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Versions: 00 01                                                         
NTP WG                                                     W. Kasch, Ed.
Internet-Draft                                           J. Burbank, Ed.
Expires: May 13, 2006                                            JHU/APL
                                                                D. Mills
                                                                 U. Del.
                                                        November 9, 2005

      The Network Time Protocol Version 4 Algorithm Specification

Status of this Memo

   By submitting this Internet-Draft, each author represents that any
   applicable patent or other IPR claims of which he or she is aware
   have been or will be disclosed, and any of which he or she becomes
   aware will be disclosed, in accordance with Section 6 of BCP 79.

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   This Internet-Draft will expire on May 13, 2006.

Copyright Notice

   Copyright (C) The Internet Society (2005).


   The Network Time Protocol (NTP) is widely used to synchronize
   computer clocks in the Internet.  This memorandum describes the
   algorithms used by Version 4 of the NTP (NTPv4) to calculate time

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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Clock Filter Algorithm . . . . . . . . . . . . . . . . . . . .  6
   3.  Clock Selection Algorithm  . . . . . . . . . . . . . . . . . .  8
   4.  Clustering Algorithm . . . . . . . . . . . . . . . . . . . . .  9
   5.  Clock Combining Algorithm  . . . . . . . . . . . . . . . . . . 10
   6.  Polling Algorithm  . . . . . . . . . . . . . . . . . . . . . . 11
   7.  Clock Discipline Algorithm . . . . . . . . . . . . . . . . . . 17
     7.1.  Poll Interval Control  . . . . . . . . . . . . . . . . . . 20
     7.2.  State Machine  . . . . . . . . . . . . . . . . . . . . . . 20
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 22
   9.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 22
   10. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 22
   11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 22
     11.1. Normative References . . . . . . . . . . . . . . . . . . . 22
     11.2. Informative References . . . . . . . . . . . . . . . . . . 23
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 24
   Intellectual Property and Copyright Statements . . . . . . . . . . 25

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1.  Introduction

   The Network Time Protocol Version 3 (NTPv3) specified in [1] has been
   widely used to synchronize computer clocks in the global Internet.
   It provides comprehensive mechanisms to access national time and
   frequency dissemination services, organize the NTP subnet of servers
   and clients and adjust the system clock in each participant.  In most
   places of the Internet of today, NTP provides accuracies of 1-50 ms,
   depending on the characteristics of the synchronization source and
   network paths.

   NTP is designed for use by clients and servers with a wide range of
   capabilities and over a wide range of network jitter and clock
   frequency wander characteristics.  Many users of NTP in the Internet
   of today use a software distribution available from www.ntp.org.  The
   distribution, which includes the full suite of NTP options,
   mitigation algorithms and security schemes, is a relatively complex,
   real-time application.  While the software has been ported to a wide
   variety of hardware platforms ranging from personal computers to
   supercomputers, its sheer size and complexity is not appropriate for
   many applications.  This facilitated the development of the Simple
   Network Time Protocol Version 4 (SNTPv4) as described in [2].

   Since the standardization of NTPv3, there has been significant
   development which has led to Version 4 of the Network Time Protocol
   (NTPv4).  This document describes NTPv4, which introduces new
   functionality to NTPv3 as described in RFC 1305, and functionality
   expanded from that of SNTPv4 as described in RFC 2030 (SNTPv4 is a
   subset of NTPv4).

   When operating with current and previous versions of NTP and SNTP,
   NTPv4 requires no changes to the protocol or implementations now
   running or likely to be implemented specifically for future NTP or
   SNTP versions.  The NTP and SNTP packet formats are the same and the
   arithmetic operations to calculate the client time, clock offset and
   round trip delay are the same.  To a NTP or SNTP server, NTP and SNTP
   clients are indistinguishable; to a NTP or SNTP client, NTP and SNTP
   servers are indistinguishable.

   NTP usually operates simultaneously with multiple servers and may
   have multiple clients of its own.  NTP employs several algorithms
   that together allow the calculation of time from messages that come
   from an NTP or SNTP server.  The overall organization of the
   algorithms is illustrated in Figure 1.  For every server there are
   two processes, a peer process which receives and processes each
   packet, and a companion poll process which sends packets to the
   server at programmed intervals.  State variables and data
   measurements are maintained separately for each pair of processes in

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   a block of memory called the peer variables.  The peer and poll
   processes together with their variables collectively belong to an
   association.  Associations can be either temporary or permanent.
   Permanent associations are described as persistent, while temporary
   associations are referred to as preemptable or ephemeral.
   . Remote   ..   Peer/Poll   ..              System       .
   . Servers  ..   Processes   ..              Process      .
   .          ..               ..                           .
   .----------..-------------..--------------               .
   .|        |->|           |..|            |               .
   .|Server 1|..|Peer/Poll 1|->|            |               .
   .|        |<-|           |..|            |               ............
   .----------..-------------..|            |               .   Clock  .
   .          ..       ^     ..|            |               .. Process .
   .          ..       |     ..|            |               ..         .
   .----------..-------------..|            |  |-----------|..         .
   .|        |->|           |..| Selection  |->|            ..-------- .
   .|Server 2|..|Peer/Poll 2|->|    and     |  | Combining |->| Loop | .
   .|        |<-|           |..| Clustering |  | Algorithm |..|Filter| .
   .----------..-------------..| Algorithms |->|           |.-----------
   .          ..       ^     ..|            |  |-----------|.     |
   .          ..       |     ..|            |               .     |
   .----------..-------------..|            |               .     |
   .|        |->|           |..|            |               .     |
   .|Server 3|..|Peer/Poll 3|->|            |               .     |
   .|        |<-|           |..|            |               .     |
   .----------..-------------..|------------|               .     |
   ....................^.....................................     |
                       |                                          |
                       |                                         \|/
                       |                                ...............
                       |                                .   /-----\   .
                       '----------------------------------<-| VFO |-<-.
                                                        .   \-----/   .
                                                        . Clock Adjust.
                                                        .   Process   .

                    Figure 1 NTPv4 Algorithm Interactions

   As each NTP packet arrives, the server time is compared to the system
   clock and an offset specific to that server is determined.  The
   system process refines these offsets using the selection, clustering
   and combining algorithms and delivers a correction to the clock
   discipline process, which functions as a lowpass filter to smooth the
   data and close the feedback loop.  The clock adjust process runs at

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   one-second intervals to amortize the corrections in small adjustments
   that approximate a continuous, monotonic clock.  The output of the
   combining algorithm represents the best estimate of the system clock
   offset relative to the server ensemble.  The discipline algorithm
   adjusts the frequency of the variable frequency oscillator (VFO) to
   minimize this offset.  Finally, the timestamps of each server are
   compared to timestamps derived from the VFO in order to calculate the
   server offsets and close the feedback loop.

   Depending on whether an NTP host is acting as server or client, or
   whether the host is an SNTP or full NTP host, the subset of
   algorithms it employs varies.  The relationship between host role/
   type and algorithm employment is summarized in Table 1.

      Table 1. Relationship between Algorithms and NTP Host Type/Role
   |      Algorithm     |                Applicability                 |
   |    Clock Filter    | Required by all NTP Servers                  |
   |   Clock Selection  | Applies to NTP hosts utilizing more than one |
   |                      source                                       |
   |     Clustering     | Applies to NTP hosts utilizing more than one |
   |                    | source                                       |
   |  Clock Combining   | Applies to NTP hosts utilizing more than one |
   |                    | source                                       |
   |      Polling       | Applies to all NTP hosts.                    |
   |  Clock Discipline  | Not required by SNTP clients.  Applies to all|
   |                    | other NTP hosts.                             |

   This document is organized as follows.  Section 2 describes the clock
   filter algorithm.  Section 3 describes the clock selection algorithm.
   Section 4 describes the clustering algorithm.  Section 5 describes
   the clock combining algorithm.  Section 6 describes the polling
   algorithm.  Section 7 describes the clock discipline algorithm.
   Sections 8 and 9 presents Security Considerations and IANA
   Considerations, respectively.  Much of the information contained
   within this document is based on material from. [3]

   NTPv4 is hereafter referred to simply as NTP, unless explicitly

   The remainder of this document contains numerous variables and

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   mathematical expressions.  Those variables take the form of Greek
   characters.  Those Greek characters are spelled out by their full
   name, with capitolized variables referring to the upper case Greek
   character.  For example Delta refers to the uppercase Greek
   character, where delta refers to the lowercase Greek character.
   Furthermore, subscripts are denoted with a '_' separating the
   variable name and the subscript.  For example 'theta_i' refers to the
   variable lowercase Greek character theta with subscript i, or
   phenotically 'theta sub i.'

2.  Clock Filter Algorithm

   The NTP clock filter algorithm selects the most appropriate sample
   data while rejecting noise spikes due to packet collisions and
   network congestion.  The clock offset (theta) and roundtrip delay
   (delta) samples are computed from the four most recent timestamps.
   Without making any assumptions about the delay distributions, but
   assuming the frequency difference or skew between the server and peer
   clocks can be neglected, let (theta, delta) represent the offset and
   delay when the path is otherwise idle; thus (theta, delta) represents
   the true offset and delay values.  The clock filter algorithm
   essentially acts as an accurate estimator and produces an estimate of
   the time, known as (theta_hat, delta_hat), from a sample sequence
   (theta_i, delta_i), where i denotes a particular sample at some time,
   collected for the path over an appropriate interval under ambient
   traffic conditions.

   The design of the clock filter algorithm was suggested by the
   observation that packet switching networks are most often operated
   well below the knee of the throughput-delay curve, which means that
   packet queues are mostly small with relatively infrequent bursts.  In
   addition, the routing algorithm most often operates to minimize the
   number of packet-switch hops and thus the number of queues.  Not only
   is the probability that an NTP packet finds a busy queue in one
   direction relatively low, but the probability of packets from a
   single exchange finding busy queuesin both directions is even lower.
   Therefore, the best offset samples should occur with the lowest

   Upon arrival of an NTP packet resulting from some poll interval at
   time t=0, a shift register containing four variables (theta_i,
   delta_i, e_i, t_i) is populated with the 0th sample, (theta_0,
   delta_0, e_0, t_0).  Here, e is the error (in seconds), which is
   initially set to precision and grown at a rate r=15 ppm for each
   epoch.  If a packet has not arrived for three successive poll
   intervals, then the sample (0, 0, 16, t) is shifted into the
   register, where t is the last current known time.  Missing data

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   samples that force this condition are never used in subsequent filter
   calculations, but do prevent very old (i.e. stale) samples from being

   Next, the register contents are copied to a temporary list and sorted
   by the metric lambda designed to avoid missing data and devalued
   samples older than the compromise Allan intercept sigma_y(x) = 1500
   s.  The Allan intercept is the intersection coordinate (x, y) of the
   phase and frequency lines.  It characterizes each particular timing
   source and clock oscillator.  A useful statistic is the x value,
   which specifies the optimum time constant for the particular source
   and oscillator combination.  The x value ranges from about 500 s to
   2000 s.  Above this value the performance is limited by oscillator
   wander, while below this value the performance is limited by system
   jitter.  For comparison, the NTPv4 clock discipline time constant is
   about 1000 s at a poll interval of 64 s.  The y statistic represents
   the best stability that can be achieved for the particular source and
   oscillator, but is not useful for performance optimization.  For this
   reason, the term Allan intercept applies to the x value at the
   intercept point.

   If e_j = infinity, then lambda_j = infinity; else, if t_j-t >
   sigma_y(x) then lambda_j = K_d + e_j; else, lambda_j = delta_j, where
   K_d = 1 s is the selection threshold.  The algorithm essentially
   sorts the data by exchanging sets; however, an exchange is not made
   unless to do so would reduce the metric by at least the value of the
   precision.  In other words, it does not make sense to change the
   order in the list, which might result in the loss of otherwise good
   samples, unless the metric change is significant.  The first entry
   (theta_0, delta_0, e_0, t_0) on the temporary list represents the
   lowest delay sample, which is used to update the peer offset theta =
   theta_0 and peer delay delta = d_0.  The peer dispersion e is
   calculated from the temporary list:

   e=sum from k=0 to k=n-1 of [e_k/(2^(k+1))].

   Finally, the temporary list is trimmed by discarding all entries
   where lambda_j = infinity and all but the first devalued entry
   lambda_j >= K_d, if one is present, leaving m (0 <= m < n) surviving
   entries on the list.  The peer jitter psi is used by the clustering
   algorithm as a quality metric and in the computation of the expected

   psi=[ (1 / (m-1) ) * (sum from k = 1 to k = m-1 of [ (theta_k -
   theta_0)^2) ]) ^ (1/2) ) ].

   A 'popcorn spike' is a transient outlier, usually only a single
   sample, that is typical of congested Internet paths.  The popcorn

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   spike suppressor is designed to detect and remove them.  Let
   theta_prime be the peer offset determined by the previous message and
   psi the current peer jitter.  If |theta - theta_prime| > (K_s * psi),
   where K_s is a tuning parameter that defaults to 3, the sample is a
   popcorn spike and is discarded.

   Note that the peer jitter will increase to protect a legitimate step

   As demonstrated by simulation and practical experience, it is prudent
   to avoid using samples more than once.  Let t_p be the epoch the peer
   variables were last updated and t_0 the epoch of the first sample on
   the temporary list.  If t_0 <= t_p, the new sample is a duplicate or
   earlier than the last one used.  If this is true, the algorithm exits
   without updating the system clock; otherwise, t_p = t_0 and the
   offset can be used to update the system clock.  The components of the
   five-tuple (theta, delta, e, psi, t_p) are called the peer variables.

3.  Clock Selection Algorithm

   In order to provide reliable synchronization, NTP uses multiple
   redundant servers and multiple disjoint network paths whenever
   possible.  When a number of associations are established, it is not
   clear beforehand which are truechimers and which are falsetickers.  A
   'truechimer' is a clock that maintains timekeeping accuracy to a
   previously published (and trusted) standard, while a 'falseticker' is
   a clock that do not maintain that level of timekeeping accuracy.
   Crucial to the success of this approach is a robust algorithm which
   finds and discards the falsetickers from the raw server population,
   since the timekeeping accuracy of a particular server may not be
   known a priori.  The clock selection algorithm determines from among
   all associations a suitable subset of truechimers capable of
   providing the most accurate and trustworthy time using principles
   similar to. [4]

   The true offset theta of a correctly operating clock relative to UTC
   must be contained in a computable range, called the confidence
   interval, equal to the root distance defined below.  Marzullo and
   Owicki devised an algorithm designed to find the intersection
   interval containing the correct time given the confidence intervals
   of m clocks, of which no more than f are considered incorrect. The
   algorithm finds the smallest intersection interval containing points
   in at least (m - f) of the given confidence intervals. [5]

   The clock selection algorithm operates as follows:

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      1.  For each of m associations, construct a correctness interval
      [(theta - rootdist()), (theta + rootdist())].

      2.  Select the lowpoint, midpoint and highpoint of these
      intervals.  Sort these values in a list from lowest to highest.
      Set the number of falsetickers f = 0.

      3.  Set the number of midpoints d = 0.  Set c = 0.  Scan from
      lowest endpoint to highest.  Add one to c for every lowpoint,
      subtract one for every highpoint, add one to d for every midpoint.
      If c >= m - f, stop; set l = current lowpoint

      4.  Set c = 0.  Scan from highest endpoint to lowest.  Add one to
      c for every highpoint, subtract one for every lowpoint, add one to
      d for every midpoint.  If c >= m - f, stop; set u = current

      5.  Is d = f and l < u?

      if yes, then follow step 5y, else, follow step 5n.

      5y.  Success: the intersection interval is [l, u].

      5n.  Add one to f.  Is f < (m / 2)?  If yes, then go to step 3
      again.  If no, then go to step 6.

      6.  Failure; a majority clique could not be found.  Stop

4.  Clustering Algorithm

   NTP configurations usually include several servers in order to
   provide sufficient redundancy for the selection algorithm to
   determine which are truechimers and which are not.  When a sizeable
   number of servers are present, the individual clock offsets for each
   are not always the same, even if each server is closely synchronized
   to UTC by one means or another.  Small systematic differences in the
   order of a millisecond or two are usually due to interface and
   network latencies.  Larger differences are due to asymmetric delays
   and in the extreme due to asymmetric satellite/landline delays.

   The clustering algorithm sifts the truechimers of the selection
   algorithm to identify the survivors providing the best accuracy.  In
   principle, the sift could result in a single survivor and its offset
   estimate used to discipline the system clock; however, a better
   estimate usually results if the offsets of a number of survivors are
   averaged together.  So, a balance must be struck between reducing the

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   selection jitter by casting off outlyers and improving the offset
   estimate by including more survivors in the average.

   The clustering algorithm steps follow:

      1.  Let (theta, phi, Lambda) represent a candidate peer with
      offset theta, jitter j and a weight factor Lambda = stratum *
      MAXDIST + rootdist().

      2.  Sort the candidates by increasing Lambda.  Let n be the number
      of candidates and NMIN the minimum number of survivors.

      3.  For each candidate compute the selection jitter jsubS (RMS
      peer offset differences between this and all other candidates).

      4.  Select j_max as the candidate with maximum j_S.

      5.  Select j_min as the candidate with minimum j_S.

      If yes, go to step 6y.  If no, go to step 6n.

      6y.  Done.  The remaining cluster survivors are correct.  The
      survivors are in the v. structure sorted by Lambda.

      6n.  Delete the outlyer candidate with j_max; reduce n by one, and
      go back to step 3.

5.  Clock Combining Algorithm

   The selection and clustering algorithms operate to select a single
   system peer based on stratum and root distance.  The result is that
   the NTP subnet forms a logical tree with the primary servers at the
   root and other servers at increasing stratum levels toward the
   leaves.  However, since each server on the tree ordinarily runs the
   NTP protocol with several other servers at equal or lower stratum,
   these servers can provide diversity paths for backup and cross
   checking.  While these other paths are not ordinarily used directly
   for synchronization, it is possible that increased accuracy can be
   obtained by averaging their offsets according to appropriately chosen

   The result of the clustering algorithm is a set of survivors (there
   must be at least one) that represent truechimers, or correct clocks.
   If only one peer survives or if the prefer peer is among the
   survivors, that peer becomes the system peer and the combining
   algorithm is not used.  Otherwise, the final clock correction is
   determined by the combining algorithm.

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   Let the three-tuple (theta_i, psi_i, Lambda_i) represent the peer
   offset, peer jitter, and root distance for the ith survivor.  Then
   the combined peer offset and peer jitter is, respectively:

   T = (a*sum) over all i of [theta_i / Lambda_i] and psi_r = (a * sum)
   over all i of [(psi_i)^2 / Lambda_i]^(1/2),

   where a is a normalization constant:

   a=1/[sum over all i of [1 / Lambda_i].

   The result T is the system offset processed by the clock discipline
   algorithm.  Note that the root distance cannot be less than the
   precision in order to avoid divide exceptions.

   Let psi_s represent the selection jitter associated with the system
   peer and psi_r as above.  Then the system jitter is defined as:

   sj=[(psi_r)^2 + (psi_s)^2]^(1/2).

   The system jitter represents the best estimate of error in computing
   the clock offset.  It is interpreted as the expected error statistic
   available to application program.

6.  Polling Algorithm

   The poll process determines whether and when to send a poll message
   to the server.  Ordinarily, polls are sent at regular intervals
   determined by the clock discipline time constant.  In some cases
   where justified by network load, performance can be improved and
   network jitter reduced by sending several messages instead of just
   one.  This can be done when the server is unreachable, when it is
   reachable or both.  The most common cases where this is advisable is
   when using very large poll intervals in the order of several hours or

   The poll interval starts out normally at about one minute.  If the
   offset is less than a tuning constant times the system jitter for
   some number of polls, it is increased, but usually not above 1024
   seconds Otherwise, it is decreased, but usually not below 64 seconds.
   The limits can be changed to a lower limit of 16 seconds and/or to an
   upper limit of 36 hours.  In order to minimize network traffic, when
   a server has not been heard for some time, the poll interval is
   increased in stages to 1024 seconds.

   The poll process sends packets to the server at designated intervals
   tau and updates the "reach" register which establishes whether the

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   server is reachable.  Table 2 shows the poll process routines and
   Table 3 the variables shared by the process routines, including
   poll(), peer_xmit(), fast_xmit() and poll_update().

                     Table 2. Poll Process Routines
   |    Name     |    Description   |        Related routines          |
   |    poll     |       poll       |   *clock_adjust, clock_filtert,  |
   |             |                  |      peer_xmit, poll_update      |
   | poll_update |    poll update   |         *packet, *poll           |
   |  peer_xmit  |   peer transmit  |           *poll, md5             |
   |  fast_xmit  |   fast transmit  |          *receive, md5           |

                     Table 3. Poll Process Variables
   |    Name     |    Process   |        Variable Description          |
   |    hpoll    |     poll     |           host poll interval         |
   |    hmode    |     poll     |               host mode              |
   |    count    |     poll     |             burst counter            |
   |    reach    |     poll     |            "reach" register          |
   |   unreach   |     poll     |             unreach counter          |
   |      t      | local clock  |              current time            |
   |     tau     | local clock  |              poll interval           |
   |     rho     |    system    |               system peer            |
   |    M_BCST   |   parameter  |            broadcast server          |
   |    M-BCLN   |   parameter  |            broadcast client          |
   |   B_BURST   |   peer flag  |              burst enable            |
   |   B_IBURST  |   peer flag  |           initial burst enable       |
   |   B_COUNT   |   parameter  |             pkts in a burst          |

   The poll() routine is described in Figure 2.  Each time the poll()
   routine is called, the reach variable is shifted left by one bit.
   When a packet is accepted by the packet() routine in the peer process
   the rightmost bit is set to one.  As long as reach is nonzero, the
   server is considered reachable.  However, if the rightmost three bits
   become zero, indicating that packets from the server have not been
   received for at least three poll intervals, a sample with MAXDIST
   dispersion is shifted in the clock filter.  This causes the server to
   be devalued in the mitigation process.  The unreach counter
   increments at each poll interval; it is reset to zero if the reach
   register is nonzero.  If the counter exceeds the UNREACH parameter,

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   the poll exponent is incremented for each succeeding poll.  This
   reduces useless network load in case of server failure.  The poll()
   routine can operate in three modes.

   Ordinarily, polls are sent at the interval selected by hpoll and
   ppoll poll exponents assigned.  However, if the iburst feature is
   enabled and the server is not reachable, a burst of eight polls is
   sent at two-second intervals.  Alternatively or in addition, if the
   burst feature is enabled and the server is reachable, a burst of
   eight polls is sent as with iburst.  This is especially useful at
   very large poll intervals of many hours.  The remaining routines are
   straightforward.  The poll() routine calls the peer_xmit() routine
   when an association has been mobilized.  The receive() routine calls
   fast_xmit() when a client mode packet is received.  Both cases are
   shown in Figure 3.  These routines copy values from the association
   (peer_xmit()) or from the arriving packet (fast_xmit()) as shown in
   the accompanying tables.  The poll_update() routine shown in Figure 4
   determines the next poll interval or burst interval.  Variable names
   in both routines are referenced in Tables 4 and 5, respectively.
     ---------------   -----------------
   |   poll()    |-->| hmode=M_BCST? |
   ---------------   -----------------
   if hmode=M_BCST == YES:
        |s.rho = NULL?|
        if s.rho=NULL == YES:
             ---------------   ---------------
             |poll_update()|-->|   exit()    |
             ---------------   ---------------
        if s.rho=NULL == NO:
             if hmode=M_BCLN == YES:
                  ---------------   ---------------
                  |poll_update()|-->|   exit()    |
                  ---------------   ---------------
             if hmode_M_BCLN == NO:
                  ---------------   ---------------   ---------------
                  | peer_xmit() |-->|poll_update()|-->|   exit()    |
                  ---------------   ---------------   ---------------
   if hmode=M_BCST == NO:
        | burst = 0?  |
        if burst = 0 == YES:
             ---------------   ---------------

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             | reach <<=1  |-->| reach = 0?  |
             ---------------   ---------------
             if reach = 0 == YES:
                  | unreach > UNREACH? |
                  if unreach > UNREACH == YES:
                     ---------------   ---------------   -----go to-----
                     |   hpoll++   |-->|  unreach++  |-->|hmode=M_BCLN?|
                     ---------------   ---------------   ---------------
                     (go to hmode=M_BCLN routine earlier in the figure)
                  if unreach > UNREACH == NO:
                      |  B_IBURST?  |
                      if B_IBURST == YES:
                           |    fit()?   |
                           if fit() == YES:
                                ----------------   -----go to-----
                                | burst=BCOUNT |-->|  unreach++  |
                                ----------------   ---------------
                           if fit() == NO:
                                -----go to-----
                                |  unreach++  |
                      if B_IBURST == NO:
                           -----go to-----
                           |  unreach++  |
             if reach = 0 == NO:
                  | unreach = 0?|
                  if unreach = 0 == YES:
                       | reach & 0x7 = 0? |
                       if reach & 0x7 = 0 == YES:
                            | clock_filter(0,0,inf,t) |
                            | hpoll = c,tau |

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                            |    B_BURST?   |
                            if B_BURST == YES:
                                 | unreach = 0?|
                                 if unreach = 0 == YES:
                                      ---------------   -----go to-----
                                      |burst=BCOUNT |-->|hmode=M_BCLN?|
                                      ---------------   ---------------
                                 if unreach = 0 == NO:
                                      -----go to-----
                            if B_BURST == NO:
                                 -----go to-----
             if unreach = 0 == NO:
                  -----go to-----
                  | hpoll=c,tau |
        if burst = 0 == NO:
             ---------------   -----go to-----
             |   burst--   |-->|hmode=M_BCLN?|
             ---------------   ---------------

                             Figure 2. Poll Routine

                     Table 4. Peer Fast Transmit Table
   |  Variable Name   |                   Description                  |
   |        T1        |      Origin Timestamp in NTP packet field      |
   |        T2        |      Receive Timestamp in NTP packet field     |
   |        T3        |                       ???                      |
   |       mac        |                       ???                      |

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                         | peer_xmit(),fast_xmit() |
                         |      *copy header       |
                         |        T1, T2           |
                         |       T3 = clock        |
                         |       mac = md5()       |
                         |      xmitpacket()       |
                         |         exit            |

                         Figure 3. Peer Fast Transmit

                   Table 5. Poll Process Variables
   |    Name     |    Process   |        Variable Description          |
   |    ppoll    |     peer     |         peer poll interval           |
   |    hpoll    |     poll     |         host poll interval           |
   |    burst    |     poll     |           burst counter              |
   |    timer    |     poll     |             poll timer               |
   |    BTIME    |   parameter  |             burst time               |
   |   MINPOLL   |   parameter  |        minimum poll interval         |
   |   MAXPOLL   |   parameter  |        maximum poll interval         |

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   |     poll_update()       |
   |       burst = 0?        |
   if burst = 0 == YES:
        |                exit                |
   if burst = 0 == NO:
        |           timer running?           |
        if timer running == YES:
             |                exit                |
        if timer running == NO:
             |          timer = BTIME             |
             |                exit                |

              Figure 4. Poll Update

7.  Clock Discipline Algorithm

   The clock discipline algorithm synchronizes the computer clock with
   respect to the best time value from each server and the best
   combination of servers.  This algorithm automatically adapts to
   changes in operating environment without manual configuration or
   real-time management functions.  The clock discipline algorithm is
   implemented as the feedback control system shown in Figure 5.

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             thetar +  |         \        +----------------+
         NTP --------->|  Phase   \  V_d  |                |  V_s
             thetac -  | Detector  ------>|  Clock Filter  |-----+
             +-------->|          /       |                |     |
             |         |         /        +----------------+     |
             |          ---------                                |
             |                                                   |
           -----                                                 |
          /     \                                                |
          | VFO |                                                |
          \     /                                                |
           -----    +-------------------------------------+      |
             ^      |            Loop Filter              |      |
             |      |                                     |      |
             |      | +---------+   x  +-------------+    |      |
             |      | |         |<-----|             |    |      |
             +------|-|  Clock  |   y  | Phase/Freq  |<---|------+
                    | | Adjust  |<-----| Prediction  |    |
                    | |         |      |             |    |
                    | +---------+      +-------------+    |
                    |                                     |

                 Figure 5. Clock Discipline Algorithm

   The variable theta_r represents the combined server reference phase
   and theta_c the control phase of the VFO.  Each update received from
   a server produces a signal V_d representing the instantaneous phase
   difference theta_r - theta_c.  The clock filter for each server
   functions as a tapped delay line, with the output taken at the tap
   selected by the clock filter algorithm.  The selection, clustering
   and combining algorithms combine the data from multiple filters to
   produce the signal V_s.  The loop filter, with impulse response F(t),
   produces the signal V_c which controls the VFO frequency omega_c.
   Thus, its phase theta_c follows:

   theta_c = integral over t of (omega_c(t) dt)

   which closes the loop.  The V_c signal is generated by an adjustment
   process which runs at intervals of one second in the NTP daemon or
   one tick in the kernel. are set to 0,

   The NTPv4 discipline includes both PLL and FLL capabilities.  The
   selection of which mode to use, FLL or PLL and in what combination,
   is made on the basis of the poll exponent tau.  In the NTPv4 design,
   PLL mode is used at smaller values of tau, while FLL mode is used at
   larger values.  In between, a combination of PLL and FLL modes is

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   used.  This improves the clock accuracy and stability, especially for
   poll intervals larger than the Allan intercept.
                     x <------(Phase Correction)<--.
                           y_FLL                   |
                            .-(FLL Predict)<-------+<--V_s
                            |                      |
                           \|/                     |
                     y <--(Sum)                    |
                            ^                      |
                            |                      |
                            '-(PLL Predict)<-------'

                    Figure 6. FLL/PLL Prediction Functions

   In PLL mode y is a time integral over all past values of V_s, so the
   PLL frequency adjustment required is:

   y_PLL = [ (V_s * mu) / ( (64 * T_c) ^ 2) ].

   where T_c is the time constant.  In FLL mode, is an average of past
   frequency changes, as computed from V_s and mu.  The goal of the
   algorithm is to reduce V_s to zero; so, to the extent this has been
   successful in the past, previous values can be assumed zero and the
   average becomes:

   y_FLL = [ (V_s - x) / (8 * mu) ].

   where x is the residual phase error computed by the clock adjust

   Finally, in both PLL and FLL modes set the phase to x = V_s and
   frequency y = [y + y_PLL + y_FLL].

   Once each second the adjustment process computes a phase increment z
   = [ x / (16 * T_c) ] and new phase adjustment x = x - z.  The phase
   increment z is passed to the kernel time adjustment function.  This
   continues until the next update which recomputes x and y.

   A key factor in the performance of the PLL/FLL hybrid algorithm are
   the weight factors for the y_PLL and y_FLL adjustments, which depend
   on the poll exponent tau which in turn determines the time constant
   T_c = (2 ^ tau), in seconds.  PLL contributions should dominate at
   the lower values of tau, while FLL contributions should dominate at
   the higher values.  The clock discipline algorithm response times to
   several PPM deviation examples is presented in . [3]

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7.1.  Poll Interval Control

   The NTPv4 algorithm aims to set the averaging time somewhere near the
   Allan intercept.  A key to this strategy is the measured clock jitter
   and oscillator wander statistics.  The clock jitter is estimated from
   phase differences psi_c = ( <Delta_x^2> ^ (1/2) ), where the brackets
   indicate an exponential average.  The oscillator wander is estimated
   from frequency differences psi_f = (T_c * <Delta_y^2> ^ (1/2) ).  As
   the poll exponent tau increases, it is expected that psisubc will
   decrease and psisubf will increase, depending on the relative
   contributions of phase noise and frequency noise.

   In the NTPv4 algorithm at each update a counter is incremented by one
   if x is within the bound |x|< (4 * psi_c), where the constant 4 is
   determined by experiment, and decremented by one otherwise.

   In order to avoid needless hunting, a degree of hysteresis is built
   into the scheme.  If the counter reaches an upper limit 30, tau is
   increased by one; if it reaches a lower limit -30, tau is reduced by
   two.  In either case the counter is reset to zero.  Under normal
   conditions tau increases in stages from a default lower limit of 6
   (64 s) to a default upper limit of 10 (1024 seconds).  However, if
   the wander increases because the oscillator frequency is deviating
   too fast, tau is quickly reduced.  Once the oscillator wander
   subsides, tau is slowly increased again.  Under typical operating
   conditions, tau hovers close to the maximum; but, on occasions of a
   heat spike when the oscillator wanders more than about 1 PPM, it
   quickly drops to lower values until the wander subsides.

7.2.  State Machine

   The clock discipline must operate over an extremely wide range of
   network jitter and oscillator wander conditions without manual
   intervention or prior configuration.  As determined by past
   experience and experiment, the data grooming algorithms work well to
   sift good data from bad, especially under conditions of light to
   moderate network and server loads.  The PLL/FLL hybrid algorithm may
   perform poorly and even become unstable under heavy network loading.
   The state machine functions to bypass some discipline functions under
   conditions of hardware or software failure, severe time or frequency
   transients and especially when the poll interval is relatively large.

   Under normal conditions the NTP discipline algorithm writes the
   current frequency offset to a file at hourly intervals.  Once the
   file is written and the daemon is restarted after reboot, for
   example, it initializes the frequency offset from the file, which
   avoids the training time, possibly several hours, to determine the
   intrinsic frequency offset when the daemon is started for the first

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   time.  When toll charges accrue for every NTP message, as in a
   telephone modem service, it is important to determine the presence of
   a possibly large intrinsic frequency offset, especially if the
   interval between telephone calls must be 15 minutes or more.  For
   instance, without the state machine it might take many calls spaced
   at 15 minutes until the frequency offset is determined and the call
   spacing can be increased.  With the state machine it usually takes
   only two calls to complete the process.

   The clock state machine transition function is shown in Table 6.  It
   determines the action and next state when an update with specified
   offset occurs in a given state shown in the first column.  The second
   column shows what happens if the offset is less than the step
   threshold, the third when the step threshold is exceeded but not the
   stepout threshold and the third when both thresholds are exceeded.
   The state machine responds to the current state and event to cause
   the action shown.

              Table 6. Clock State Machine Transition Function
   | State |   abs(T) < STEP   |   abs(T) > STEP   |    Comments       |
   | NSET  | > FREQ; adjust    | > FREQ; step      | no frequency      |
   |       | time              | time              | file              |
   | FSET  | > SYNC; adjust    | > SYNC; step      | frequency file    |
   |       | time              | time              |                   |
   | SPIK  | > SYNC; adjust    | if (<900 s)>SPIK  | outlier detected  |
   |       | freq, adjust time | else SYNC; step   |                   |
   |       |                   | freq; step time   |                   |
   | FREQ  | if (<900 s)> FREQ | if (<900 s)>FREQ  | initial frequency |
   |       | else >SYNC; step  | else >SYNC; step  |                   |
   |       | freq, adjust time | freq, adjust time |                   |
   | SYNC  | >SYNC; adjust freq| if (<900 s)>SPIK  | normal operation  |
   |       | adjust time       | else >SYNC; step  |                   |
   |       |                   | freq; step time   |                   |

   The actions listed in the state diagram include adjust-frequency,
   step-frequency, adjust-time and step-time actions.  The normal action
   in the SYNC state is to adjust both frequency and time.  The step-
   time action is to set the system clock, while the step-frequency
   action is to calculate the frequency offset directly.  This has to be
   done carefully to avoid contamination of the frequency estimate by
   the phase adjustment since the last update.

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   The machine can be initialized in two states, FSET if the frequency
   file is present or NSET if it has not yet been created.  If the file
   is not present, this may be the first time the discipline has ever
   been activated, so it may have to quickly determine the oscillator
   intrinsic frequency offset.  It is important to realize that a number
   of NTP messages may be exchanged before the mitigation algorithms
   determine a reliable time offset and call the clock discipline

   When the first valid offset arrives in the NSET state, (1) the time
   is stepped to that offset, if necessary, (2) the watchdog counter is
   started and (3) the machine exits to the FREQ state.  Subsequently,
   updates will be ignored until the stepout threshold has been reached,
   at which time the frequency is stepped, the time is stepped if
   necessary, and the machine exits to SYNC state.  When the first valid
   offset arrives in the FSET state, the frequency has already been
   initialized, so the machine does the same things as in the NSET
   state, but exits to the SYNC state.

   In the SYNC state the machine watches for outliers above the step
   threshold.  If one is found, the machine exits to SPIK state and
   starts the watchdog timer.  If another offset less than the step
   threshold is found, the counter is stopped and the machine exits to
   the SYNC state.  If the watchdog timer reaches the stepout threshold,
   the time and frequency are both stepped as required and the machine
   exits to the SYNC state.

8.  Security Considerations

   There are no security considerations.

9.  IANA Considerations

   There are no IANA considerations.

10.  Acknowledgements

11.  References

11.1.  Normative References

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11.2.  Informative References

   [1]  Mills, D., "Network Time Protocol (Version 3) Specification,
        Implementation", RFC 1305, March 1992.

   [2]  Mills, D., "Simple Network Time Protocol (SNTP) Version 4 for
        IPv4, IPv6 and OSI", RFC 2030, October 1996.

   [3]  "D. Mills, "Computer Network Time Synchronization: The Network
        Time Protocol", DRAFT.",  .

   [4]  "Dolev, D., Halpern, J., Simons, B., and Strong R., "Dynamic
        Fault-Tolerant Clock Synchronization," JACM 42, January 1995,
        pp. 143-185.",  .

   [5]  "Berthaud, J.M., "Time Synchronization over Networks using
        Convex Closures," IEEE/ACM Transactions on Networking, April
        2000, pp. 265-277.",  .

   [6]  "Burbank, J., Martin, J., and Mills, D., Network Time Protocol
        Version 4 Protocol Specification,
        <draft-ietf-ntp-ntpv4-proto-01.txt>, October 2005, work in
        progress.",  .

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Authors' Addresses

   William Kasch (editor)
   The Johns Hopkins University Applied Physics Lab
   11100 Johns Hopkins Road
   Laurel, Maryland  20723-6099
   United States

   Phone: +1 443 778 7463
   Email: william.kasch@jhuapl.edu

   Jack Burbank (editor)
   The Johns Hopkins University Applied Physics Laboratory
   11100 Johns Hopkins Road
   Laurel, Maryland  20723-6099
   United States

   Phone: +1 443 778 7127
   Email: jack.burbank@jhuapl.edu

   Dr. David L. Mills
   University of Delaware
   Newark, Delaware  19716
   United States

   Phone: +1 302 831 8247
   Email: mills@udel.edu

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