. This includes the case where all normal
primary servers (e.g., highly accurate WWVB radio clock operating at the
lowest synchronization distances) on a possibly partitioned subnet fail,
but one or more backup primary servers (e.g., less accurate WWV radio
clock operating at higher synchronization distances) continue operation.
However, should all primary servers throughout the subnet fail, the
remaining secondary servers will synchronize among themselves while

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distances ratchet upwards to a preselected maximum <169>infinity<170>
due to the well-known properties of the Bellman-Ford algorithm. Upon
reaching the maximum on all paths, a server will drop off the subnet and
free-run using its last determined time and frequency. Since these
computations are expected to be very precise, especially in frequency,
even extended outage periods can result in timekeeping errors not
greater than a few milliseconds per day with appropriately stabilized
oscillators (see Section 5).

In the case of multiple primary servers, the spanning-tree computation
will usually select the server at minimum synchronization distance.
However, when these servers are at approximately the same distance, the
computation may result in random selections among them as the result of
normal dispersive delays. Ordinarily, this does not degrade accuracy as
long as any discrepancy between the primary servers is small compared to
the synchronization distance. If not, the filter and selection
algorithms will select the best of the available servers and cast out
outlyers as intended.

Network Time Protocol

This section consists of a formal definition of the Network Time
Protocol, including its data formats, entities, state variables, events
and event-processing procedures. The specification is based on the
implementation model illustrated in Figure 1, but it is not intended
that this model is the only one upon which a specification can be based.
In particular, the specification is intended to illustrate and clarify
the intrinsic operations of NTP, as well as to serve as a foundation for
a more rigorous, comprehensive and verifiable specification.

Data Formats

All mathematical operations expressed or implied herein are in two's-
complement, fixed-point arithmetic. Data are specified as integer or
fixed-point quantities, with bits numbered in big-endian fashion from
zero starting at the left, or high-order, position. Since various
implementations may scale externally derived quantities for internal
use, neither the precision nor decimal-point placement for fixed-point
quantities is specified. Unless specified otherwise, all quantities are
unsigned and may occupy the full field width with an implied zero
preceding bit zero. Hardware and software packages designed to work with
signed quantities will thus yield surprising results when the most
significant (sign) bit is set. It is suggested that externally derived,
unsigned fixed-point quantities such as timestamps be shifted right one
bit for internal use, since the precision represented by the full field
width is seldom justified.

Since NTP timestamps are cherished data and, in fact, represent the main
product of the protocol, a special timestamp format has been
established. NTP timestamps are represented as a 64-bit unsigned fixed-

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point number, in seconds relative to 0h on 1 January 1900. The integer
part is in the first 32 bits and the fraction part in the last 32 bits.
This format allows convenient multiple-precision arithmetic and
conversion to Time Protocol representation (seconds), but does
complicate the conversion to ICMP Timestamp message representation
(milliseconds). The precision of this representation is about 200
picoseconds, which should be adequate for even the most exotic

Timestamps are determined by copying the current value of the local
clock to a timestamp when some significant event, such as the arrival of
a message, occurs. In order to maintain the highest accuracy, it is
important that this be done as close to the hardware or software driver
associated with the event as possible. In particular, departure
timestamps should be redetermined for each link-level retransmission. In
some cases a particular timestamp may not be available, such as when the
host is rebooted or the protocol first starts up. In these cases the 64-
bit field is set to zero, indicating the value is invalid or undefined.

Note that since some time in 1968 the most significant bit (bit 0 of the
integer part) has been set and that the 64-bit field will overflow some
time in 2036. Should NTP be in use in 2036, some external means will be
necessary to qualify time relative to 1900 and time relative to 2036
(and other multiples of 136 years). Timestamped data requiring such
qualification will be so precious that appropriate means should be
readily available. There will exist an 200-picosecond interval,
henceforth ignored, every 136 years when the 64-bit field will be zero
and thus considered invalid.

State Variables and Parameters

Following is a summary of the various state variables and parameters
used by the protocol. They are separated into classes of system
variables, which relate to the operating system environment and local-
clock mechanism; peer variables, which represent the state of the
protocol machine specific to each peer; packet variables, which
represent the contents of the NTP message; and parameters, which
represent fixed configuration constants for all implementations of the
current version. For each class the description of the variable is
followed by its name and the procedure or value which controls it. Note
that variables are in lower case, while parameters are in upper case.
Additional details on formats and use are presented in later sections
and Appendices.

Common Variables

The following variables are common to two or more of the system, peer
and packet classes. Additional variables are specific to the optional
authentication mechanism as described in Appendix C. When necessary to
distinguish between common variables of the same name, the variable

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identifier will be used.

Peer Address (peer.peeraddr, pkt.peeraddr), Peer Port (peer.peerport,
pkt.peerport): These are the 32-bit Internet address and 16-bit port
number of the peer.

Host Address (peer.hostaddr, pkt.hostaddr), Host Port (peer.hostport,
pkt.hostport): These are the 32-bit Internet address and 16-bit port
number of the host. They are included among the state variables to
support multi-homing.

Leap Indicator (sys.leap, peer.leap, pkt.leap): This is a two-bit code
warning of an impending leap second to be inserted in the NTP timescale.
The bits are set before 23:59 on the day of insertion and reset after
00:00 on the following day. This causes the number of seconds (rollover
interval) in the day of insertion to be increased or decreased by one.
In the case of primary servers the bits are set by operator
intervention, while in the case of secondary servers the bits are set by
the protocol. The two bits, bit 0 and bit 1, respectively, are coded as
ABOVE(.0830), BELOW(.0830), HGUTTER(.0560), KEEP(OFF), ALIGN(CT)


00, no warning

01, last minute has 61 seconds

10, last minute has 59 seconds

11, alarm condition (clock not synchronized)


In all except the alarm condition (112), NTP itself does nothing with
these bits, except pass them on to the time-conversion routines that are
not part of NTP. The alarm condition occurs when, for whatever reason,
the local clock is not synchronized, such as when first coming up or
after an extended period when no primary reference source is available.

Mode (peer.mode, pkt.mode): This is an integer indicating the
association mode, with values coded as follows:

ABOVE(.0830), BELOW(.0830), HGUTTER(.0560), KEEP(OFF), ALIGN(CT)


0, unspecified

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1, symmetric active

2, symmetric passive

3, client

4, server

5, broadcast

6, reserved for NTP control messages

7, reserved for private use


Stratum (sys.stratum, peer.stratum, pkt.stratum): This is an integer
indicating the stratum of the local clock, with values defined as

ABOVE(.0830), BELOW(.0830), HGUTTER(.0560), KEEP(OFF), ALIGN(CT)


0, unspecified

1, primary reference (e.g.,, calibrated atomic clock,, radio clock)

2-255, secondary reference (via NTP)


For comparison purposes a value of zero is considered greater than any
other value. Note that the maximum value of the integer encoded as a
packet variable is limited by the parameter NTP.MAXSTRATUM.

Poll Interval (sys.poll, peer.hostpoll, peer.peerpoll, pkt.poll): This
is a signed integer indicating the minimum interval between transmitted
messages, in seconds as a power of two. For instance, a value of six
indicates a minimum interval of 64 seconds.

Precision (sys.precision, peer.precision, pkt.precision): This is a
signed integer indicating the precision of the various clocks, in
seconds to the nearest power of two. The value must be rounded to the
next larger power of two; for instance, a 50-Hz (20 ms) or 60-Hz (16.67
ms) power-frequency clock would be assigned the value -5 (31.25 ms),
while a 1000-Hz (1 ms) crystal-controlled clock would be assigned the
value -9 (1.95 ms).

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Root Delay (sys.rootdelay, peer.rootdelay, pkt.rootdelay): This is a
signed fixed-point number indicating the total roundtrip delay to the
primary reference source at the root of the synchronization subnet, in
seconds. Note that this variable can take on both positive and negative
values, depending on clock precision and skew.

Root Dispersion (sys.rootdispersion, peer.rootdispersion,
pkt.rootdispersion): This is a signed fixed-point number indicating the
maximum error relative to the primary reference source at the root of
the synchronization subnet, in seconds. Only positive values greater
than zero are possible.

Reference Clock Identifier (sys.refid, peer.refid, pkt.refid): This is a
32-bit code identifying the particular reference clock. In the case of
stratum 0 (unspecified) or stratum 1 (primary reference source), this is
a four-octet, left-justified, zero-padded ASCII string, for example (see
Appendix A for comprehensive list):

WIDTH(4.1700), ABOVE(.1670), BELOW(.0830), HGUTTER(.3330),


Stratum, Code, Meaning


0, DCN, DCN routing protocol

0, TSP, TSP time protocol

1, ATOM, Atomic clock (calibrated)

1, WWVB, WWVB LF (band 5) radio

1, GOES, GOES UHF (band 9) satellite


1, WWV, WWV HF (band 7) radio


In the case of stratum 2 and greater (secondary reference) this is the
four-octet Internet address of the peer selected for synchronization.

Reference Timestamp (sys.reftime, peer.reftime, pkt.reftime): This is
the local time, in timestamp format, when the local clock was last

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updated. If the local clock has never been synchronized, the value is

Originate Timestamp (, This is the local time, in
timestamp format, at the peer when its latest NTP message was sent. If
the peer becomes unreachable the value is set to zero.

Receive Timestamp (peer.rec, pkt.rec): This is the local time, in
timestamp format, when the latest NTP message from the peer arrived. If
the peer becomes unreachable the value is set to zero.

Transmit Timestamp (peer.xmt, pkt.xmt): This is the local time, in
timestamp format, at which the NTP message departed the sender.

System Variables

Table 1<$&tab1> shows the complete set of system variables. In addition
to the common variables described previously, the following variables
are used by the operating system in order to synchronize the local

Local Clock (sys.clock): This is the current local time, in timestamp
format. Local time is derived from the hardware clock of the particular
machine and increments at intervals depending on the design used. An
appropriate design, including slewing and skew-Compensation mechanisms,
is described in Section 5.

Clock Source (sys.peer): This is a selector identifying the current
synchronization source. Usually this will be a pointer to a structure
containing the peer variables. The special value NULL indicates there is
no currently valid synchronization source.

Peer Variables

Table 2 shows the complete set of peer variables. In addition to the
common variables described previously, the following variables are used
by the peer management and measurement functions.

Configured Bit (peer.config): This is a bit indicating that the
association was created from configuration information and should not be
demobilized if the peer becomes unreachable.

Update Timestamp (peer.update): This is the local time, in timestamp
format, when the most recent NTP message was received. It is used in
calculating the skew dispersion.

Reachability Register (peer.reach): This is a shift register of
NTP.WINDOW bits used to determine the reachability status of the peer,
with bits entering from the least significant (rightmost) end. A peer is
considered reachable if at least one bit in this register is set to one.

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Peer Timer (peer.timer): This is an integer counter used to control the
interval between transmitted NTP messages. Once set to a nonzero value,
the counter decrements at one-second intervals until reaching zero, at
which time the transmit procedure is called. Note that the operation of
this timer is independent of local-clock updates, which implies that the
timekeeping system and interval-timer system architecture must be
independent of each other.<$&tab2>

Packet Variables

Table 3<$&tab3> shows the complete set of packet variables. In addition
to the common variables described previously, the following variables
are defined.

Version Number (pkt.version): This is an integer indicating the version
number of the sender. NTP messages will always be sent with the current
version number NTP.VERSION and will always be accepted if the version
number matches NTP.VERSION. Exceptions may be advised on a case-by-case
basis at times when the version number is changed. Specific guidelines
for interoperation between this version and previous versions of NTP are
summarized in Appendix D.

Clock-Filter Variables

When the filter and selection algorithms suggested in Section 4 are
used, the following state variables are defined in addition to the
variables described previously.

Filter Register (peer.filter): This is a shift register of NTP.SHIFT
stages, where each stage stores a 3-tuple consisting of the measured
delay, measured offset and calculated dispersion associated with a
single observation. These 3-tuples enter from the most significant
(leftmost) right and are shifted towards the least significant
(rightmost) end and eventually discarded as new observations arrive.

Valid Data Counter (peer.valid): This is an integer counter indicating
the valid samples remaining in the filter register. It is used to
determine the reachability state and when the poll interval should be
increased or decreased.

Offset (peer.offset): This is a signed, fixed-point number indicating
the offset of the peer clock relative to the local clock, in seconds.

Delay (peer.delay): This is a signed fixed-point number indicating the
roundtrip delay of the peer clock relative to the local clock over the
network path between them, in seconds. Note that this variable can take
on both positive and negative values, depending on clock precision and
skew-error accumulation.

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Dispersion (peer.dispersion): This is a signed fixed-point number
indicating the maximum error of the peer clock relative to the local
clock over the network path between them, in seconds. Only positive
values greater than zero are possible.

Authentication Variables

When the authentication mechanism suggested in Appendix C is used, the
following state variables are defined in addition to the variables
described previously. These variables are used only if the optional
authentication mechanism described in Appendix C is implemented.

Authentication Enabled Bit (peer.authenable): This is a bit indicating
that the association is to operate in the authenticated mode.

Authenticated Bit (peer.authentic): This is a bit indicating that the
last message received from the peer has been correctly authenticated.

Key Identifier (peer.hostkeyid, peer.peerkeyid, pkt.keyid): This is an
integer identifying the cryptographic key used to generate the message-
authentication code.

Cryptographic Keys (sys.key): This is a set of 64-bit DES keys. Each key
is constructed as in the Berkeley Unix distributions, which consists of
eight octets, where the seven low-order bits of each octet correspond to
the DES bits 1-7 and the high-order bit corresponds to the DES odd-
parity bit 8.

Crypto-Checksum (pkt.check): This is a crypto-checksum computed by the
encryption procedure.


Table 4<$&tab4> shows the parameters assumed for all implementations
operating in the Internet system. It is necessary to agree on the values
for these parameters in order to avoid unnecessary network overheads and
stable peer associations. The following parameters are assumed fixed and
applicable to all associations.

Version Number (NTP.VERSION): This is the current NTP version number

NTP Port (NTP.PORT): This is the port number (123) assigned by the
Internet Assigned Numbers Authority to NTP.

Maximum Stratum (NTP.MAXSTRATUM): This is the maximum stratum value that
can be encoded as a packet variable, also interpreted as
<169>infinity<170> or unreachable by the subnet routing algorithm.

Maximum Clock Age (NTP.MAXAGE): This is the maximum interval a reference

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clock will be considered valid after its last update, in seconds.

Maximum Skew (NTP.MAXSKEW): This is the maximum offset error due to skew
of the local clock over the interval determined by NTP.MAXAGE, in
seconds. The ratio <$Ephi~=~roman {NTP.MAXSKEW over NTP.MAXAGE}> is
interpreted as the maximum possible skew rate due to all causes.

Maximum Distance (NTP.MAXDISTANCE): When the selection algorithm
suggested in Section 4 is used, this is the maximum synchronization
distance for peers acceptable for synchronization.

Minimum Poll Interval (NTP.MINPOLL): This is the minimum poll interval
allowed by any peer of the Internet system, in seconds to a power of

Maximum Poll Interval (NTP.MAXPOLL): This is the maximum poll interval
allowed by any peer of the Internet system, in seconds to a power of

Minimum Select Clocks (NTP.MINCLOCK): When the selection algorithm
suggested in Section 4 is used, this is the minimum number of peers
acceptable for synchronization.

Maximum Select Clocks (NTP.MAXCLOCK): When the selection algorithm
suggested in Section 4 is used, this is the maximum number of peers
considered for selection.

Minimum Dispersion (NTP.MINDISPERSE): When the filter algorithm
suggested in Section 4 is used, this is the minimum dispersion increment
for each stratum level, in seconds.

Maximum Dispersion (NTP.MAXDISPERSE): When the filter algorithm
suggested in Section 4 is used, this is the maximum peer dispersion and
the dispersion assumed for missing data, in seconds.

Reachability Register Size (NTP.WINDOW): This is the size of the
reachability register (peer.reach), in bits.

Filter Size (NTP.SHIFT): When the filter algorithm suggested in Section
4 is used, this is the size of the clock filter (peer.filter) shift
register, in stages.
Filter Weight (NTP.FILTER): When the filter algorithm suggested in
Section 4 is used, this is the weight used to compute the filter

Select Weight (NTP.SELECT): When the selection algorithm suggested in
Section 4 is used, this is the weight used to compute the select

Modes of Operation

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Except in broadcast mode, an NTP association is formed when two peers
exchange messages and one or both of them create and maintain an
instantiation of the protocol machine, called an association. The
association can operate in one of five modes as indicated by the host-
mode variable (peer.mode): symmetric active, symmetric passive, client,
server and broadcast, which are defined as follows:

Symmetric Active (1): A host operating in this mode sends periodic
messages regardless of the reachability state or stratum of its peer. By
operating in this mode the host announces its willingness to synchronize
and be synchronized by the peer.

Symmetric Passive (2): This type of association is ordinarily created
upon arrival of a message from a peer operating in the symmetric active
mode and persists only as long as the peer is reachable and operating at
a stratum level less than or equal to the host; otherwise, the
association is dissolved. However, the association will always persist
until at least one message has been sent in reply. By operating in this
mode the host announces its willingness to synchronize and be
synchronized by the peer.

Client (3): A host operating in this mode sends periodic messages
regardless of the reachability state or stratum of its peer. By
operating in this mode the host, usually a LAN workstation, announces
its willingness to be synchronized by, but not to synchronize the peer.

Server (4): This type of association is ordinarily created upon arrival
of a client request message and exists only in order to reply to that
request, after which the association is dissolved. By operating in this
mode the host, usually a LAN time server, announces its willingness to
synchronize, but not to be synchronized by the peer.

Broadcast (5): A host operating in this mode sends periodic messages
regardless of the reachability state or stratum of the peers. By
operating in this mode the host, usually a LAN time server operating on
a high-speed broadcast medium, announces its willingness to synchronize
all of the peers, but not to be synchronized by any of them.

A host operating in client mode occasionally sends an NTP message to a
host operating in server mode, perhaps right after rebooting and at
periodic intervals thereafter. The server responds by simply
interchanging addresses and ports, filling in the required information
and returning the message to the client. Servers need retain no state
information between client requests, while clients are free to manage
the intervals between sending NTP messages to suit local conditions. In
these modes the protocol machine described in this document can be
considerably simplified to a simple remote-procedure-call mechanism
without significant loss of accuracy or robustness, especially when
operating over high-speed LANs.

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In the symmetric modes the client/server distinction (almost)
disappears. Symmetric passive mode is intended for use by time servers
operating near the root nodes (lowest stratum) of the synchronization
subnet and with a relatively large number of peers on an intermittent
basis. In this mode the identity of the peer need not be known in
advance, since the association with its state variables is created only
when an NTP message arrives. Furthermore, the state storage can be
reused when the peer becomes unreachable or is operating at a higher
stratum level and thus ineligible as a synchronization source.

Symmetric active mode is intended for use by time servers operating near
the end nodes (highest stratum) of the synchronization subnet. Reliable
time service can usually be maintained with two peers at the next lower
stratum level and one peer at the same stratum level, so the rate of
ongoing polls is usually not significant, even when connectivity is lost
and error messages are being returned for every poll.

Normally, one peer operates in an active mode (symmetric active, client
or broadcast modes) as configured by a startup file, while the other
operates in a passive mode (symmetric passive or server modes), often
without prior configuration. However, both peers can be configured to
operate in the symmetric active mode. An error condition results when
both peers operate in the same mode, but not symmetric active mode. In
such cases each peer will ignore messages from the other, so that prior
associations, if any, will be demobilized due to reachability failure.

Broadcast mode is intended for operation on high-speed LANs with
numerous workstations and where the highest accuracies are not required.
In the typical scenario one or more time servers on the LAN send
periodic broadcasts to the workstations, which then determine the time
on the basis of a preconfigured latency in the order of a few
milliseconds. As in the client/server modes the protocol machine can be
considerably simplified in this mode; however, a modified form of the
clock selection algorithm may prove useful in cases where multiple time
servers are used for enhanced reliability.

Event Processing

The significant events of interest in NTP occur upon expiration of a
peer timer (peer.timer), one of which is dedicated to each peer with an
active association, and upon arrival of an NTP message from the various
peers. An event can also occur as the result of an operator command or
detected system fault, such as a primary reference source failure. This
section describes the procedures invoked when these events occur.

Notation Conventions

The NTP filtering and selection algorithms act upon a set of variables
for clock offset (<$Etheta ,~THETA>), roundtrip delay (<$Edelta

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,~DELTA>) and dispersion (<$Eepsilon ,~EPSILON>). When necessary to
distinguish between them, lower-case Greek letters are used for
variables relative to a peer, while upper-case Greek letters are used
for variables relative to the primary reference source(s), i.e., via the
peer to the root of the synchronization subnet. Subscripts will be used
to identify the particular peer when this is not clear from context. The
algorithms are based on a quantity called the synchronization distance
(<$Elambda ,~LAMBDA>), which is computed from the roundtrip delay and
dispersion as described below.

As described in Appendix H, the peer dispersion <$Eepsilon> includes
contributions due to measurement error <$Erho~=~1~<< <<~roman
sys.precision>, skew-error accumulation <$Ephi tau>, where
<$Ephi~=~roman {NTP.MAXSKEW over NTP.MAXAGE}> is the maximum skew rate
and <$Etau~=~roman {sys.clock~-~peer.update}> is the interval since the
last update, and filter (sample) dispersion <$Eepsilon sub sigma>
computed by the clock-filter algorithm. The root dispersion <$EEPSILON>
includes contributions due to the selected peer dispersion <$Eepsilon>
and skew-error accumulation <$Ephi tau>, together with the root
dispersion for the peer itself. The system dispersion includes the
select (sample) dispersion <$Eepsilon sub xi> computed by the clock-
select algorithm and the absolute initial clock offset <$E| THETA |>
provided to the local-clock algorithm. Both <$Eepsilon> and <$EEPSILON>
are dynamic quantities, since they depend on the elapsed time <$Etau>
since the last update, as well as the sample dispersions calculated by
the algorithms.

Each time the relevant peer variables are updated, all dispersions
associated with that peer are updated to reflect the skew-error
accumulation. The computations can be summarized as follows:

<$Etheta~==~roman peer.offset> ,
<$Edelta~==~roman peer.delay> ,
<$Eepsilon~==~roman peer.dispersion~=~rho~+~phi tau~+~epsilon sub sigma>
<$Elambda~==~epsilon~+~{| delta |} over 2> ,

where <$Etau> is the interval since the original timestamp (from which
<$Etheta> and <$Edelta> were determined) was transmitted to the present
time and <$Eepsilon sub sigma> is the filter dispersion (see clock-
filter procedure below). The variables relative to the root of the
synchronization subnet via peer i are determined as follows:

<$ETHETA sub i~==~theta sub i> ,
<$EDELTA sub i~==~roman peer.rootdelay~+~delta sub i> ,
<$EEPSILON sub i~==~roman peer.rootdispersion~+~epsilon sub i~+~phi tau
sub i> ,
<$ELAMBDA sub i~==~EPSILON sub i~+~{| DELTA sub i |} over 2> ,

where all variables are understood to pertain to the ith peer. Finally,

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assuming the ith peer is selected for synchronization, the system
variables are determined as follows:

<$ETHETA~=~>combined final offset ,
<$EDELTA~=~DELTA sub i> ,
<$EEPSILON~=~EPSILON sub i~+~epsilon sub xi~+~| THETA |> ,
<$ELAMBDA~=~LAMBDA sub i> ,

where <$Eepsilon sub xi> is the select dispersion (see clock-selection
procedure below).

Informal pseudo-code which accomplishes these computations is presented
below. Note that the pseudo-code is represented in no particular
language, although it has many similarities to the C language. Specific
details on the important algorithms are further illustrated in the C-
language routines in Appendix I.

Transmit Procedure

The transmit procedure is executed when the peer timer decrements to
zero for all modes except client mode with a broadcast server and server
mode in all cases. In client mode with a broadcast server messages are
never sent. In server mode messages are sent only in response to
received messages. This procedure is also called by the receive
procedure when an NTP message arrives that does not result in a
persistent association.

begin transmit procedure

The following initializes the packet buffer and copies the packet
variables. The value skew is necessary to account for the skew-error
accumulated over the interval since the local clock was last set.

        <$Eroman pkt.peeraddr~<<-~roman peer.hostaddr>;         /* copy
system and peer variables */
        <$Eroman pkt.peerport~<<-~roman peer.hostport>;
        <$Eroman pkt.hostaddr~<<-~roman peer.peeraddr>;
        <$Eroman pkt.hostport~<<-~roman peer.peerport>;
        <$Eroman pkt.leap~<<-~roman sys.leap>;
        <$Eroman pkt.version~<<-~roman NTP.VERSION>;
        <$Eroman pkt.mode~<<-~roman peer.mode>;
        <$Eroman pkt.stratum~<<-~roman sys.stratum>;
        <$Eroman pkt.poll~<<-~roman peer.hostpoll>;
        <$Eroman pkt.precision~<<-~roman sys.precision>;
        <$Eroman pkt.rootdelay~<<-~roman sys.rootdelay>;
        if (sys.leap = 112 or (sys.clock <196> sys.reftime) >>
                <$Eskew~<<-~roman NTP.MAXSKEW>;
                <$Eskew~<<-~phi roman {(sys.clock~-~sys.reftime)}>;

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        <$Eroman {pkt.rootdispersion~<<-~roman
sys.rootdispersion~+~(1~<< <<~sys.precision)}~+~skew>;
        <$Eroman pkt.refid~<<-~roman sys.refid>;
        <$Eroman pkt.reftime~<<-~roman sys.reftime>;

The transmit timestamp pkt.xmt will be used later in order to validate
the reply; thus, implementations must save the exact value transmitted.
In addition, the order of copying the timestamps should be designed so
that the time to format and copy the data does not degrade accuracy.

/* copy timestamps */
        <$Eroman pkt.rec~<<-~roman peer.rec>;
        <$Eroman pkt.xmt~<<-~roman sys.clock>;
        <$Eroman peer.xmt~<<-~roman pkt.xmt>;

The call to encrypt is implemented only if authentication is
implemented. If authentication is enabled, the delay to encrypt the
authenticator may degrade accuracy. Therefore, implementations should
include a system state variable (not mentioned elsewhere in this
specification) which contains an offset calculated to match the expected
encryption delay and correct the transmit timestamp as obtained from the
local clock.

        #ifdef (authentication implemented)     /* see Appendix C */
                call encrypt;
        send packet;

The reachability register is shifted one position to the left, with zero
replacing the vacated bit. If all bits of this register are zero, the
clear procedure is called to purge the clock filter and reselect the
synchronization source, if necessary. If the association was not
configured by the initialization procedure, the association is

        <$Eroman peer.reach~<<-~roman peer.reach~<< <<~1>;              
/* update reachability */
        if (<$Eroman peer.reach~=~0> and <$Eroman peer.config~=~0>)
                demobilize association;

If valid data have been shifted into the filter register at least once
during the preceding two poll intervals (low-order bit of peer.reach set
to one), the valid data counter is incremented. After eight such valid
intervals the poll interval is incremented. Otherwise, the valid data
counter and poll interval are both decremented and the clock-filter
procedure called with zero values for offset and delay and

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NTP.MAXDISPERSE for dispersion. The clock-select procedure is called to
reselect the synchronization source, if necessary.

        if (<$Eroman peer.reach~&~6~!=~0>)                      /* test
two low-order bits (shifted) */ 
                if (<$Eroman peer.valid~<<~roman NTP.SHIFT>)    /* valid
data received */
                        <$Eroman peer.valid~<<-~roman peer.valid~+~1>;
                        else <$Eroman peer.hostpoll~<<-~roman
        else begin
                <$Eroman peer.valid~<<-~roman peer.valid~-~1>;  /*
nothing heard */
                <$Eroman peer.hostpoll~<<-~roman peer.hostpoll~-~1>);
                call clock-filter(0, 0, NTP.MAXDISPERSE);
                call clock-select;                      /* select clock
source */
        call poll-update;
        end transmit procedure;

Receive Procedure

The receive procedure is executed upon arrival of an NTP message. It
validates the message, interprets the various modes and calls other
procedures to filter the data and select the synchronization source. If
the version number in the packet does not match the current version, the
message may be discarded; however, exceptions may be advised on a case-
by-case basis at times when the version is changed. If the NTP control
messages described in Appendix B are implemented and the packet mode is
6 (control), the control-message procedure is called. The source and
destination Internet addresses and ports in the IP and UDP headers are
matched to the correct peer. If there is no match a new instantiation of
the protocol machine is created and the association mobilized.

begin receive procedure
        if (<$Eroman pkt.version~!=~roman NTP.VERSION>) exit;
        #ifdef (control messages implemented)
                if (<$Eroman pkt.mode~=~6>) call control-message;
        for (all associations)                  /* access control goes
here */
                match addresses and ports to associations;
        if (no matching association)
                call receive-instantiation procedure;   /* create
association */

The call to decrypt is implemented only if authentication is

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        #ifdef (authentication implemented)     /* see Appendix C */
                call decrypt;

If the packet mode is nonzero, this becomes the value of mode used in
the following step; otherwise, the peer is an old NTP version and mode
is determined from the port numbers as described in Section 3.3.

        if (pkt.mode = 0)                               /* for
compatibility with old versions */
                <$Emode~<<-~>(see Section 3.3);
                <$Emode~<<-~roman pkt.mode>;

Table 5<$&tab5> shows for each combination of peer.mode and mode the
resulting case labels.

        case (mode, peer.hostmode)              /* see Table 5 */

If error the packet is simply ignored and the association demobilized,
if not previously configured.
error:          if (<$Eroman peer.config~=~0>) demobilize association;  
/* see no evil */

If recv the packet is processed and the association marked reachable if
tests five through eight (valid header) enumerated in the packet
procedure succeed. If, in addition, tests one through four succeed
(valid data), the clock-update procedure is called to update the local
clock. Otherwise, if the association was not previously configured, it
is demobilized.

recv:           call packet;                            /* process
packet */
                if (valid header) begin         /* if valid header,
update local clock */
                        <$Eroman peer.reach~<<-~roman peer.reach~|~1>;
                        if (valid data) call clock-update;
                        if (<$Eroman peer.config~=~0>) demobilize

If xmit the packet is processed and an immediate reply is sent. The
association is then demobilized if not previously configured.

xmit:           call packet;                            /* process
packet */
                <$Eroman peer.hostpoll~<<-~roman peer.peerpoll>;        

Top       Page 33 
/* send immediate reply */
                call poll-update;
                call transmit;
                if (<$Eroman peer.config~=~0>) demobilize association;

If pkt the packet is processed and the association marked reachable if
tests five through eight (valid header) enumerated in the packet
procedure succeed. If, in addition, tests one through four succeed
(valid data), the clock-update procedure is called to update the local
clock. Otherwise, if the association was not previously configured, an
immediate reply is sent and the association demobilized.

pkt:            call packet;                            /* process
packet */
                if (valid header) begin         /* if valid header,
update local clock */
                        <$Eroman peer.reach~<<-~roman peer.reach~|~1>;
                        if (valid data) call clock-update;
                else if (<$Eroman peer.config~=~0>) begin
                        <$Eroman peer.hostpoll~<<-~roman
peer.peerpoll>; /* send immediate reply */
                        call poll-update;
                        call transmit;
                        demobilize association;
        end receive procedure;

Packet Procedure

The packet procedure checks the message validity, computes delay/offset
samples and calls other procedures to filter the data and select the
synchronization source. Test 1 requires the transmit timestamp not match
the last one received from the same peer; otherwise, the message might
be an old duplicate. Test 2 requires the originate timestamp match the
last one sent to the same peer; otherwise, the message might be out of
order, bogus or worse. In case of broadcast mode (5) the apparent
roundtrip delay will be zero and the full accuracy of the time-transfer
operation may not be achievable. However, the accuracy achieved may be
adequate for most purposes. The poll-update procedure is called with
argument peer.hostpoll (peer.peerpoll may have changed).

begin packet procedure
        <$Eroman peer.rec~<<-~roman sys.clock>;                 /*
capture receive timestamp */
        if (<$Eroman pkt.mode ~!=~5>) begin
                <$Etest1~<<-~( roman {pkt.xmt~!})>;   /* test
1 */

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                <$Etest2~<<-~( roman {})>;    /* test
2 */
        else begin
                <$Eroman<<-~roman peer.rec>;                   
/* fudge missing timestamps */
                <$Eroman pkt.rec~<<-~roman pkt.xmt>;
                <$Etest1~<<-~bold roman true>;                          
/* fake tests */
                <$Etest2~<<-~bold roman true>;
        <$Eroman<<-~roman pkt.xmt>;                           
/* update originate timestamp */
        <$Eroman peer.peerpoll~<<-~roman pkt.poll>;                     
/* adjust poll interval */
        call poll-update(peer.hostpoll);

Test 3 requires that both the originate and receive timestamps are
nonzero. If either of the timestamps are zero, the association has not
synchronized or has lost reachability in one or both directions.

        <$Etest3~<<-~( roman!=~0> and <$Eroman pkt.rec~!=~0)>; 
/* test 3 */

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 2<$&fig2> and let i be an even integer. Then Ti-3, Ti-2,
Ti-1 and Ti are the contents of the, pkt.rec, pkt.xmt and
peer.rec variables, respectively. The clock offset <$Etheta>, roundtrip
delay <$Edelta> and dispersion <$Eepsilon> of the host relative to the
peer is:

<$Edelta~=~(T sub i~-~T sub {i - 3} )~-~(T sub {i - 1}~-~T sub {i - 2}
)> ,
<$Etheta~=~{(T sub {i - 2}~-~T sub {i-3})~+~(T sub {i-1}~-~T sub i ) }
over 2> ,
<$Eepsilon~=~roman {(1~<< <<~sys.precision})~+~phi (T sub i ~-~T sub {i-
3} )> ,

where, as before, <$Ephi~=~roman{ NTP.MAXSKEW over NTP.MAXAGE}>. The
quantity <$Eepsilon> represents the maximum error or dispersion due to
measurement error at the host and local-clock skew accumulation over the
interval since the last message was transmitted to the peer.
Subsequently, the dispersion will be updated by the clock-filter

The above method amounts to a continuously sampled, returnable-time
system, which is used in some digital telephone networks [BEL86]. Among
the advantages are that the order and timing of the messages are
unimportant and that reliable delivery is not required. Obviously, the

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