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RFC 1305 - Network Time Protocol (Version 3) Specification, Implementation
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
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
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
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
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.
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
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
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.
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
subnet.
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
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-
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
requirements.
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
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
follows:
@Z_TBL_BEG = COLUMNS(2), DIMENSION(IN), COLWIDTHS(E1,E8), WIDTH(5.0000),
ABOVE(.0830), BELOW(.0830), HGUTTER(.0560), KEEP(OFF), ALIGN(CT)
@Z_TBL_BODY = TABLE TEXT, TABLE TEXT
00, no warning
01, last minute has 61 seconds
10, last minute has 59 seconds
11, alarm condition (clock not synchronized)
@Z_TBL_END =
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:
@Z_TBL_BEG = COLUMNS(2), DIMENSION(IN), COLWIDTHS(E1,E8), WIDTH(5.0000),
ABOVE(.0830), BELOW(.0830), HGUTTER(.0560), KEEP(OFF), ALIGN(CT)
@Z_TBL_BODY = TABLE TEXT, TABLE TEXT
0, unspecified
1, symmetric active
2, symmetric passive
3, client
4, server
5, broadcast
6, reserved for NTP control messages
7, reserved for private use
@Z_TBL_END =
Stratum (sys.stratum, peer.stratum, pkt.stratum): This is an integer
indicating the stratum of the local clock, with values defined as
follows:
@Z_TBL_BEG = COLUMNS(2), DIMENSION(IN), COLWIDTHS(E1,E8), WIDTH(5.0000),
ABOVE(.0830), BELOW(.0830), HGUTTER(.0560), KEEP(OFF), ALIGN(CT)
@Z_TBL_BODY = TABLE TEXT, TABLE TEXT
0, unspecified
1, primary reference (e.g.,, calibrated atomic clock,, radio clock)
2-255, secondary reference (via NTP)
@Z_TBL_END =
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).
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):
@Z_TBL_BEG = COLUMNS(3), DIMENSION(IN), COLWIDTHS(E2,E2,E5),
WIDTH(4.1700), ABOVE(.1670), BELOW(.0830), HGUTTER(.3330),
BOX(Z_SINGLE), KEEP(ON), ALIGN(CT), L1(R1C0..R1C3)
@Z_TBL_BODY = TABLE CENTER, TABLE HEADER, TABLE HEADER
Stratum, Code, Meaning
@Z_TBL_BODY = TABLE CENTER, TABLE TEXT, TABLE TEXT
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
@Z_TBL_BODY = TABLE CENTER, TABLE HEADER, TABLE HEADER
1, WWV, WWV HF (band 7) radio
@Z_TBL_END =
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
updated. If the local clock has never been synchronized, the value is
zero.
Originate Timestamp (peer.org, pkt.org): 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
clock.
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.
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.
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.
Parameters
Table 4<$&tab4> shows the parameters assumed for all implementations
operating in the Internet system. It is necessary to agree on the values
for these parameters in order to avoid unnecessary network overheads and
stable peer associations. The following parameters are assumed fixed and
applicable to all associations.
Version Number (NTP.VERSION): This is the current NTP version number
(3).
NTP Port (NTP.PORT): This is the port number (123) assigned by the
Internet Assigned Numbers Authority to NTP.
Maximum Stratum (NTP.MAXSTRATUM): This is the maximum stratum value that
can be encoded as a packet variable, also interpreted as
<169>infinity<170> or unreachable by the subnet routing algorithm.
Maximum Clock Age (NTP.MAXAGE): This is the maximum interval a reference
clock will be considered valid after its last update, in seconds.
Maximum Skew (NTP.MAXSKEW): This is the maximum offset error due to skew
of the local clock over the interval determined by NTP.MAXAGE, in
seconds. The ratio <$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
two.
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
two.
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
dispersion.
Select Weight (NTP.SELECT): When the selection algorithm suggested in
Section 4 is used, this is the weight used to compute the select
dispersion.
Modes of Operation
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.
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
,~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,
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) >>
NTP.MAXAGE)
<$Eskew~<<-~roman NTP.MAXSKEW>;
else
<$Eskew~<<-~phi roman {(sys.clock~-~sys.reftime)}>;
<$Eroman {pkt.rootdispersion~<<-~roman
sys.rootdispersion~+~(1~<< <<~sys.precision)}~+~skew>;
<$Eroman pkt.refid~<<-~roman sys.refid>;
<$Eroman pkt.reftime~<<-~roman sys.reftime>;
The transmit timestamp pkt.xmt will be used later in order to validate
the reply; thus, implementations must save the exact value transmitted.
In addition, the order of copying the timestamps should be designed so
that the time to format and copy the data does not degrade accuracy.
<$Eroman pkt.org~<<-~roman peer.org>;
/* copy timestamps */
<$Eroman pkt.rec~<<-~roman peer.rec>;
<$Eroman pkt.xmt~<<-~roman sys.clock>;
<$Eroman peer.xmt~<<-~roman pkt.xmt>;
The call to encrypt is implemented only if authentication is
implemented. If authentication is enabled, the delay to encrypt the
authenticator may degrade accuracy. Therefore, implementations should
include a system state variable (not mentioned elsewhere in this
specification) which contains an offset calculated to match the expected
encryption delay and correct the transmit timestamp as obtained from the
local clock.
#ifdef (authentication implemented) /* see Appendix C */
call encrypt;
#endef
send packet;
The reachability register is shifted one position to the left, with zero
replacing the vacated bit. If all bits of this register are zero, the
clear procedure is called to purge the clock filter and reselect the
synchronization source, if necessary. If the association was not
configured by the initialization procedure, the association is
demobilized.
<$Eroman peer.reach~<<-~roman peer.reach~<< <<~1>;
/* update reachability */
if (<$Eroman peer.reach~=~0> and <$Eroman peer.config~=~0>)
begin
demobilize association;
exit;
endif
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
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
peer.hostpoll~+~1>;
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 */
endif
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;
#endef
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
implemented.
#ifdef (authentication implemented) /* see Appendix C */
call decrypt;
#endef
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 */
<$Emode~<<-~>(see Section 3.3);
else
<$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 */
break;
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 */
<$Eroman peer.reach~<<-~roman peer.reach~|~1>;
if (valid data) call clock-update;
endif
else
if (<$Eroman peer.config~=~0>) demobilize
association;
break;
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 */
<$Eroman peer.hostpoll~<<-~roman peer.peerpoll>;
/* send immediate reply */
call poll-update;
call transmit;
if (<$Eroman peer.config~=~0>) demobilize association;
break;
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 */
<$Eroman peer.reach~<<-~roman peer.reach~|~1>;
if (valid data) call clock-update;
endif
else if (<$Eroman peer.config~=~0>) begin
<$Eroman peer.hostpoll~<<-~roman
peer.peerpoll>; /* send immediate reply */
call poll-update;
call transmit;
demobilize association;
endif
endcase
end receive procedure;
Packet Procedure
The packet procedure checks the message validity, computes delay/offset
samples and calls other procedures to filter the data and select the
synchronization source. Test 1 requires the transmit timestamp not match
the last one received from the same peer; otherwise, the message might
be an old duplicate. Test 2 requires the originate timestamp match the
last one sent to the same peer; otherwise, the message might be out of
order, bogus or worse. In case of broadcast mode (5) the apparent
roundtrip delay will be zero and the full accuracy of the time-transfer
operation may not be achievable. However, the accuracy achieved may be
adequate for most purposes. The poll-update procedure is called with
argument peer.hostpoll (peer.peerpoll may have changed).
begin packet procedure
<$Eroman peer.rec~<<-~roman sys.clock>; /*
capture receive timestamp */
if (<$Eroman pkt.mode ~!=~5>) begin
<$Etest1~<<-~( roman {pkt.xmt~!=~peer.org})>; /* test
1 */
<$Etest2~<<-~( roman {pkt.org~=~peer.xmt})>; /* test
2 */
endif
else begin
<$Eroman pkt.org~<<-~roman peer.rec>;
/* fudge missing timestamps */
<$Eroman pkt.rec~<<-~roman pkt.xmt>;
<$Etest1~<<-~bold roman true>;
/* fake tests */
<$Etest2~<<-~bold roman true>;
endif
<$Eroman peer.org~<<-~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 pkt.org~!=~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.org, 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
procedure.
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
accuracies achievable depend upon the statistical properties of the
outbound and inbound data paths. Further analysis and experimental
results bearing on this issue can be found in [MIL90] and in Appendix H.
Test 4 requires that the calculated delay be within <169>reasonable<170>
bounds:
<$Etest4~<<-~(| delta |~<<~roman NTP.MAXDISPERSE~bold
and~epsilon~<<~roman NTP.MAXDISPERSE)>; /* test 4 */
Test 5 is implemented only if the authentication mechanism described in
Appendix C is implemented. It requires either that authentication be
explicitly disabled or that the authenticator be present and correct as
determined by the decrypt procedure.
#ifdef (authentication implemented) /* test 5 */
<$Etest5~<<-~( roman {(peer.config~=~1~bold
and~peer.authenable~=~0)~bold or~ peer.authentic~=~1})>;
#endef
Test 6 requires the peer clock be synchronized and the interval since
the peer clock was last updated be positive and less than NTP.MAXAGE.
Test 7 insures that the host will not synchronize on a peer with greater
stratum. Test 8 requires that the header contains <169>reasonable<170>
values for the pkt.rootdelay and pkt.rootdispersion fields.
<$Etest6~<<-~( roman pkt.leap~!=~11 sub 2> and /* test
6 */
<$Eroman
{pkt.reftime~<<=~pkt.xmt~<<~pkt.reftime~+~NTP.MAXAGE}>)
<$Etest7~<<-~roman {pkt.stratum ~<<=~sys.stratum}> and /* test
7 */
<$Eroman {pkt.stratum ~<<~NTP.MAXSTRATUM}>;
<$Etest8~<<-~( roman {| pkt.rootdelay |~<<~NTP.MAXDISPERSE}>
and /* test 8 */
<$Eroman {pkt.rootdispersion~<<~NTP.MAXDISPERSE})>;
With respect to further processing, the packet includes valid
(synchronized) data if tests one through four succeed
<$E(test1~&~test2~&~test3~&~test4~=~1)>, regardless of the remaining
tests. Only packets with valid data can be used to calculate offset,
delay and dispersion values. The packet includes a valid header if tests
five through eight succeed <$E(test5~&~test6~&~test7~&~test8~=~1)>,
regardless of the remaining tests. Only packets with valid headers can
be used to determine whether a peer can be selected for synchronization.
Note that <$Etest1> and <$Etest2> are not used in broadcast mode (forced
to true), since the originate and receive timestamps are undefined.
The clock-filter procedure is called to produce the delay (peer.delay),
offset (peer.offset) and dispersion (peer.dispersion) for the peer.
Specification of the clock-filter algorithm is not an integral part of
the NTP specification, since there may be other algorithms that work
well in practice. However, one found to work well in the Internet
environment is described in Section 4 and its use is recommended.
if (not valid header) exit;
<$Eroman peer.leap~<<-~roman pkt.leap>; /* copy
packet variables */
<$Eroman peer.stratum~<<-~roman pkt.stratum>;
<$Eroman peer.precision~<<-~roman pkt.precision>;
<$Eroman peer.rootdelay~<<-~roman pkt.rootdelay>;
<$Eroman peer.rootdispersion~<<-~roman pkt.rootdispersion>;
<$Eroman peer.refid~<<-~roman pkt.refid>;
<$Eroman peer.reftime~<<-~roman pkt.reftime>;
if (valid data) call clock-filter(<$Etheta ,~delta ,~epsilon>);
/* process sample */
end packet procedure;
Clock-Update Procedure
The clock-update procedure is called from the receive procedure when
valid clock offset, delay and dispersion data have been determined by
the clock-filter procedure for the current peer. The result of the
clock-selection and clock-combining procedures is the final clock
correction <$ETHETA>, which is used by the local-clock procedure to
update the local clock. If no candidates survive these procedures, the
clock-update procedure exits without doing anything further.
begin clock-update procedure
call clock-select; /* select clock
source */
if (<$Eroman sys.peer~!=~peer>) exit;
It may happen that the local clock may be reset, rather than slewed to
its final value. In this case the clear procedure is called for every
peer to purge the clock filter, reset the poll interval and reselect the
synchronization source, if necessary. Note that the local-clock
procedure sets the leap bits sys.leap to <169>unsynchronized<170> 112 in
this case, so that no other peer will attempt to synchronize to the host
until the host once again selects a peer for synchronization.
The distance procedure calculates the root delay <$EDELTA>, root
dispersion <$EEPSILON> and root synchronization distance <$ELAMBDA> via
the peer to the root of the synchronization subnet. The host will not
synchronize to the selected peer if the distance is greater than
NTP.MAXDISTANCE. The reason for the minimum clamp at NTP.MINDISPERSE is
to discourage subnet route flaps that can happen with Bellman-Ford
algorithms and small roundtrip delays.
<$ELAMBDA~
<~>an distance (peer)>; /* update system
variables */
if (<$ELAMBDA~>>=~roman NTP.MAXDISTANCE>) exit;
<$Eroman sys.leap~<<-~roman peer.leap>;
<$Eroman sys.stratum~<<-~roman peer.stratum~+~1>;
<$Eroman sys.refid~<<-~roman peer.peeraddr>;
call local-clock;
if (local clock reset) begin /* if reset,
clear state variables */
<$Eroman sys.leap~<<-~11 sub 2>;
for (all peers) call clear;
endif
else begin
<$Eroman sys.peer~<<-~peer>; /* if
not, adjust local clock */
<$Eroman sys.rootdelay~<<-~DELTA>;
<$Eroman sys.rootdispersion~<<-~EPSILON~+~max ( epsilon
sub xi~+~| THETA |,~roman NTP.MINDISPERSE)>;
endif
<$Eroman sys.reftime~<<-~roman sys.clock>;
end clock-update procedure;
In some system configurations a precise source of timing information is
available in the form of a train of timing pulses spaced at one-second
intervals. Usually, this is in addition to a source of timecode
information, such as a radio clock or even NTP itself, to number the
seconds, minutes, hours and days. In these configurations the system
variables are set to refer to the source from which the pulses are
derived. For those configurations which support a primary reference
source, such as a radio clock or calibrated atomic clock, the stratum is
set at one as long as this is the actual synchronization source and
whether or not the primary-clock procedure is used.
Specification of the clock-selection and local-clock algorithms is not
an integral part of the NTP specification, since there may be other
algorithms which provide equivalent performance. However, a clock-
selection algorithm found to work well in the Internet environment is
described in Section 4, while a local-clock algorithm is described in
Section 5 and their use is recommended. The clock-selection algorithm
described in Section 4 usually picks the peer at the lowest stratum and
minimum synchronization distance among all those available, unless that
peer appears to be a falseticker. The result is that the algorithms all
work to build a minimum-weight spanning tree relative to the primary
reference time servers and thus a hierarchical-master-slave
synchronization subnet.
Primary-Clock Procedure
When a primary reference source such as a radio clock is connected to
the host, it is convenient to incorporate its information into the data
base as if the clock were represented as an ordinary peer. In the
primary-clock procedure the clock is polled once a minute or so and the
returned timecode used to produce a new update for the local clock. When
peer.timer decrements to zero for a primary clock peer, the transmit
procedure is not called; rather, the radio clock is polled, usually
using an ASCII string specified for this purpose. When a valid timecode
is received from the radio clock, it is converted to NTP timestamp
format and the peer variables updated. The value of peer.leap is set
depending on the status of the leap-warning bit in the timecode, if
available, or manually by the operator. The value for peer.peeraddr,
which will become the value of sys.refid when the clock-update procedure
is called, is set to an ASCII string describing the clock type (see
Appendix A).
begin primary-clock-update procedure
<$Eroman peer.leap~<<-~"from"~radio~or~operator>; /* copy
variables */
<$Eroman peer.peeraddr~<<-~ASCII~identifier>;
<$Eroman peer.rec~<<-~radio~timestamp>;
<$Eroman peer.reach~<<-~1>;
call clock-filter(<$Eroman {sys.clock~-~peer.rec,~0,~1~<<
<<~peer.precision}>); /* process sample */
call clock-update; /* update local
clock */
end primary-clock-update procedure;
Initialization Procedures
The initialization procedures are used to set up and initialize the
system, its peers and associations.
Initialization Procedure
The initialization procedure is called upon reboot or restart of the NTP
daemon. The local clock is presumably undefined at reboot; however, in
some equipment an estimate is available from the reboot environment,
such as a battery-backed clock/calendar. The precision variable is
determined by the intrinsic architecture of the local hardware clock.
The authentication variables are used only if the authentication
mechanism described in Appendix C is implemented. The values of these
variables are determined using procedures beyond the scope of NTP
itself.
begin initialization procedure
#ifdef (authentication implemented) / * see Appendix C */
<$Eroman sys.keys~<<-~as~required>;
#endef;
<$Eroman sys.leap~<<-~11 sub 2>;
/* copy variables */
<$Eroman sys.stratum~<<-~0~(undefined)>;
<$Eroman sys.precision~<<-~host~precision>;
<$Eroman sys.rootdelay~<<-~0~(undefined)>;
<$Eroman sys.rootdispersion~<<-~0~(undefined)>;
<$Eroman sys.refid~<<-~0~(undefined)>;
<$Eroman sys.reftime~<<-~0~(undefined)>;
<$Eroman sys.clock~<<-~external~reference>;
<$Eroman sys.peer~<<-~roman NULL>;
<$Eroman sys.poll~<<-~roman NTP.MINPOLL>;
for (all configured peers) /* create
configured associations */
call initialization-instantiation procedure;
end initialization procedure;
Initialization-Instantiation Procedure
This implementation-specific procedure is called from the initialization
procedure to define an association. The addresses and modes of the peers
are determined using information read during the reboot procedure or as
the result of operator commands. The authentication variables are used
only if the authentication mechanism described in Appendix C is
implemented. The values of these variables are determined using
procedures beyond the scope of NTP itself. With the authentication bits
set as suggested, only properly authenticated peers can become the
synchronization source.
begin initialization-instantiation procedure
<$Eroman peer.config~<<-~1>;
#ifdef (authentication implemented) /* see Appendix C */
<$Eroman peer.authenable~<<-~1~(suggested)>;
<$Eroman peer.authentic~<<-~0>;
<$Eroman peer.hostkeyid~<<-~as~required>;
<$Eroman peer.peerkeyid~<<-~0>;
#endef;
<$Eroman peer.peeraddr~<<-~peer~IP~address>; /* copy
variables */
<$Eroman peer.peerport~<<-~roman NTP.PORT>;
<$Eroman peer.hostaddr~<<-~host~IP~address>;
<$Eroman peer.hostport~<<-~roman NTP.PORT>;
<$Eroman peer.mode~<<-~host~mode>;
<$Eroman peer.peerpoll~<<-~0~(undefined)>;
<$Eroman peer.timer~<<-~0>;
<$Eroman peer.delay~<<-~0~(undefined)>;
<$Eroman peer.offset~<<-~0~(undefined)>;
call clear; /* initialize
association */
end initialization-instantiation procedure;
Receive-Instantiation Procedure
The receive-instantiation procedure is called from the receive procedure
when a new peer is discovered. It initializes the peer variables and
mobilizes the association. If the message is from a peer operating in
client mode (3), the host mode is set to server mode (4); otherwise, it
is set to symmetric passive mode (2). The authentication variables are
used only if the authentication mechanism described in Appendix C is
implemented. If implemented, only properly authenticated non-configured
peers can become the synchronization source.
begin receive-instantiation procedure
#ifdef (authentication implemented) /* see Appendix C */
<$Eroman peer.authenable~<<-~0>;
<$Eroman peer.authentic~<<-~0>;
<$Eroman peer.hostkeyid~<<-~as~required>;
<$Eroman peer.peerkeyid~<<-~0>;
#endef
<$Eroman peer.config~<<-~0>; /* copy
variables */
<$Eroman peer.peeraddr~<<-~roman pkt.peeraddr>;
<$Eroman peer.peerport~<<-~roman pkt.peerport>;
<$Eroman peer.hostaddr~<<-~roman pkt.hostaddr>;
<$Eroman peer.hostport~<<-~roman pkt.hostport>;
if (pkt.mode = 3) /* determine
mode */
<$Eroman peer.mode~<<-~4>;
else
<$Eroman peer.mode~<<-~2>;
<$Eroman peer.peerpoll~<<-~0~(undefined)>;
<$Eroman peer.timer~<<-~0>;
<$Eroman peer.delay~<<-~0~(undefined)>;
<$Eroman peer.offset~<<-~0~(undefined)>;
call clear; /* initialize
association */
end receive-instantiation procedure;
Primary Clock-Instantiation Procedure
This procedure is called from the initialization procedure in order to
set up the state variables for the primary clock. The value for
peer.precision is determined from the radio clock specification and
hardware interface. The value for peer.rootdispersion is nominally ten
times the inherent maximum error of the radio clock; for instance,
<$E10~mu s> for a calibrated atomic clock, 10 ms for a WWVB or GOES
radio clock and 100 ms for a less accurate WWV radio clock.
begin clock-instantiation procedure
<$Eroman peer.config~<<-~1>; /* copy
variables */
<$Eroman peer.peeraddr~<<-~0~undefined>;
<$Eroman peer.peerport~<<-~0~(not~used)>;
<$Eroman peer.hostaddr~<<-~0~(not~used)>;
<$Eroman peer.hostport~<<-~0~(not~used)>;
<$Eroman peer.leap~<<-~11 sub 2>;
<$Eroman peer.mode~<<-~0~(not~used)>;
<$Eroman peer.stratum~<<-~0>;
<$Eroman peer.peerpoll~<<-~0~(undefined)>;
<$Eroman peer.precision~<<-~clock~precision>;
<$Eroman peer.rootdelay~<<-~0>;
<$Eroman peer.rootdispersion~<<-~clock~dispersion>;
<$Eroman peer.refid~<<-~0~(not~used)>;
<$Eroman peer.reftime~<<-~0~(undefined)>;
<$Eroman peer.timer~<<-~0>;
<$Eroman peer.delay~<<-~0~(undefined)>;
<$Eroman peer.offset~<<-~0~(undefined)>;
call clear; /* initialize
association */
end clock-instantiation procedure;
In some configurations involving a calibrated atomic clock or LORAN-C
receiver, the primary reference source may provide only a seconds pulse,
but lack a complete timecode from which the numbering of the seconds,
etc., can be derived. In these configurations seconds numbering can be
derived from other sources, such as a radio clock or even other NTP
peers. In these configurations the primary clock variables should
reflect the primary reference source, not the seconds-numbering source;
however, if the seconds-numbering source fails or is known to be
operating incorrectly, updates from the primary reference source should
be suppressed as if it had failed.
Clear Procedure
The clear procedure is called when some event occurs that results in a
significant change in reachability state or potential disruption of the
local clock.
begin clear procedure
<$Eroman peer.org~<<-~0~(undefined)>; /* mark
timestamps undefined */
<$Eroman peer.rec~<<-~0~(undefined)>;
<$Eroman peer.xmt~<<-~0~(undefined)>;
<$Eroman peer.reach~<<-~0>; /* reset
state variables */
<$Eroman peer.filter~<<-~[0,~,0,~roman NTP.MAXDISPERSE]>; /*
all stages */
<$Eroman peer.valid~<<-~0>;
<$Eroman peer.dispersion~<<-~roman NTP.MAXDISPERSE>;
<$Eroman {peer.hostpoll~<<-~NTP.MINPOLL}>; /* reset
poll interval */
call poll-update;
call clock-select; /* select clock
source */
end clear procedure;
Poll-Update Procedure
The poll-update procedure is called when a significant event occurs that
may result in a change of the poll interval or peer timer. It checks the
values of the host poll interval (peer.hostpoll) and peer poll interval
(peer.peerpoll) and clamps each within the valid range. If the peer is
selected for synchronization, the value is further clamped as a function
of the computed compliance (see Section 5).
begin poll-update procedure
<$Etemp~<<-~roman peer.hostpoll>; /*
determine host poll interval */
if (<$Epeer~=~roman sys.peer>)
<$Etemp~<<-~min (temp,~roman {sys.poll,~NTP.MAXPOLL)}>;
else
<$Etemp~<<-~min (temp,~roman NTP.MAXPOLL)>;
<$Eroman peer.hostpoll~<<-~max (temp,~roman NTP.MINPOLL)>;
<$Etemp~<<-~1~<< << ~min ( roman {peer.hostpoll,~max
(peer.peerpoll,~NTP.MINPOLL)})>;
If the poll interval is unchanged and the peer timer is zero, the timer
is simply reset. If the poll interval is changed and the new timer value
is greater than the present value, no additional action is necessary;
otherwise, the peer timer must be reduced. When the peer timer must be
reduced it is important to discourage tendencies to synchronize
transmissions between the peers. A prudent precaution is to randomize
the first transmission after the timer is reduced, for instance by the
sneaky technique illustrated.
if (peer.timer = 0) /* reset peer
timer */
<$Eroman peer.timer~<<-~temp>;
else if (<$Eroman peer.timer~>>~temp>)
<$Eroman peer.timer~<<-~( roman sys.clock~&~(temp~-
~1))~+~1>;
end poll-update procedure;
Synchronization Distance Procedure
The distance procedure calculates the synchronization distance from the
peer variables for the peer peer.
begin distance(peer) procedure;
<$EDELTA~<<-~roman {peer.rootdelay~+~|peer.delay|}>;
<$EEPSILON~<<-~roman
{peer.rootdispersion~+~peer.dispersion~+~phi (sys.clock~-~peer.update)
}>;
<$ELAMBDA~<<-~EPSILON~+~{| DELTA |} over 2> ;
end distance procedure;
Note that, while <$EDELTA> may be negative in some cases, both
<$EEPSILON> and <$ELAMBDA> are always positive.
Access Control Issues
The NTP design is such that accidental or malicious data modification
(tampering) or destruction (jamming) at a time server should not in
general result in timekeeping errors elsewhere in the synchronization
subnet. However, the success of this approach depends on redundant time
servers and diverse network paths, together with the assumption that
tampering or jamming will not occur at many time servers throughout the
synchronization subnet at the same time. In principle, the subnet
vulnerability can be engineered through the selection of time servers
known to be trusted and allowing only those time servers to become the
synchronization source. The authentication procedures described in
Appendix C represent one mechanism to enforce this; however, the
encryption algorithms can be quite CPU-intensive and can seriously
degrade accuracy, unless precautions such as mentioned in the
description of the transmit procedure are taken.
While not a required feature of NTP itself, some implementations may
include an access-control feature that prevents unauthorized access and
controls which peers are allowed to update the local clock. For this
purpose it is useful to distinguish between three categories of access:
those that are preauthorized as trusted, preauthorized as friendly and
all other (non-preauthorized) accesses. Presumably, preauthorization is
accomplished by entries in the configuration file or some kind of
ticket-management system such as Kerberos [STE88]. In this model only
trusted accesses can result in the peer becoming the synchronization
source. While friendly accesses cannot result in the peer becoming the
synchronization source, NTP messages and timestamps are returned as
specified.
It does not seem useful to maintain a secret clock, as would result from
restricting non-preauthorized accesses, unless the intent is to hide the
existence of the time server itself. Well-behaved Internet hosts are
expected to return an ICMP service-unavailable error message if a
service is not implemented or resources are not available; however, in
the case of NTP the resources required are minimal, so there is little
need to restrict requests intended only to read the clock. A simple but
effective access-control mechanism is then to consider all associations
preconfigured in a symmetric mode or client mode (modes 1, 2 and 3) as
trusted and all other associations, preconfigured or not, as friendly.
If a more comprehensive trust model is required, the design can be based
on an access-control list with each entry consisting of a 32-bit
Internet address, 32-bit mask and three-bit mode. If the logical AND of
the source address (pkt.peeraddr) and the mask in an entry matches the
corresponding address in the entry and the mode (pkt.mode) matches the
mode in the entry, the access is allowed; otherwise an ICMP error
message is returned to the requestor. Through appropriate choice of
mask, it is possible to restrict requests by mode to individual
addresses, a particular subnet or net addresses, or have no restriction
at all. The access-control list would then serve as a filter controlling
which peers could create associations.
Filtering and Selection Algorithms
A most important factor affecting the accuracy and reliability of time
distribution is the complex of algorithms used to reduce the effect of
statistical errors and falsetickers due to failure of various subnet
components, reference sources or propagation media. The algorithms
suggested in this section were developed and refined over several years
of operation in the Internet under widely varying topologies, speeds and
traffic regimes. While these algorithms are believed the best available
at the present time, they are not an integral part of the NTP
specification, since other algorithms with similar or superior
performance may be devised in future.
However, it is important to observe that not all time servers or clients
in an NTP synchronization subnet must implement these algorithms. For
instance, simple workstations may dispense with one or both of them in
the interests of simplicity if accuracy and reliability requirements
justify. Nevertheless, it would be expected that an NTP server providing
synchronization to a sizable community, such as a university campus or
research laboratory, would be expected to implement these algorithms or
others proved to have equivalent functionality. A comprehensive
discussion of the design principles and performance is given in
[MIL91a].
In order for the NTP filter and selection algorithms to operate
effectively, it is useful to have a measure of recent sample variance
recorded for each peer. The measure adopted is based on first-order
differences, which are easy to compute and effective for the purposes
intended. There are two measures, one called the filter dispersion
<$Eepsilon sub sigma> and the other the select dispersion <$Eepsilon sub
xi>. Both are computed as the weighted sum of the clock offsets in a
temporary list sorted by synchronization distance. If <$Etheta sub i
~(0~<<=~i~<<~n)> is the offset of the ith entry, then the sample
difference <$Eepsilon sub ij> of the ith entry relative to the jth entry
is defined <$Eepsilon sub ij~<~>=~| theta sub i~-~theta sub j |> . The
dispersion relative to the jth entry is defined <$Eepsilon sub j> and
computed as the weighted sum
<$Eepsilon sub j~=~sum from {i~=~0} to {n~-~1}~epsilon sub ij~w~sup
{i+1}> ,
where w is a weighting factor chosen to control the influence of
synchronization distance in the dispersion budget. In the NTP algorithms
w is chosen less than <$E1 / 2>: <$Ew~=~roman NTP.FILTER> for filter
dispersion and <$Ew~=~roman NTP.SELECT> for select dispersion. The
(absolute) dispersion <$Eepsilon sub sigma> and <$Eepsilon sub xi> as
used in the NTP algorithms are defined relative to the 0th entry
<$Eepsilon sub 0>.
There are two procedures described in the following, the clock-filter
procedure, which is used to select the best offset samples from a given
clock, and the clock-selection procedure, which is used to select the
best clock among a hierarchical set of clocks.
Clock-Filter Procedure
The clock-filter procedure is executed upon arrival of an NTP message or
other event that results in new data samples. It takes arguments of the
form (<$Etheta ,~delta ,~epsilon>), where <$Etheta> is a sample clock
offset measurement and <$Edelta> and <$Eepsilon> are the associated
roundtrip delay and dispersion. It determines the filtered clock offset
(peer.offset), roundtrip delay (peer.delay) and dispersion
(peer.dispersion). It also updates the dispersion of samples already
recorded and saves the current time (peer.update).
The basis of the clock-filter procedure is the filter shift register
(peer.filter), which consists of NTP.SHIFT stages, each stage containing
a 3-tuple <$E[ theta sub i ,~delta sub i ,~epsilon sub i ]>, with
indices numbered from zero on the left. The filter is initialized with
the value <$E[0,~0,~roman NTP.MAXDISPERSE]> in all stages by the clear
procedure. New data samples are shifted into the filter at the left end,
causing first NULLs then old samples to fall off the right end. The
packet procedure provides samples of the form (<$Etheta ,~delta
,~epsilon>) as new updates arrive, while the transmit procedure provides
samples of the form <$E[0,~0,~roman NTP.MAXDISPERSE]> when two poll
intervals elapse without a fresh update. While the same symbols
(<$Etheta ,~delta ,~epsilon>) are used here for the arguments, clock-
filter contents and peer variables, the meaning will be clear from
context. The following pseudo-code describes this procedure.
begin clock-filter procedure (<$Etheta ,~delta ,~epsilon>)
The dispersion <$Eepsilon sub i> for all valid samples in the filter
register must be updated to account for the skew-error accumulation
since the last update. These samples are also inserted on a temporary
list with entry format <$E[distance,index]>. The samples in the register
are shifted right one stage, with the overflow sample discarded and the
new sample inserted at the leftmost stage. The temporary list is then
sorted by increasing distance. If no samples remain in the list, the
procedure exits without updating the peer variables.
for (i from NTP.SIZE <196> 1 to 1) begin /* update
dispersion */
<$E[ theta sub i ,~delta sub i ,~epsilon sub i ]~<<-~[
theta sub {i-1} ,~delta sub {i-1} ,~epsilon sub {i-1} ]>;
/* shift stage right */
<$Eepsilon sub i~=~epsilon sub i~+~phi tau>;
add <$E[ lambda sub i~==~epsilon sub i~+~{| delta sub i
|} over 2 ,~i]> to temporary list;
endfor;
<$E[ theta sub 0 ,~delta sub 0 ,~epsilon sub 0 ]~<<-~[ theta
,~delta ,~epsilon ]>; /* insert new sample */
add <$E[ lambda~==~epsilon~+~{| delta |} over 2 ,~0]> to
temporary list;
<$Eroman peer.update~<<-~roman sys.clock>;
/* reset base time */
sort temporary list by increasing <$E[distance~||index]>;
where <$E[distance~||index]> represents the concatenation of the
distance and index fields and distance is the high-order field. The
filter dispersion <$Eepsilon sub sigma> is computed and included in the
peer dispersion. Note that for this purpose the temporary list is
already sorted.
<$Eepsilon sub sigma~<<-~0>;
for (i from NTP.SHIFT<196>1 to 0) /* compute
filter dispersion */
if (<$Eroman peer.dispersion sub index[i]~>>=~roman
NTP.MAXDISPERSE> or
<$E| theta sub i~-~theta sub 0 |~>>~roman
NTP.MAXDISPERSE>)
<$Eepsilon sub sigma~<~><<-~( epsilon sub
sigma~+~roman NTP.MAXDISPERSE)~times~roman NTP.FILTER>;
else
<$Eepsilon sub sigma~<~><<-~( epsilon sub
sigma~+~| theta sub i~-~theta sub 0 |)~times~roman NTP.FILTER>;
The peer offset <$Etheta sub 0>, delay <$Edelta sub 0> and dispersion
<$Eepsilon sub 0> are chosen as the values corresponding to the minimum-
distance sample; in other words, the sample corresponding to the first
entry on the temporary list, here represented as the 0th subscript.
<$Eroman peer.offset~<<-~theta sub 0>;
/* update peer variables */
<$Eroman peer.delay~<<-~delta sub 0>;
<$Eroman peer.dispersion~<<-~min ( epsilon sub 0~+~epsilon sub
sigma ,~roman NTP.MAXDISPERSE)>;
end clock-filter procedure
The peer.offset and peer.delay variables represent the clock offset and
roundtrip delay of the local clock relative to the peer clock. Both of
these are precision quantities and can usually be averaged over long
intervals in order to improve accuracy and stability without bias
accumulation (see Appendix H). The peer.dispersion variable represents
the maximum error due to measurement error, skew-error accumulation and
sample variance. All three variables are used in the clock-selection and
clock-combining procedures to select the peer clock(s) used for
synchronization and to maximize the accuracy and stability of the
indications.
Clock-Selection Procedure
The clock-selection procedure uses the peer variables <$ETHETA>,
<$EDELTA>, <$EEPSILON> and <$Etau> and is called when these variables
change or when the reachability status changes. It consists of two
algorithms, the intersection algorithm and the clustering algorithm. The
intersection algorithm constructs a list of candidate peers eligible to
become the synchronization source, computes a confidence interval for
each and casts out falsetickers using a technique adapted from Marzullo
and Owicki [MAR85]. The clustering algorithm sorts the list of surviving
candidates in order of stratum and synchronization distance and
repeatedly casts out outlyers on the basis of select dispersion until
only the most accurate, precise and stable survivors are left. A bit is
set for each survivor to indicate the outcome of the selection process.
The system variable sys.peer is set as a pointer to the most likely
survivor, if there is one, or to the NULL value if not.
Intersection Algorithm
begin clock-selection procedure
Each peer is examined in turn and added to an endpoint list only if it
passes several sanity checks designed to avoid loops and use of
exceptionally noisy data. If no peers survive the sanity checks, the
procedure exits without finding a synchronization source. For each of m
survivors three entries of the form <$E[endpoint,~type]> are added to
the endpoint list: <$E[ THETA~-~LAMBDA ,~-~1]>, <$E[ THETA ,~0]> and
<$E[ THETA~+~LAMBDA ,~1]>. There will be <$E3 m> entries on the list,
which is then sorted by increasing endpoint.
<$Em~<<-~0>;
for (each peer) /* calling all peers */
if (<$Eroman {peer.reach~!=~0~bold
and~peer.dispersion~<<~NTP.MAXDISPERSE}> and
not (peer.stratum >> 1 and peer.refid =
peer.hostaddr)) begin
<$ELAMBDA~
<~>an distance (peer)>; /* make list entry */
add <$E[ THETA~-~LAMBDA ,~-1]> to endpoint list;
add <$E[ THETA ,~0]> to endpoint list;
add <$E[ THETA~+~LAMBDA ,~1]> to endpoint list;
<$Em~<<-~m~+~1>;
endif
endfor
if (<$Em~=~0>) begin /* skedaddle if
no candidates */
<$Eroman sys.peer~<<-~roman NULL>;
<$Eroman sys.stratum~<<-~0~(undefined)>;
exit;
endif
sort endpoint list by increasing endpoint||type;
The following algorithm is adapted from DTS [DEC89] and is designed to
produce the largest single intersection containing only truechimers. The
algorithm begins by initializing a value f and counters i and c to zero.
Then, starting from the lowest endpoint of the sorted endpoint list, for
each entry <$E[endpoint,~type]> the value of type is subtracted from the
counter i, which is the number of intersections. If type is zero,
increment the value of c, which is the number of falsetickers (see
Appendix H). If <$Ei~>>=~m~-~f> for some entry, endpoint of that entry
becomes the lower endpoint of the intersection; otherwise, f is
increased by one and the above procedure is repeated. Without resetting
f or c, a similar procedure is used to find the upper endpoint, except
that the value of type is added to the counter.. If after both endpoints
have been determined <$Ec~<<=~f>, the procedure continues having found
<$Em~-~f> truechimers; otherwise, f is increased by one and the entire
procedure is repeated.
for (f from 0 to <$Ef~>>=~m over 2>) begin /*
calling all truechimers */
<$Ec~<<-~0>;
<$Ei~<<-~0>;
for (each [endpoint, type] from lowest) begin /* find
low endpoint */
<$Ei~<<-~i~-~type>;
<$Elow~<<-~endpoint>;
if (<$Ei~>>=~m~-~f>) break;
if (<$Etype~=~0>) <$Ec~<<-~c~+~1>;
endfor;
<$Ei~<<-~0>;
for (each [endpoint, type] from highest) begin /* find
high endpoint */
<$Ei~<<-~i~+~type>;
<$Ehigh~<<-~endpoint>;
if (<$Ei~>>=~m~-~f>) break;
if (<$Etype~=~0>) <$Ec~<<-~c~+~1>;
endfor;
if (<$Ec~<<=~f>) break; /* continue
until all falsetickers found */
endfor;
if (<$Elow~>>~high>) begin /* quit
if no intersection found */
<$Eroman sys.peer~<<-~roman NULL>;
exit;
endif;
Note that processing continues past this point only if there are more
than <$Em over 2> intersections. However, it is possible, but not highly
likely, that there may be fewer than <$Em over 2> truechimers remaining
in the intersection.
Clustering Algorithm
In the original DTS algorithm the clock-selection procedure exits at
this point with the presumed correct time set midway in the computed
intersection <$E[low,~high]>. However, this can lead to a considerable
loss in accuracy and stability, since the individual peer statistics are
lost. Therefore, in NTP the candidates that survived the preceding steps
are processed further. The candidate list is rebuilt with entries of the
form <$E[distance,~index]>, where distance is computed from the (scaled)
peer stratum and synchronization distance <$ELAMBDA>. The scaling factor
provides a mechanism to weight the combination of stratum and distance.
Ordinarily, the stratum will dominate, unless one or more of the
survivors has an exceptionally high distance. The list is then sorted by
increasing distance.
<$Em~<<-~0>;
for (each peer) begin /* calling all peers */
if (<$Elow~<<=~theta~<<=~high>) begin
<$ELAMBDA~<<-~roman distance (peer)>;
/* make list entry */
<$Edist~<<-~roman
{peer.stratum~times~NTP.MAXDISPERSE~+~LAMBDA }>
add <$E[ dist ,~peer]> to candidate list;
<$Em~<<-~m~+~1>;
endif;
endfor;
sort candidate list by increasing dist;
The next steps are designed to cast out outlyers which exhibit
significant dispersions relative to the other members of the candidate
list while minimizing wander, especially on high-speed LANs with many
time servers. Wander causes needless network overhead, since the poll
interval is clamped at sys.poll as each new peer is selected for
synchronization and only slowly increases when the peer is no longer
selected. It has been the practical experience that the number of
candidates surviving to this point can become quite large and can result
in significant processor cycles without materially enhancing stability
and accuracy. Accordingly, the candidate list is truncated at
NTP.MAXCLOCK entries.
Note <$Eepsilon sub {xi i}> is the select (sample) dispersion relative
to the ith peer represented on the candidate list, which can be
calculated in a manner similar to the filter dispersion described
previously. The <$EEPSILON sub j> is the dispersion of the jth peer
represented on the list and includes components due to measurement
error, skew-error accumulation and filter dispersion. If the maximum
<$Eepsilon sub {xi i}> is greater than the minimum <$EEPSILON sub j> and
the number of survivors is greater than NTP.MINCLOCK, the ith peer is
discarded from the list and the procedure is repeated. If the current
synchronization source is one of the survivors and there is no other
survivor of lower stratum, then the procedure exits without doing
anything further. Otherwise, the synchronization source is set to the
first survivor on the candidate list. In the following i, j, k, l are
peer indices, with k the index of the current synchronization source
(NULL if none) and l the index of the first survivor on the candidate
list.
while begin
for (each survivor <$E[distance,~index]>) begin /*
compute dispersions */
find index i for max <$Eepsilon sub {xi i}>;
find index j for min <$EEPSILON sub j>;
endfor
if (<$Eepsilon sub {xi i}~<<=~EPSILON sub j> or
<$Em~<<=~roman NTP.MINCLOCK>) break;
<$Eroman peer.survivor [i]~<<-~0> ; /*
discard ith peer */
if (<$Ei~=~k>) <$Eroman sys.peer~<<-~roman NULL>;
delete the ith peer from the candidate list;
<$Em~<<-~m~-~1>;
endwhile
if (<$Eroman peer.survivor [k]~=~0> or <$Eroman peer.stratum
[k]~>>~roman peer.stratum [l]>) begin
<$Eroman sys.peer~<<-~l>;
/* new clock source */
call poll-update;
endif
end clock-select procedure;
The algorithm is designed to favor those peers near the head of the
candidate list, which are at the lowest stratum and distance and
presumably can provide the most accurate and stable time. With proper
selection of weight factor v (also called NTP.SELECT), entries will be
trimmed from the tail of the list, unless a few outlyers disagree
significantly with respect to the remaining entries, in which case the
outlyers are discarded first. The termination condition is designed to
avoid needless switching between synchronization sources when not
statistically justified, yet maintain a bias toward the low-stratum,
low-distance peers.
Local Clocks
In order to implement a precise and accurate local clock, the host must
be equipped with a hardware clock consisting of an oscillator and
interface and capable of the required precision and stability. A logical
clock is then constructed using these components plus software
components that adjust the apparent time and frequency in response to
periodic updates computed by NTP or some other time-synchronization
protocol such as Hellospeak [MIL83b] or the Unix 4.3bsd TSP [GUS85a].
This section describes the Fuzzball local-clock model and
implementation, which includes provisions for precise time and frequency
adjustment and can maintain time to within 15 ns and frequency to within
0.3 ms per day. The model is suitable for use with both compensated and
uncompensated quartz oscillators and can be adapted to power-frequency
oscillators. A summary of the characteristics of these and other types
of oscillators can be found in Appendix E, while a comprehensive
mathematical analysis of the NTP local-clock model can be found in
Appendix G.
It is important to note that the particular implementation described is
only one of possibly many implementations that provide equivalent
functionality. However, it is equally important to note that the clock
model described in Appendix G and which is the basis of the
implementation involves a particular kind of control-feedback loop that
is potentially unstable if the design rules are broken. The model and
parameter described in Appendix G are designed to provide accurate and
stable time under typical operating conditions using conventional
hardware and in the face of disruptions in hardware or network
connectivity. The parameters have been engineered for reliable operation
in a multi-level hierarchical subnet where unstable operation at one
level can disrupt possibly many other levels.
Fuzzball Implementation
The Fuzzball local clock consists of a collection of hardware and
software registers, together with a set of algorithms, which implement a
logical clock that functions as a disciplined oscillator and
synchronizes to an external source. Following is a description of its
components and manner of operation. Note that all arithmetic is two's
complement integer and all shifts <169><<<<<170> and <169>>>>><170> are
arithmetic (sign-fill for right shifts and zero-fill for left shifts).
Also note that <$Ex~<< <<~n> is equivalent to <$Ex~>> >>~-~n>.
The principal components of the local clock are shown in Figure
3,<$&fig3> in which the fraction points shown are relative to whole
milliseconds. The 48-bit Clock register and 32-bit Prescaler function as
a disciplined oscillator which increments in milliseconds relative to
midnight at the fraction point. The 32-bit Clock-Adjust register is used
to adjust the oscillator phase in gradual steps to avoid discontinuities
in the indicated timescale. Its contents are designated x in the
following. The 32-bit Skew-Compensation register is used to trim the
oscillator frequency by adding small phase increments at periodic
adjustment intervals and can compensate for frequency errors as much as
.01% or æ100 ppm. Its contents are designated y in the
following. The 16-bit Watchdog counter and 32-bit Compliance register
are used to determine validity, as well as establish the PLL bandwidth
and poll interval (see Appendix G). The contents of the Compliance
register are designated z in the following. The 32-bit PPS-Adjust
register is used to hold a precision time adjustment when a source of 1-
pps pulses is available, while the 8-bit PPS counter is used to verify
presence of these pulses. The two-bit Flags register contains the two
leap bits described elsewhere (leap).
All registers except the Prescaler register are ordinarily implemented
in memory. In typical clock interface designs such as the DEC KWV11-C,
the Prescaler register is implemented as a 16-bit buffered counter
driven by a quartz-controlled oscillator at some multiple of 1000 Hz. A
counter overflow is signalled by an interrupt, which results in an
increment of the Clock register at the bit corresponding to the
overflow. The time of day is determined by reading the Prescaler
register, which does not disturb the counting process, and adding its
value to that of the Clock register with fraction points aligned as
shown and with unimplemented low-order bits set to zero. In other
interface designs, such as the LSI-11 event-line mechanism, each tick of
the clock is signalled by an interrupt at intervals of 16-2/3 ms or 20
ms, depending on interface and mains frequency. When this occurs the
appropriate increment in fractional milliseconds is added to the Clock
register.
The various parameters used are summarized in Table 6, in which certain
parameters have been rescaled from those given in Appendix G due to the
units here being in milliseconds.<$&tab6> When the system is
initialized, all registers and counters are cleared and the leap bits
set to 112 (unsynchronized). At adjustment intervals of CLOCK.ADJ
seconds CLOCK.ADJ is subtracted from the PPS counter, but only if the
previous contents of the PPS counter are greater than zero. Also,
CLOCK.ADJ is added to the Watchdog counter, but the latter is clamped
not to exceed NTP.MAXAGE divided by CLOCK.ADJ (one full day). In
addition, if the Watchdog counter reaches this value, the leap bits are
set to 112 (unsynchronized).
In some system configurations a precise source of timing information is
available in the form of a train of timing pulses spaced at one-second
intervals. Usually, this is in addition to a source of timecode
information, such as a radio clock or even NTP itself, to number the
seconds, minutes, hours and days. In typical clock interface designs
such as the DEC KWV11-C, a special input is provided which can trigger
an interrupt as each pulse is received. When this happens the PPS
counter is set to CLOCK.PPS and the current time offset is determined in
the usual way. Then, the PPS-Adjust register is set to the time offset
scaled to milliseconds. Finally, if the PPS-Adjust register is greater
than or equal to 500, 1000 is subtracted from its contents. As described
below, the PPS-Adjust register and PPS counters can be used in
conjunction with an ordinary timecode to produce an extremely accurate
local clock.
Gradual Phase Adjustments
Left uncorrected, the local clock runs at the offset and frequency
resulting from its last update. An update is produced by an event that
results in a valid clock selection. It consists of a signed 48-bit
integer in whole milliseconds and fraction, with fraction point to the
left of bit 32. If the magnitude is greater than the maximum aperture
CLOCK.MAX, a step adjustment is required, in which case proceed as
described later. Otherwise, a gradual phase adjustment is performed.
Normally, the update is computed by the NTP algorithms described
previously; however, if the PPS counter is greater than zero, the value
of the PPS-Adjust register is used instead. Let u be a 32-bit quantity
with bits 0-31 set as bits 16-47 of the update. If some of the low-order
bits of the update are unimplemented, they are set as the value of the
sign bit. These operations move the fraction point of u to the left of
bit 16 and minimize the effects of truncation and roundoff errors. Let b
be the number of leading zeros of the absolute value of the Compliance
register and let c be the number of leading zeros of the Watchdog
counter, both of which are easily computed by compact loops. Then, set b
to
<$Eb~=~b~-~16~+~roman CLOCK.COMP>
and clamp it to be not less than zero. This represents the logarithm of
the loop time constant. Then, set c to
<$Ec~=~10~-~c>
and clamp it to be not greater than NTP.MAXPOLL <196> NTP.MINPOLL. This
represents the logarithm of the integration interval since the last
update. The clamps insure stable operation under typical conditions
encountered in the Internet. Then, compute new values for the Clock-
Adjust and Skew-Compensation registers
<$Ex~=~u~>> >>~b> ,
<$Ey~=~y~+~(u~>> >>~(b~+~b~-~c))> .
Finally, compute the exponential average
<$Ez~=~z~+~(u~<< <<~(b~+~ roman CLOCK.MULT)~-~z)~>> >>~ roman
CLOCK.WEIGHT> ,
where the left shift realigns the fraction point for greater precision
and ease of computation.
At each adjustment interval the final clock correction consisting of two
components is determined. The first (phase) component consists of the
quantity
<$Ex~>> >>~ roman CLOCK.PHASE> ,
which is then subtracted from the previous contents of the Clock-Adjust
register to form the new contents of that register. The second
(frequency) component consists of the quantity
<$Ey~>> >>~ roman CLOCK.FREQ> .
The sum of the phase and frequency components is the final clock
correction, which is then added to the Clock register. FInally, the
Watchdog counter is set to zero. Operation continues in this way until a
new correction is introduced.
The value of b computed above can be used to update the poll interval
system variable (sys.poll). This functions as an adaptive parameter that
provides a very valuable feature which reduces the polling overhead,
especially if the clock-combining algorithm described in Appendix F is
used:
<$Eroman sys.poll~<<-~b~+~roman NTP.MINPOLL> .
Under conditions when update noise is high or the hardware oscillator
frequency is changing relatively rapidly due to environmental
conditions, the magnitude of the compliance increases. With the
parameters specified, this causes the loop bandwidth (reciprocal of time
constant) to increase and the poll interval to decrease, eventually to
NTP.MINPOLL seconds. When noise is low and the hardware oscillator very
stable, the compliance decreases, which causes the loop bandwidth to
decrease and the poll interval to increase, eventually to NTP.MAXPOLL
seconds.
The parameters in Table 6 have been selected so that, under good
conditions with updates in the order of a few milliseconds, a precision
of a millisecond per day (about .01 ppm or 10-8), can be achieved. Care
is required in the implementation to insure monotonicity of the Clock
register and to preserve the highest precision while minimizing the
propagation of roundoff errors. Since all of the multiply/divide
operations (except those involved with the 1-pps pulses) computed in
real time can be approximated by bitwise-shift operations, it is not
necessary to |
