Network Working Group                                 C.Demichelis                                      C. Demichelis
INTERNET-DRAFT                                                     CSELT

expires  May
Expiration Date: December 1999                               P. Chimento
                                                                    CTIT
                                                              June  1999

          Instantaneous Packet Delay Variation Metric for IPPM
                     <draft-ietf-ippm-ipdv-02.txt>
                     <draft-ietf-ippm-ipdv-03.txt>

1. Status of this Memo

   This document is an Internet Draft. Internet Drafts Internet-Draft and is in full conformance with    |
   all provisions of Section 10 of RFC2026.

   Internet-Drafts are working doc-
 uments documents of the Internet Engineering
   Task Force (IETF), its areas, and its working groups.  Note that
   other groups may also distribute work-
 ing working documents as Internet Internet-
   Drafts.

 Internet Drafts

   Internet-Drafts are draft documents valid for a maximum of six
 months, months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet Drafts Internet-Drafts as reference
   material or to cite them other than as ``work "work in progress''.

 To learn the progress."

   The list of current status Internet-Drafts can be accessed at                |
   http://www.ietf.org/ietf/1id-abstracts.txt                            |

   The list of any Internet Draft, please check the
 ``1id-abstracts.txt'' listing contained in the Internet Drafts Internet-Draft shadow directories on ftp.is.co.za (Africa), nic.nordu.net (Europe),
 munnari.oz.au (Pacific Rim), ds.internic.net (US East Coast), or
 ftp.isi.edu (US West Coast). can be accessed at      |
   http://www.ietf.org/shadow.html

   This memo provides information for the Internet community.  This memo
   does not specify an Internet standard of any kind.  Distribution of
   this memo is unlimited.

2. Abstract

   This memo refers to a metric for variation in delay of packets across
   Internet paths. The metric is based on statistics of the difference
   in One-Way-Delay of consecutive packets. This particular definition
   of variation is called "Instantaneous Packet Delay Variation (ipdv)".

   The metric is valid for measurements between two hosts both in the
   case that they have synchronized clocks and in the case that they are
   not synchronized. In the second case it allows an evaluation of the
   reciprocal skew. Measurements performed on both directions (Two-ways (Two-way
   measurements) allow a better estimation of clock differences. The
   precision that can be obtained is evaluated.

I-D                         Ipdv Metric                    November 1998

3. Introduction

   This memo takes as a reference the Draft-ietf "One-Way-Delay metric   |
   for IPPM" that it is supposed to be known. [1].  Part of the text in this memo is directly taken from
   that Draft.

   This memo defines a metric for variation in delay of packets that
   flow from one host to another one through an IP path. Since the
   metric is related to a variation, different definitions are possible
   according to what the variation is measured against.

NOTE: The terminology used in this Draft will be re-visited as soon as
a terminology document will be available.
So far the following is considered:
-

   "Jitter" commonly has two meanings: The term Jitter first meaning is derived from the well known definition given for
  transmission          |
   variation of electrical pulses associated to a clock, and it seems
  to be able to describe variations signal with respect to an expected some clock signal, where the    |
   arrival
  time.
- Each entity adopted as a reference for variation measurements defines
  a specific metric. Each metric describes a specific aspect or effect time of the behavior signal is expected to coincide with the arrival   |
   of the System Under Test (SUT).
- Among entities that can be adopted, as an example, it is possible clock signal. The second meaning has to
  consider a reference delay for do with the path, variation  |
   of a metric (e.g. delay) with respect to some reference metric (e.g.  |
   average delay for the Src
  Dst pair, the Mean One-Way-Delay over a period or minimum delay). The form of interest, the Delay
  variation "jitter" that can be derived considering the difference between the
  actual and we talk    |
   about here has to do almost exclusively with the expected arrival time, second meaning,      |
   rather than the difference between first. See the
  delay of a packet and section on the last measured similar delay. relationship with other |
   standards.

3.1. Definition

   A definition of the Instantaneous Packet Delay Variation (ipdv) can
   be given for a pair of packets or for a packet inside a stream of
   packets.

   For a pair of packets:
-

   +  The ipdv of a pair of IP packets, that are transmitted from the measu-
  rement
      measurement point MP1 to the measurement point MP2, is the
      difference between the One-Way-Delay measured for the second
      packet and the One-
  Way-Delay One-Way-Delay measured for the first packet of the
      pair.

   For a stream of packets:
 -

   +  The Instantaneous Packet Delay Variation of an IP packet, inside a
      stream of packets, going from the measurement point MP1 to the measu-
  rement
      measurement point MP2, is the difference of the One-Way-Delay of
      that packet and the One-Way-Delay of the preceding packet in the
      stream.

I-D                         Ipdv Metric                    November 1998

3.2. Motivation

   A number of services that can be supported by IP are sensitive to the
   regular delivery of packets and can be disturbed by instantaneous va-
 riations
   variations in delay, while they are not disturbed by slow variations,
   that can last a relatively long time. A specific metric for quick va-
 riations
   variations is therefore desirable. Metrics that can be derived from
   the analysis of statistics of ipdv can also be used, for example, for |
   buffer dimensioning, but this memo is not intended in that sense. dimensioning.  The scope of this metric is to provide a way
   for measurement of the quality delivered by a path.

   In addition, this type of metric is particularly robust with respect
   differences and variations of the clocks of the two hosts. This allow
   allows the use of the metric even if the two hosts that support the measure-
 -ment
   measurement points are not synchronized. In the latter case
   indications on of reciprocal skew of the clocks can be derived from the
   measurement and corrections are possible. The related precision is
   often comparable with the one that can be achieved with synchronized
   clocks, being of the same order of magnitude of synchronization
   errors. This will be discussed below.

3.3. General Issues Regarding Time

 All what is

   Everything contained in the paragraph Section 2.2. of the Draft ippm on One-
 Way Delay metric (2.2. General Issues Regarding Time) [2] applies also in this  |
   case.

   In addition, it is we assume here considered that the reciprocal skew of the two
   clocks can be decomposed into two parts:
 *

   +  A fixed one, called in this context "skew", given, for example, by
      tolerances in physical dimensions of crystals.
 *

   +  A variable one, called in this context "drift", given, for
      example, by changes in temperature or other conditions of
      operation. Both of this these components are part of the term "skew" as
      defined in the referenced Draft and in the Framework document.

   NOTE: The drift of a clock, as it is above defined over a long period
   must have an average value that tends to zero while the period
   becomes large since the frequency of the clock has a finite (and little)
   small) range. In order to underline the order of magnitude of this
   effect,it is considered that the maximum range of drift for
   commercial crystals is about 50 part per million (ppm). Since it is
   mainly connected with variations in operating temperature (from 0 to
   70 degrees Celsius), it is expected that a host will have a nearly
   constant temperature during its operation period, and variations in
   temperature, even if quick, could be less than one Celsius per
   second, and range in the order of

I-D                           Ipdv Metric                  November 1998 few degrees. The total range of the
   drift is usually related to varia-
 -tions variations from 0 to 70 Celsius. These
   are important points for evaluation of precision of ipdv
   measurements, as it will see be seen below.

4. Structure of this memo

   The metric will be defined as applicable to a stream of packets that
   flow from a source host to a destination host (one-way ipdv). The ini-
 tial
   initial assumption is that source and destination hosts have
   synchronized clocks. The definition of a singleton of one-way ipdv
   metric is first consi-
 -dered, considered, and then a definition of samples for ipdv
   will be given.

   Then the case of application to not synchronized non-synchronized hosts will be dis-
 cussed,
   discussed, and the precision will be compared with the one of the previous
 case.
   synchronized clocks.

   A bidirectional ipdv metric will be defined, as well as the
   methodology for error corrections. This will not be a two-ways two-way metric,
   but a "paired" one-way in opposite directions. Some statistics
   describing the IP path's behavior will be proposed.

 In the Appendix A a more detailed analysis is reported of the ipdv
 theory and of the characteristics of ipdv distribution.

5. A singleton definition of a One-way ipdv metric                       |

   This definition makes use of the corresponding definition of type-P-
 One-Way-Delay, that is supposed to be known.
   One-Way-Delay metric [2]. This section makes use of those parts of
   the One-Way-Delay Draft that directly apply to the One-Way-ipdv
   metric, or makes direct references to that Draft.

5.1. Metric name

   Type-P-One-way-ipdv

5.2. Metric parameters

   + Scr,  Src, the IP address of a host

   +  Dst, the IP address of a host

   +  T1, a time

   +  T2, a time. It is explicitly noted that also the difference T2-T1
      is a parameter of the measurement though this is already implicit,
      since the times T1 and T2 exactly define the time conditions in
      which the measurement takes place.

I-D                         Ipdv Metric                    November 1998

 + Path,

   Note that the path from Src to Dst; in cases where there packet length is only one
 path from Src to Dst, this optional an implicit parameter can be omitted.
 {Comment: the presence of path is motivated by cases such as with
 Merit's NetNow setup, in which a Src on one NAP can reach a Dst on
 another NAP by either of several different backbone networks.
 Generally, both the      |
   Type-P-One-way-delay metric and the Type-P-One-way-ipdv metric, since |
   this optional parameter is useful only when several dif-
 -ferent routes are possible from Src contributes to Dst. Using the loose source
 route IP option is avoided since it would often artificially worsen overall one-way delay. We assume that the performance observed, and since it might not be supported along
 some paths.}

5.2.     |
   packets sent for ipdv measurements are all of the same length.

5.3. Metric unit

   The value of a Type-P-One-way-ipdv is either a real number of seconds
   (positive, zero or negative) or an undefined number of seconds.

5.3.

5.4. Definition

   Type-P-One-way-ipdv is defined for two (consecutive) packets from Src
   to Dst, as the difference between the value of the type-P-One-way-
   delay from Src to Dst at T2 [via path] and the value of the type-P-
   One-Way-Delay from Src to Dst at T1 [via path]. T1 is the wire-time
   at which Scr sent the first bit of the first packet, and T2 is the
   wire-time at which Src sent the first bit of the second packet. This
   metric is therefore ideally derived from the One-Way-Delay metric.

   NOTE: The requirement of "consecutive" packets is not essential. The
   measured value is anyway the difference in One-Way-Delay at the times
   T1 and T2, which is meaningful by itself, as long as the times T1 and |
   T2 are such to describe denote the investigated charac-
       -teristics. These wire times will be better defined later. of the packets sent from Src to Dst.

   Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to
   Dst at T1, T2 [via path] is ddT" means that Src sent two consecutive
 packets whose
   packets, the first at wire-time T1 (first bit), and the second at
   wire-time T2 (first bit) and the packets were received by Dst at wire
 -time
   wire-time dT1+T1 (last bit of the first packet), and, respectively, and at wire-time
   dT2+T2 (last bit of the second packet), and that dT2-dT1=ddT.

   "The type-P-one-way-ipdv from Src to Dst at T1,T2 [via path] is unde-
 fined"
   undefined" means that Src sent the first bit of a packet at T1 and
   the first bit of a second packet at T2 and that Dst did not receive
   one or both packets.

I-D                          Ipdv Metric                   November 1998

5.4.

5.5. Discussion

   Type-P-One-way-ipdv is a metric that makes use of the same
   measurement methods provided for delay metrics.

   The following practical issues have to be considered:

   +  Being a differential measurement, this metric is less sensitive to
      clock synchronization problems. This issue will be more carefully
      examined in section 6. 7 of this memo. It is pointed out that, if the
      reciprocal clock conditions change in time, the accuracy of the
      measurement will depend on the time inter-
        -val interval T2-T1 and the amount
      magnitude of possible errors will be discussed below.

   +  A given methodology will have to include a way to determine
      whether a delay value is infinite or whether it is merely very
      large (and the packet is yet to arrive at Dst).  As noted by
      Mahdavi and Paxson, simple upper bounds (such as the 255 seconds
      theoretical upper bound on the lifetimes of IP packets [Postel:
      RFC 791]) could be used, but good engineering, including an
      understanding of packet lifetimes, will be nee-
        -ded needed in practice.
      {Comment: Note that, for many applications of these metrics, the
      harm in treating a large delay as infinite might be zero or very
      small. A TCP data packet, for example, that arrives only after
      several multiples of the RTT may as well have been lost.}

   + Usually a path is such that if  As with other 'type-P' metrics, the first packet is largely delayed,
        it can "stop" value of the second packet metric may depend
      on such properties of the pair and vary its delay.
        This is not a problem for the definition since is, in any case,
        part of the description of the path's behavior.
 + As with other 'type-P' metrics, the value of the metric may de-
        -pend on such properties of the packet as protocol,(UDP or TCP)
        port number, size, packet as protocol,(UDP or TCP) port
      number, size, and arrangement for special treatment (as with IP
      precedence or with RSVP).

   +  If the packet is duplicated along the path (or paths!) so that
      multiple non-corrupt copies arrive at the destination, then the
      packet is counted as received, and the first copy to arrive
      determines the packet's One-Way-Delay.

   +  If the packet is fragmented and if, for whatever reason, reas-
        -sembly
      reassembly does not occur, then the packet will be deemed lost.

5.5.

5.6. Methodologies

   As with other Type-P-* metrics, the detailed methodology will depend
   on the Type-P (e.g., protocol number, UDP/TCP port number, size,
   precedence).

I-D                         Ipdv Metric                   November 1998  Generally, for a given Type-P, the methodology would
   proceed as fol-
 lows: follows:

   +  The need of synchronized clocks for Src and Dst will be discus-
        -sed discussed
      later. Here a methodology is supposed that is based on
      synchronized clocks.

   +  At the Src host, select Src and Dst IP addresses, and form two
      test packets of Type-P with these addresses. Any 'padding' por-
        -tion portion
      of the packet needed only to make the test packet a given size
      should be filled with randomized bits to avoid a situation in
      which the measured delay is lower than it would otherwise be due
      to compression techniques along the path.

   + Optionally, select a specific path and arrange for Src to send
        the packets to that path. {Comment: This could be done, for
        example, by installing a temporary host-route for Dst in Src's
        routing table.}
 +  At the Dst host, arrange to receive the packets.

   +  At the Src host, place a timestamp in the prepared  first Type-P packet,
      and send it towards Dst [via path].

   +  If the packet arrives within a reasonable period of time, take a
      timestamp as soon as possible upon the receipt of the packet. By
      subtracting the two timestamps, an estimate of One-Way-Delay can
      be computed.

   +  Record this first delay value.

   +  At the Src host, place a timestamp in the prepared second Type-P packet,
      and send it towards Dst [via path].

   +  If the packet arrives within a reasonable period of time, take a
      timestamp as soon as possible upon the receipt of the packet. By
      subtracting the two timestamps, an estimate of One-Way-Delay can
      be computed.

   +  By subtracting the second value of One-Way-Delay from the first
      value the ipdv value of the pair of packets is obtained.

   +  If one or both packets fail to arrive within a reasonable period
      of time, the ipdv is taken to be undefined.

5.6.

5.7. Errors and Uncertainties

   In the singleton metric of ipdv, factors that affect the measurement
   are the same that can affect the One-Way-Delay measurement, even if,
   in this case, the influence is different.

   The Framework document [1] provides general guidance on this point,
   but we note here the following specifics related to delay metrics:

   +  Errors/uncertainties due to uncertainties in the clocks of the Src
      and Dst hosts.

   +  Errors/uncertainties due to the difference between 'wire time' and
      'host time'.

I-D                         Ipdv Metric                    November 1998

   Each of these type of  errors are is discussed in more detail in the next
   paragraphs.

5.6.1.

5.7.1. Errors/Uncertainties related to Clocks

   If, as a first approximation, the error that affects the first measu-
 rement
   measurement of One-Way-Delay were the same of the one affecting the
   second measurement, they will cancel each other when calculating
   ipdv. The residual error related to clocks is the difference of the said
   errors that are supposed to change from the time T1, at which the
   first measurement is performed, to the time T2 at which the second measure-
   measure ment is performed. Synchronization, skew, accuracy and
   resolution are here considered with the following notes:

   +  Errors in synchronization between source and destination clocks
      contribute to errors in both of the delay measurements required
      for calculating ipdv.

   +  If the synchronization error affecting the One-Way-Delay
      measurement is Tsync, and it is a linear function of time, through
      the skew value "sk", at time T1 the error will be Tsync1 and at
      time T2 the error will be Tsync2. The ipdv measurement will be
      affected by the error: Tsync2-Tsync1 = sk x (T2 - T1) depending on
      skew and T2-T1. To minimize this error it is pos-
        sible possible to reduce
      the time interval T2-T1, but this could limit the generality of
      the metric.  Methods for evaluating the synchronization error will
      be discus-
        sed discussed below, since they come from a statistic over a
      significant sample.  If the measurement conditions do not allow to neglect
      neglecting the drift,
        supposed as assumed linear in the interval T2-T1, and
      having a value of "dr" expressed in ppm / sec., the ipdv error
      will become: Tsync2-Tsync1 = sk x (T2 - T1) + [dr x (T2-T1) x
      (T2-T1)] / 2
        It has to be noted that the presence of drift Drift varies the skew value in the time. The limits
      in which the skew can vary are anyway limited and little, small, so that a
      given drift cannot act indefinitely. Section 7 and Appendix A
      provide more information on this point.

   +  As far as accuracy and resolution are concerned, what is noted in
      the above referenced  Draft on One-Way-Delay at [2] in section 3.7.1, applies also in
      this case, with the further consideration, about resolution, that
      in this case the uncertainty introduced is two times the one of a
      single delay measurement. Errors introduced by these effects are
      often larger than the ones introduced by the drift.

I-D                          Ipdv Metric                   November 1998

5.6.2.

5.7.2. Errors/uncertainties related to Wire-time vs Host-time

   The content of sec. 3.7.2 of the above referenced Draft [2] applies also in this case, with the
   following further consideration: The difference between Host-time and
   Wire-time can be in general de-
 composed decomposed into two components, whose of which
   one is constant and the other is
 variable around zero. variable. Only the variable
   components will produce measu-
 rement measurement errors, while the constant one
   will be canceled while calcu-
 lating calculating ipdv.

6. Definitions for Samples of One-way ipdv

   Starting from the definition of the singleton metric of one-way ipdv,

 some ways of building |
   we define a sample of such singletons are here described.
 In particular two "discontinuous" samples  and one "continuous" sample
 are defined, and the last one is proposed, being the most suitable for
 describing the aspect of the path's behavior underlined in the motiva-
 tion. singletons.  In the following, the two     |
   packets needed for a singleton measurement will be called a "pair".

6.1. "Discontinuous" definitions   |

   A general definition can be stream of test packets is generated  where the following: second packet of a   |
   pair is, at the same time, the first packet of the next pair.         |

   +  Given particular binding of the parameters Src, Dst, path, Dst and Type-P, a  |
      sample of values of parameters parameter T1 and T2 is defined.
        The means for defining  To define the values |
      of T1 is to T1, select a beginning time T0, a final time Tf, and an average |
      rate lambda, then define a pseudo-random Poisson arrival process   |
      of rate lambda, whose values fall between T0 and Tf. The time      |
      interval between successive values of T1 will then average         |
      1/lambda. Another si-
        milar, but independent, pseudo-random Poisson arrival process
        based on T0', Tf' and lambda', will produce a series of t'
        values. The time interval between successive t' values will then
        average 1/lambda'. For each From the second value on, T1 value that has been obtained
        by of the first process, it is then possible to calculate the
        successive pair n         |
      coincides with T2 values as the successive T1 values plus the
        successive intervals of t'.

        The result is shown in figure 1.

 This general definition is likely go give problems, if no limits are
 considered for the obtained values. For example, the emission
 time of pair n-1, and the first packet of a pair, could fall before the emission
 time of pair n  |
      coincides with the second packet of the preceding pair. Probably this could
 be acceptable (provided that there are means to recognize pairs -e.g.

I-D                          Ipdv pair n-1.                  |

6.1. Metric                   November 1998

use of sequence numbers-), but name

   Type-P-One-way-ipdv-stream

6.2. Parameters

   +  Src, the concept itself of ipdv would be,at
 least, slightly changed. A way for avoiding this type IP address of philosophical
 problems can be to give some rules on a host

   +  Dst, the values IP address of a host

   +  T0, a time

   +  Tf, a time

   +  lambda,
 T0', Tf', lambda', without changing the meaning a rate in reciprocal seconds

6.3. Metric Units:

   A sequence of the metric.

             |<- average interval 1/lambda ->|
             |                               |
             |<- av.int. |                   |<- av.int.   |
             |1/lambda'->|                   |  1/lambda'->|
        _____|___________|___________________|_____________|________
               pair i                           pair i+1
                             Figure 1

 As triads whose elements are:

   +  T, a time

   +  Ti, a time interval.

   +  dT a real number or an example, it could be undefined number of seconds

6.4. Definition

   A pseudo-random Poisson process is defined such that the it begins at or
   before T0, with average arrival rate lambda, and ends at or after Tf.
   Those time values T(i) greater than or equal to T0 and less than or
   equal to Tf are then selected. Starting from time T0, at each pair of
   times T(i), T(i+1) of this process a value of Type-P-One-way-ipdv is
   obtained. The value of sorting the
 interval between pairs starts after sample is the sequence made up of the
   resulting <time, time interval, ipdv> triple, where the time interval between packets in a
 pair
   is expired, obtaining given by T(i+1)-T(i). Each time T(i), excluding the result first and the
   last, is therefore at the same time the the second time of pair i and
   the first time of pair i+1. The result is shown in figure 2:

                          |<--- av. int.......|
..........................|     1/lambda  --->|
                          |                   |
              |<- av.int. |                   |<- av.int.   |
              |1/lambda'->|                   |  1/lambda'->|
         _____|___________|___________________|_____________|________ 3

                 |T(i-2)    |T(i-1)             |T(i)      |T(i+1)
            _____|__________|___________________|__________|________
                   pair i-1        pair i         pair i+1

                                  Figure 2

Still other problems can be envisaged with these two definitions which
are described in some more detail in Appendix A.

6.2. A "continuous" definition

 A way for naturally avoiding the previous problems and producing 3

6.5. Discussion

   Note first that, since a
 testing environment closer to actual scenarios pseudo-random number sequence is to adopt employed,
   the follo-
 wing "continuous" definition.
 A continuous stream sequence of test packets can be supposed, where times, and hence the second
 packet value of a pair is, at the same time, the first packet sample, is not
   fully specified. Pseudo-random number generators of good quality will
   be needed to achieve the next
 pair. Therefore the preceding definitions become:

    + Given particular binding desired qualities.

   The sample is defined in terms of a Poisson process both to avoid the parameters Src, Dst, path,
   effects of self-synchronization and
        Type-P, also capture a sample of values of parameter T1 that is defined.
        The means for defining the values
   statistically as unbiased as possible. {Comment: there is, of T1 is course,
   no claim that real Internet traffic arrives according to select a beginning
        time T0, a final time Tf, and an average rate lambda, then
        define a pseudo-random Poisson
   arrival process of rate lambda,

I-D                          Ipdv Metric                   November 1998

        whose values fall between T0 and Tf. The time interval between
        successive values of T1 will then average 1/lambda. From the
        second value on, T1 value of the pair n coincides with T2 of process.}

6.6. Methodology

   Since packets can be lost or duplicated or can arrive in a different
   order than the pair n-1, and order sent, in order to recognize the first packet pairs of pair n coincides test
   packets, they should be marked with the
        second packet of the pair n-1. a sequence number. For duplicated
   packets only the moment, in the following, this last definition will first received copy should be con-
 sidered. Further refinement is required and is for further discussion.

6.3. Metric name

 Type-P-One-way-ipdv-stream

6.4. Parameters
 + Src, the IP address of considered. If a host
 + Dst, the IP address
   packet is lost, two values of a host

 + Path, the path* from Src to Dst; in cases where there ipdv will be undefined, since each
   packet is only
 one path from Src common to Dst, this optional parameter two pairs.

   Steps for measurement can be omitted the following:

   + T0,  Starting from a given time
 + Tf, T, Src generates a time
 + lambda, test packet as for a rate
      singleton metrics, inserts in reciprocal seconds

6.5. Metric Units:

 A sequence of triads whose elements are:
 + T, the packet a sequence number and the
      transmission time stamp Tx, then sorts the time Ti at which the
      next packet has to be sent.

   + Ti, a  At time interval. Ti, Src repeats the previous step, unless T(i) > Tf.

   + dT  On reception of the first packet, or the first packet after a real
      sequence number or an undefined error, Dst records sequence number of seconds

6.6. Definition

 A pseudo-random Poisson process is defined such and
      transmission timestamp that it begins at or
 before T0, with average arrival rate lambda, and ends at or after Tf.
 Those time values Ti greater than or equal to T0 and less than or
 equal to Tf are then selected. Starting from time T, at each pair of
 times T(i), T(i+1)of this process a value of Type-P-One-way-ipdv is
 obtained. The value of contained in the sample is packet and the sequence made up
      reception time Rx as "old values".

   +  On reception of the
 resulting <time, time interval, ipdv> triad, where other packets Dst verifies the time interval seuqence number
      and if it is given correct, by T(i+1)-T(i). Each obtained time T(i), excluding using the first "old values" and the last, newly
      received ones, a value of ipdv is therefore at computed. Then Dst records the
      new sequence number, transmit and receive timestamps as "old
      values".

6.7. Errors and uncertainties

   The same time considerations apply that have been made about the singleton
   metric. An additional error can be introduced by the second time of
 pair i pseudo-random
   Poisson process as focused in [2].  Further considerations will be
   made in section 7, and the first time in Appendix A.

6.8. Distribution of pair i+1. One-way-ipdv values                                 |

   The result is shown in figure 3

              |T(i-2)    |T(i-1)             |T(i)      |T(i+1)
         _____|__________|___________________|__________|________
                pair i-1        pair i         pair i+1

                               Figure 3
 I-D                          Ipdv Metric                   November 1998

6.7. Discussion

 Note first that, since a pseudo-random number sequence is employed,
 the sequence one-way-ipdv values are limited by virtue of times, the fact that there  |
   are upper and hence lower bounds on the one-way-delay values. Specifically, |
   one-way-delay is upper bounded by the value of chosen as the sample, maximum     |
   beyond which a packet is not
 fully specified. Pseudo-random number generators of good quality
 will be needed to achieve the desired qualities.

 The sample counted as lost. It is defined in terms of a Poisson process both to avoid the
 effects of self-synchronization lower bounded by      |
   propagation, transmission and also capture a sample nodal transit delays assuming that is
 statistically as unbiased as possible. {Comment:      |
   there is, of
 course, are no claim queues or variable nodal delays in the path. Denote the  |
   upper bound of one-way-delay by U and the lower bound by L and we see |
   that real Internet traffic arrives according to a
 Poisson arrival process.}

6.8. Methodology

 Since packets one-way-ipdv can be lost only take on values in the (open) interval (L-  |
   U, U-L).                                                              |

   In any finite interval, the one-way-delay can vary monotonically      |
   (non-increasing or duplicated non-decreasing) or of course it can arrive vary in a different
 order with respect the one of emission, both   |
   directions in order to recognize the
 pairs of test packets, they should be marked with a Sequence Number
 or make use interval, within the limits of any other tool suitable to the scope. For duplicated
 packets only half-open        |
   interval [L,U). Accordingly, within that interval, the first received copy should be considered. If a pac-
 ket is lost, two one-way-ipdv   |
   values of ipdv will can be undefined, since each packet,
 in positive, negative, or a mixture (including 0).         |

   Since the supposed "continuous" definition, range of values is common to two pairs.

 Steps limited, the one-way-ipdv cannot         |
   increase or decrease indefinitely. Suppose, for measurement can be example, that the following:
 +  Starting from a given time T, Src generates     |
   ipdv has a test packet as for positive 'run' (i.e. a singleton metrics, inserts long sequence of positive values).  |
   At some point in this 'run', the packet a Sequence Number
        and the transmission Time Stamp Tx,then sorts positive values must approach 0 (or  |
   become negative) if the time Ti at
        which one-way-delay remains finite. Otherwise, the next packet has to  |
   one-way-delay bounds would be sent.
 +	At time Ti, Src repeats the previous step, unless T(i) > Tf.
 +  On reception of the first packet, or the first packet after violated. If such a SN
        error, Dst records SN and Tx timestamp that run were to         |
   continue infinitely long, the sample mean (assuming no packets are contained in    |
   lost) would approach 0 (because the packet and one-way-ipdv values must approach |
   0). Note, however, that this says nothing about the reception time Rx as "old values".
 +  On reception shape of the other packets Dst verifies the SN and if      |
   distribution, or whether it is
        correct, by using the "old values" and symmetric. Note further that over      |
   significant intervals, depending on the newly received ones,
        a value width of ipdv is computed. Then Dst records the new SN, Tx
        and Rx timestamps as "old values".

6.9. Errors and uncertainties

 The same considerations apply interval [L,U),  |
   that have been made about the single-
 ton metric. An additional error can be introduced by the pseudo-ran-
 dom Poisson process as focused in the above referenced Draft.
 Further considerations will sample mean one-way-ipdv could be made in section 7, and in Appendix A.

6.10 positive, negative or 0.

6.9. Some statistics for One-way-ipdv

   Some statistics are here considered, that suggested which can provide useful informa-
 -tion information in |
   analyzing the behavior of the packets flowing from Src to Dst

I-D                          Ipdv Metric                   November 1998

 These statistics are given having in mind a practical use of them. Dst. The    |
   focus is on the instantaneous behavior of the connection, while buffer
 dimensioning is not in the scope of this document. connection.  Other      |
   statistics can be defined if needed.

6.10.1.

6.9.1. Type-P-One-way-ipdv-inverse-percentile

   Given a Type-P-One-way-ipdv-Stream and a time threshold, that can be
   either positive or negative, the fraction of all the ipdv values in
   the Stream less than or equal to the threshold, if the threshold is
   positive, or greater or equal to the threshold if the threshold is ne-
 gative.
   negative.

   For many real-time services that require a regular delivery of the
   packets, this statistics can give the amount of packets received
   beyond acceptable limits.

6.10.2 Type-P-One-way-ipdv-standard-deviation

 Given a Type-P-One-way-ipdv-Stream, the distribution of ipdv values
 is considered

6.9.2. Type-P-One-way-ipdv-jitter                                        |

   This metric was defined in [7] and is simply the Standard Deviation can be calculated as an
 indication of regularity absolute value of delivery. For practical purposes it    |
   the Type-P-One-way-ipdv. This can be
 useful used to define derive a total standard deviation, computed over number of       |
   metrics.                                                              |

7. Discussion on clock synchronization

   This section gives some considerations about the com-
 plete set of value, and a standard deviation computed over the sub-
 set of those values that do not exceed given positive and negative
 thresholds. This allows a more accurate description of the performan-
 ce experienced by packets. Details on the shape of the ipdv distribu-
 tion are given in Appendix A.

6.10.3 Type-P-One-way-ipdv-average

 This statistic should tend to a value of ZERO for a number of ipdv
 values that tend to infinite. The behavior of Type-P-One-way-ipdv-
 average, and its meaning, are issues for the next section 7.

7. Discussion on clock synchronization

 This section gives some considerations about the need need of having syn-
 chronized
   synchronized clocks at Src and Dst. These considerations are given as
   a basis for discussion, they require further investigation. We start
   from the analysis of the mean value of the ipdv distribution related
   to a "continuous" sample. Some more detailed calculations are
   presented in Appendix A.

I-D                         Ipdv Metric                    November 1998

7.1. Mean value Effects of ipdv distribution.

 If D(i) is synchronization errors

   We refer here to the delay two components that can generate this type of packet "i", and ipdv(i) is
   errors that are the i-th value reciprocal "skew" and "drift" of
 ipdv in the distribution Src and Dst
   clocks. It is first of a sample all noted that the variable component "drift"
   is physically limited and its effects can be interpreted by saying
   that the total reciprocal skew of "n" values, collected with the described methodology, we two clocks can write:

 ipdv(1) = D1 - D0
 ..........
 ipdv(i) = D(i) - D(i-1)
 ..........
 ipdv(n) = D(n) - D(n-1)

 The mean vary, ranging
   from a min to a max. value in the time. This type of ipdv distribution will result variation takes
   place very slowly being mostly connected to variations in

 E(ipdv) = (D(n) - D(0))/n

 If an actual
   temperature.

   We suppose to perform a measurement is performed, between a Src and a Dst that lasts have
   a period reciprocal, initial skew of time
 long enough to contain "ts1" and a number "n" sufficiently large and, supposing
 synchronized clocks, reciprocal drift such that that,
   after the network conditions (traffic) allow
 to find a D(n) not too different from D(0), e.g. a time of n x 24
 hours, E(ipdv) will tend to zero, since T the difference D(n) - D(0) will
 remain finite and little.

7.2. Effects of total skew is "ts2". It is not here a varying traffic

 If limitation
   to consider that at the mean values beginning of delay D time T the two clocks indicate
   the same time T0.

   In order to analyze the effects produced by this situation we suppose
   that packets are changing inside transferred, from Src to Dst, with a given period constant delay
   D In this conditions the measured ipdv should always be zero, and
   what is actually measured is the error.

   An ipdv value is measured at the beginning of
 time, for example they are increasing due to time T with two packets
   having an increment interval of traffic,
 we can consider, as a first approximation, the Ti(1).Another ipdv values as decom-
 posed into value is measured at the end
   of T with two components, one being instantaneous and another one
 as packets having a constant rate dD and corresponding time interval Ti(2).

   On our purposes other errors (like wire-time vs host-time) are not
   considered since they are not relevant in this analysis, being common
   to all the increment "per
 interval" of measurement methods.

   It is then possible to calculate the mean value values of D. the Tx and Rx
   timestamps as they are seen by the two clocks, and the related two
   ipdv values.

   The mean first ipdv value of the distribution will be shifted of the be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1)
   The second ipdv value dD corresponding to will be: ipdv2 = ts2*Ti(2) +((ts2-ts1)/T)*Ti(2)

   The error is given by the mean value effect of the skew during the time interval
   Ti(i) between test packets. This will happen only during the
 monotonic variation, two packets of the pair, and is not a distortion, since it is second order term
   due to the record variation of that skew in the instantaneous behavior. When the conditions will come back same interval.

   If, as in the most of practical cases, the drift can be considered
   close to zero, then ts1 = ts2, and the initial ones, error is not depending on the distribution will resume a mean value around
 zero. As for
   time at which the case of drift, also in this case a monotonic varia-
 -tion cannot take place indefinitely. measurement is done. In Appendix A a method addition, this type of
   error can be corrected as it is given
 for subdividing indicated in the variation into these two components over short
 periods, next paragraph and
   discussed in order to have indications Appendix A.

   In any case the maximum error on variations of traffic condi-
 -tions.

7.3. Effects of synchronization errors

 We refer here an ipdv value will correspond to the two components that can generate this type
   effect of
 errors that are the maximum reciprocal "skew" and "drift" of skew on the Src maximum interval between
   packets.

7.2. Related precision

   This means that:

   +  If the skew is constant and Dst
 clocks. It is first of = ts all noted that the variable component "drift"

I-D                          Ipdv Metric                   November 1998 ipdv(i) values are
      increased by the quantity Ti(i)*ts with respect the actual value.
      The mean ipdv value will therefore increased of the quantity
      E[Ti(i)]*ts, which is physically limited and its effects measured. Also E[Ti(i)] can be interpreted by saying measured, and
      should be related to lambda. That means that the total reciprocal skew of the two clocks ts can vary, ranging from be
      calculated. If together with ipdv(i), also the corresponding Ti(i)
      are collected, for each ipdv(i) value a min to correcting term is
      available, and a max. value in the time. This type sample of variation takes place
 very slowly being mostly connected to variations in temperature.

 We suppose to perform a measurement between "corrected" c-ipdv(i) values is
      obtained, where c-ipdv(i) = ipdv(i) - Ti(i)*st.

   +  Considering the total skew as subdivided into a Src fixed part and a Dst that have
 a reciprocal, initial skew of "ts1"
      variable part (skew and a reciprocal drift such that,
 after drift),respectively, ts and + or - td,
      from the time T mean ipdv value and the total mean emission interval the
      average skew can be derived in the period of interest (Appendix
      A). The preceding correction can then be applied. The maximum
      residual error on an ipdv value is "ts2". It is not here a limitation
 to consider that given by the difference between
      the actual skew at the beginning of time T in which the two clocks indicate value has been measured
      and the average skew, multiplied by the same time T0.

 In order to analyze interval between the effects produced by this situation we suppose
 that
      packets that have generated that ipdv value. Considerations on the
      number of values in the sample affected by errors are transferred, from Src to Dst, with a constant delay D
 In this conditions reported in
      Appendix A.

   +  If the measured ipdv should always be zero, and what duration of the measurement is actually measured such that it is possible to  |
      consider that the error.

 An ipdv value (without skew) is measured at close to zero, the beginning of time T with two packets
 having an interval mean
      value of Ti(1).Another the ipdv distribution will have the value is measured at of the end average
      skew multiplied by the mean value of T with two packets having a time interval Ti(2).

 On our purposes other errors (like wire-time vs host-time) are not
 considered since they are not relevant in this analysis, being common
 to all the measurement methods.

 It is then possible emission interval, as
      supposed above.

   +  We observe that the displacement due to calculate the values skew does not change
      the shape of the Tx and Rx time-
 stamps as they are seen by distribution, and, for example the two clocks, and Standard
      Deviation remains the related two ipdv
 values.

 The first ipdv value will be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1)
 The second ipdv value will be: ipdv2 = ts2*Ti(2) +((ts2-ts1)/T)*Ti(2)

 The error same. What introduces a distortion is given by the
      effect of the skew during drift, also when the time inter-
 val Ti(i) between mean value of this effect is
      zero at the two packets end of the pair, and a second order
 term due measurement. The value of this distortion
      is limited to the variation effect of that the total skew in variation on the same
      emission interval.

 If,

   +  In what has been said, skew and drift have been considered as in the most
      "reciprocal". In Appendix A it will be considered that each of practical cases, the
      two clocks have a skew and a drift can be considered
 close to zero, then ts1 = ts2, with respect a "true time", and
      it will be observed that the error difference is not depending on negligible with respect
      the
 time at situation in which one of the measurement two clocks is done. In addition, this type of
 error can be corrected taken as it is indicated in the next paragraph and
 discussed in Appendix A.

 In any case the maximum error on an ipdv value will correspond to "true
      time".

8. Definition for a bidirectional ipdv metric

   We now consider that the
 effect action of the maximum reciprocal skew on the maximum interval between
 packets.

I-D                          Ipdv Metric                   November 1998

7.4. Related precision

 This means that:
 1) + If the skew is constant and one direction is = ts all the ipdv(i) values are
    increased by the quantity Ti(i)*ts
   same, with respect opposite sign, of the actual value. action on the other direction. The mean ipdv value will therefore increased
   idea of performing at the quantity
    E[Ti(i)]*ts, which is measured. Also E[Ti(i)] can be measured, and
    should be related to lambda. That means that the skew ts can be
    calculated. If together with ipdv(i), also same time two independent measurements in
   the corresponding Ti(i)
    are collected, for each ipdv(i) value a correcting term two directions is avai-
    -lable, and suggested by this fact.

   If, after a sample long measurement, the variable conditions of "corrected" c-ipdv(i) values is obtained,
    where c-ipdv(i) = ipdv(i) - Ti(i)*st.
 2) + Considering the total skew as subdivided into a fixed part and system
   under test have reached the situation of a
    variable part (skew and drift),respectively, ts and + or - td,
    from contribution close to zero
   to the mean ipdv value and of the mean emission interval ipdv distribution, it is expected that only
   the action of the average skew can be derived in has modified the period of interest (Appendix A). The
    preceding correction can then be applied. The maximum residual er-
    -ror measured mean value.
   It is therefore expected that on an ipdv one direction that value is given by the difference between the actual
    skew at the time in which equal
   and opposite to the value has been one measured and in the ave-
    -rage skew, multiplied by the time interval between the packets
    that have generated that ipdv value. Considerations on other direction.

   This fact offers the number possibility of values in the sample affected by errors are reported defining a theoretical reference
   measurement duration in
    Appendix A.
 3) + If the following way:

   The reference duration of the a bidirectional ipdv measurement between an
   host E and an host W is reached at time Tf such that it for each time T
   > Tf the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where
   epsilon is possible
    to what we can consider that the effect of the items at points 7.1 and 7.2,
    are close to as zero, is always verified. This is
   one, but not the mean value of only method for verifying that the mean ipdv distribution will
    have value
   has reached the value of the average skew multiplied by reciprocal skew.

   At this point it is possible to evaluate the reciprocal skew.  This
   will require the knowledge of the mean value of the emission interval, as supposed above.
 4) + We observe intervals between
   consecutive packets, that can be calculated over the displacement due to transmitted
   stream, by using the skew does collected time stamps.

   A bidirectional measurement can be defined not change only as twin one-way
   independent metrics that take place (nearly) at the shape same time, but
   also as a two-way metric making use of packets looped back at one
   end. This metric, that can be object of further study/Draft, would be
   able to measure also the distribution, and, for example Round Trip Delay and its variations.
   Problems will anyway arise on the Standard Devi-
    ation remains characterization of emission
   intervals in the same. What introduces a distortion is backward direction. They would be produced by the effect
   combination of the drift, also when original Poisson arrival process and the mean value of this effect is zero at
    the end of
   ipdv on the measurement. The value of forward direction. It has to be studied if this distortion sequence
   of intervals is limited
    to still suitable for the effect of measurement. also other
   possibilities can be envisaged for obtaining a proper backward
   sequence and still maintain the total skew variation loopback concept.

9. Relationship to other standards                                       |

   The ITU definitions are based on the emission interval.
 5) + In what has been said, skew and drift have been considered delay variation as
    reciprocal". In Appendix A it defined for ATM   |
   cells [5]. We will be considered that each of discuss these briefly first and then discuss the   |
   ITU's definition for IP packets [3].                                  |

9.1. 1-Point Cell Delay Variation                                        |

   The ITU looks at cell delay variation from two clocks have different points of    |
   view. The first, called 1-point cell delay variation, is essentially  |
   a skew and measure of how a drift with respect cell stream varies from a "true time", and
    it will be observed that the difference is negligible with respect stated cell rate (e.g.   |
   the situation in which one of peak cell rate). The basic idea behind the two clocks measurement is taken as      |
   follows: The observer at the "true
    time".

I-D                          Ipdv Metric                  November 1998

8. Definition for measurement point notes cell arrival     |
   times and clock ticks. The clock ticks at a bidirectional ipdv metric

 We now consider that the action of the skew constant rate, based on one direction is the
 same, with opposite sign, of   |
   the action on peak cell rate for the other direction. cell stream. The
 idea of performing at difference between the same time two independent measurements in    |
   cell arrival times and the two directions clock ticks is suggested by this fact.

 If, after a long measurement, the variable conditions of the system
 under test have reached the situation of 1-point cell delay      |
   variation. If a contribution close to zero
 to cell arrives later than the mean value of clock tick, the ipdv distribution, it is expected that only clock     |
   "restarts" at the action actual cell arrival time, and continues to tick at  |
   a constant rate from that point.                                      |

   The purpose of the average skew has modified the measured mean value.
 It this measure is therefore expected that on one direction that value to identify what is equal called "cell       |
   clumping" and
 opposite non-conforming cells. That is, to idenify cells that    |
   violate the one measured in the other direction.

 This fact offers leaky bucket parameters defined for that cell stream.     |
   That is why the possibility of defining clock skips when a theoretical reference
 measurement duration in cell is later than the following way:

 The reference duration normal      |
   inter-cell time defined by the peak cell rate. It is of a bidirectional ipdv measurement between
 an host E much less     |
   interest when cells are late than when they arrive too close          |
   together.                                                             |

9.2. 2-Point Delay Variation, Cells and an host W Packets                          |

   2-Point cell delay variation, as defined in [5] is closer to what is  |
   defined here. The basic idea behind this metric is reached at time Tf such that for two           |
   measurement points, whose clocks are synchronized, observe a cell     |
   stream and timestamp when each time
 T > Tf cell passes. The difference in the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where
 epsilon     |
   timestamps for a cell is what essentially the one-way delay. There is also |
   assumed to be a one-way cell delay for a reference cell which we can consider as zero, will |
   denote d0. The cell delay variation for the ith cell is always verified. This then di-d0.   |
   Note that this is
 one, but not the only method for verifying an absolute value, but that the mean ipdv value
 has reached the value of cell delay      |
   variation can be either positive or negative. [5] does not specify    |
   how to choose the average reciprocal skew.

 At this point it reference cell delay.                               |

   In [3] there is possible an informative appendix describing packet delay       |
   variation, which means that the material is not binding as a          |
   standard. The definitions are very similar to evaluate [5] with "packet"       |
   subsituting for "cell" in most places. One difference is that [3]     |
   offers two ways to define the reciprocal skew.
 This will require reference packet (with the knowledge default      |
   being the first):                                                     |

   +  Take the delay of the mean value first packet of the intervals
 between consecutive packets, that can be calculated over sequence as the trans-
 -mitted stream, by using          |
      reference time.                                                    |

   +  Take the collected time stamps.

 A bidirectional measurement can be defined not only as twin average one-way
 independent metrics that take place (nearly) at the same time, but
 also packet delay as the reference time.       |

9.3. Discussion                                                          |

9.3.1. Differences                                                       |

   Demichelis [4] points out a two-ways metric making use of packets looped back at one
 end. This metric, that can be object number of further study/Draft, would be
 able to measure also the Round Trip Delay and its variations. Problems
 will anyway arise on problems with the characterization of emission intervals 2-point PDV   |
   definition in the
 backward direction. They would be produced by the combination [3]. First of all is the
 original Poisson arrival process and the effect issue of ipdv on choosing the forward
 direction. It has to be studied if          |
   reference delay time. If this sequence of intervals is still
 suitable for chosen arbitrarily, it becomes       |
   uncertain how to compare the measurement. also other possibilities measurements taken from two non-         |
   overlapping periods. If it is chosen as an average, that can also be
 envisaged for obtaining  |
   a proper backward sequence and still maintain problem, because over long periods of time in a network, the loopback concept.

I-D                          Ipdv Metric                  November 1998

9. References

 V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP Performance
 Metrics", Internet Draft <draft-ietf-ippm-framework-01.txt> Feb. 1998

 G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", Internet
 Draft <draft-ietf-ippm-delay-01.txt> Nov. 1997

10. Author's Address

 Carlo Demichelis <carlo.demichelis@cselt.it>
 CSELT - Centro Studi E Laboratori Telecomunicazioni S.p.A
 Via G. Reiss Romoli 274
 10148 - TORINO
 Italy
 Phone +39 11 228 5057
 Fax. +39 11 228 5069

I-D                          Ipdv Metric                  November 1998

APPENDIX        |
   average one-way delay can vary widely. A

This Appendix considers twenty-four hour average as  |
   the scenario in which two hosts have clocks
that are both not synchronized. Between reference time can seriously overestimate the two hosts, in an inde-
-pendent way and actual delay        |
   variation at the same a given time in both direction an ipdv measure-
-ment is performed according the methodology that is described in the
main body of this Draft.
This hypothetical scenario is only supposed for discussing the theory
and day because the characteristics of night-time hours, when   |
   the ipdv metric and its results, without
considering implementation issues.

A.1 - Initial positions

The two hosts will delay can be called West (W) and East (E). The two measure-
-ments start at expected to approach the same propagation and node time, while  |
   is included in the end of average. On the measurement it other hand, there is
supposed no clear way  |
   to be decided by the results of the measurement itself.

At the beginning of the measurement partition the time declared by the West
clock is T0w, the in order to find averages for certain periods   |
   of time declared by and compute the East clock delay variation with reference to these       |
   averages.                                                             |

   Another problem pointed out in [4] is T0e, while the
true time is T0t.

The W-clock is affected by an absolute skew of skw ppm and fact that 2-point PDV       |
   requires synchronized clocks, whereas in this document Demichelis     |
   shows that synchronized clocks are not absolutely necessary for ipdv. |

9.3.2. Relationship between the E-clock
by an absolute skew of skw ppm. metrics                                  |

   The W-clock ipdv metric described here and the 1-point cell delay variation   |
   metric described in [5] do not really have much in common (see also   |
   [4]). 1-point delay variation is affected by an absolute drift ranging from -drw ppm really intended to
+drw ppm, talk about the E-clock by an absolute drift ranging from -dre ppm to
+dre ppm.

A.2 - Evaluation    |
   relationship of skew and drift effects

In order cell arrival times to evaluate the effect of the drift on this type of metric,
it a given periodic event, and     |
   consequently is necessary more closely related to consider the time in which the variation first definition of the skew
takes place. We consider the two extreme cases       |
   "jitter" given in which the Section  3 above.                                   |

   2-point delay variation
takes place uniformly from (actually, the beginning packet variant described in    |
   [3]) is related to ipdv, and this relationship can be made precise as |
   follows: Suppose that an arbitrarily chosen packet is designated as   |
   the end of reference packet for the 2-point measurement and also as the variation takes place suddenly at a generic time along      |
   start packet of the ipdv measurement. Let TM be the measurement time.

A.2.1 - Mean Denote this packet by p(0).     |
   Then given ipdv value

Since measurements for a series of packets, the mean ipdv value, as it has been seen, 2-point     |
   delay variation for packet i is p(0) + the difference sum from k=1 to i of
the last       |
   ipdv(k).                                                              |

   Similarly, given a sequence of 2-point delay minus variation measurements   |
   we can derive the first, divided by ipdv measurement as follows: Denote the number of considered
values, we consider what, in the two cases, is measured 2-point     |
   delay variation measurement for first and
last delay.

We call trueDf the true first Delay and trueDl packet i as v(i). Then the true last Delay.

I-D                          Ipdv Metric                  November 1998

For ipdv value |
   for the evaluation that we want to do, it pair of packets p(k-1), p(k) is not a limitation to con-
-sider that they simply v(k)-v(k-1) [6].       |

9.3.3. Summary                                                           |

   As described above, there are equal and have a value number of disadvantages of trueD. We also consider
as time 0 the true time at which        |
   2-point packet delay variation approach. Further, the transmission of ipdv approach   |
   described here is general enough to provide the first same information as   |
   the 2-point packet
starts from West toward East.

In case delay variation measurements. Because of continuous drift we define a "drift per second" as:
drpsW = 2*drw / TM this, and   drpsE = 2*dre / TM
along the measurement this will bring |
   because of the skew from a value of:
skWmin = skw - drw     ;    skEmin = ske - dre
to a value (possibly) looser clock synchronization requirements   |
   of
skWmax = skw + drw     ;    skEmax = ske + dre

What is measured as first Delay is:

measured first Rx time - measured first Tx time
OffsetEast + trueD*[1 + skEmin + (1/2)*drpsE] - OffsetWest

What is measured as last Delay is:

measured last Rx time - measured last Tx time
OffsetEast + (TM + trueD)*[1 + skEmin + (1/2)*2*dre] -
    - OffsetWest - TM*[1 + skWmin + (1/2)*2*drw] ipdv, we recommend the one-way-ipdv approach for the delay         |
   variation measurement.                                                |

10. Security Considerations                                              |

   The difference between one-way-ipdv metric has the last same security properties as the one-  |
   way-delay metric [2]. The packets contain no user information, and first Delay so |
   privacy of user data is therefore:

TM*(skEmin - skWmin + dre - drw) - trueD*drpsE/(2*TM)

if TM = 10 hours drpsE not a concern. It is in the order of 50*10E-6 / 36000 still possible that is
about 10E-9 and the second term      |
   there could be an attempt at a denial of service attack by sending    |
   many measurement packets into the expression is network; there could also be        |
   attempts to disrupt measurements by diverting packets or corrupting   |
   them.                                                                 |

   In general, legitimate measurements must have their parameters        |
   selected carefully in the order of
10E-14 for true delays to avoid interfering with normal traffic  |
   in the order of 1 sec (negligible term).
We consider that, with very good approximation:

Mean emission interval (mti) = TM / number network. Such measurements should also be authorized and       |
   authenticated in some way so that attacks can be identified and       |
   intercepted.                                                          |

11. Acknowledgements                                                     |

   Thanks to Matt Zekauskas from Advanced and Ruediger Geib from         |
   Deutsche Telekom for discussions relating to the contents of ipdv values (N)
Therefore:

mean ipdv = (measured last Delay this     |
   revised draft.                                                        |

12. References                                                           |
   [1]    V.Paxon, G.Almes, J.Mahdavi, M.Mathis - measured first Delay) / N =
          = mti*(skEmin "Framework for IP      |
        Performance Metrics", RFC 2330  Feb. 1998                        |

   [2]    G.Almes, S.Kalidindi - skWmin + dre "A One-Way-Delay Metric for IPPM",      |
        Internet Draft <draft-ietf-ippm-delay-07.txt> May 1999           |

   [3]    Draft New ITU-T Recommendation I.380 "Internet  Protocol Data  |
        Communication Service - drw)

but we considered skEmin = ske IP Packet Transfer and Availability      |
        Performance Parameters"                                          |

   [4]    Demichelis, Carlo - dre "Packet Delay Variation Comparison between |
        ITU-T and skWmin = skw IETF Draft Definitions" March 1999                     |

   [5]    ITU-T Recommendation I.356 "B-ISDN ATM Layer Cell Transfer     |
        Performance"                                                     |

   [6]    e-mail exchanges with Ruediger Geib                            |

   [7]    V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding  |
        PHB", Internet Draft, November 1998 <draft-ietf-diffserv-phb-    |
        ef-01.txt>                                                       |

13. Authors' Addresses                                                   |

   Carlo Demichelis <carlo.demichelis@cselt.it>
   CSELT - drw
and therefore:

mean ipdv = (meas.lastD Centro Studi E Laboratori Telecomunicazioni S.p.A
   Via G. Reiss Romoli 274
   10148 - meas.firstD) / mti*(reciprocal mean skew) TORINO
   Italy
   Phone +39 11 228 5057
   Fax. +39 11 228 5069

   Philip Chimento <chimento@ctit.utwente.nl>
   CTIT - Centre for Telematics and Information Technology
   University of Twente
   Postbox 217
   7500 AE Enschede
   The previous procedure is now applied to Netherlands
   Phone +31 53 489 4331
   FAX   +31 53 489 4524

   APPENDIX A

   This Appendix considers the case scenario in which two hosts have clocks
   that are both not synchronized. Between the total
drift takes place two hosts, in a very short time. Some cases are possible, an
   independent way and
we consider at the one same time in which at both direction an ipdv
   measurement is performed according the beginning methodology that is described
   in the West clock has
skWmax main body of this Draft.  This hypothetical scenario is only
   supposed for discussing the theory and the East clock has skEmin, at time txW characteristics of the
   ipdv metric and its results, without considering implementation
   issues.

14. Initial positions

   The two hosts will be called West clock
assumes skWmin (W) and East (E). The two
   measurements start at time txE the East clock assumes skEmax.

I-D                          Ipdv Metric                  November 1998

What is measured as first Delay is now:

measured first Rx time - measured first Tx time
OffsetEast + trueD*(1 + skEmin) - OffsetWest

What same time, while the end of the measurement
   it is measured as last Delay is:

measured last Rx time - measured last Tx time
+ OffsetEast + txE*(1 + skEmin) + (TM - txE)*(1 + skEmax) +
+ trueD*(1 + skEmax) -
- OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin)

but supposed to be decided by the mean skew values will be:

mskw = [skWmax*txW + skWmin*(TM - txW)] / TM
mske = [skEmin*txE + skEmax*(TM - txE)] / TM results of the difference between measurement
   itself.

   At the two delays therefore is:

TM*(mske - mskw) + 2*trueD*dre beginning of the measurement the time declared by the West
   clock is T0w, the time declared by the East clock is T0e, while the
   true time is T0t.

   The W-clock is affected by an absolute skew of skw ppm and the mean ipdv value will be:

mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TM E-
   clock by an absolute skew of skw ppm.

   The W-clock is affected by an absolute drift ranging from -drw ppm to
   +drw ppm, the second term E-clock by an absolute drift ranging from -dre ppm to
   +dre ppm.

14.1. Evaluation of skew and drift effects

   In order to evaluate the second member in effect of the previous hypotheses drift on this type of metric,
   it is necessary to consider the time in which the order variation of the nanosecond, and we neglect it. Also
   skew takes place. We consider the two extreme cases in this case, from which the mean ipdv value, and knowing
   variation takes place uniformly from the mean emission interval, beginning to the rela-
-tive skew end of the clocks can be obtained.

More in general, independently on how
   measurement and the drift acts inside its limits,
we assert that always variation takes place suddenly at a generic time
   along the mean measurement. Let TM be the measurement time.

14.1.1. Mean ipdv value divided by

   Since the mean emission
interval produces the value of ipdv value, as it has been seen, is the mean reciprocal skew difference of
   the two
clocks, provided that last delay minus the first, divided by the collected number of ipdv values considered
   values, we consider what, in the two cases, is signi-
-ficant measured for first and
   last delay.

   We call trueDf the statistics.

A.2.2 - Errors true first Delay and corrections

If trueDl the drift is always close true last Delay.
   For the evaluation that we want to zero, do, it is possible not a limitation to obtain the
true
   consider that they are equal and have a value of trueD. We also
   consider as time 0 the reciprocal skew and correct all true time at which the ipdv values. Each transmission of them is associated to an emission interval ti between the two
packets that have produced
   first packet starts from West toward East.

   In case of continuous drift we define a "drift per second" as: drpsW
   = 2*drw / TM     and   drpsE = 2*dre / TM along the value itself. Then measurement this
   will bring the skew from a better ipdv value
will be:
corr.ipdv(i) of: skWmin = meas.ipdv(i) skw - ti * skew
This is drw     ;
   skEmin = ske - dre to a better value but not exactly the true one, since we supposed
that both clocks are not synchronized to the true time. Two errors are
affecting the corrective terms which are:

I-D                          Ipdv Metric                  November 1998 of skWmax = skw + drw     ;    skEmax =
   ske + dre

   What is measured as first Delay is:

   measured first Rx time - measured first Tx time OffsetEast + trueD*[1
   + skEmin + (1/2)*drpsE] - OffsetWest

   What is measured as last Delay is:

   measured last Rx time - measured last Tx time OffsetEast + (TM +
   trueD)*[1 + skEmin + (1/2)*2*dre] -
      - OffsetWest - TM*[1 + skWmin + (1/2)*2*drw]

   The reciprocal skew is measured as referred to difference between the Src clock last and first Delay is therefore:

   TM*(skEmin - skWmin + The interval ti dre - drw) - trueD*drpsE/(2*TM)
   if TM = 10 hours drpsE is measured by the Src clock.
These are second order errors since the measured skew will be affected
by a "relative" error in the order of the Src skew, an the same is
for the error affecting the ti value.

If the drift 50*10E-6 / 36000 that is significant
   about 10E-9 and it can range from the lower to the
upper limit of its field, the measured average of the skew will depend
on the type second term of variation. Some cases are considered that demonstrate
that actually the proposed correction expression is not so much effective in this
case. Only the fixed part order of the total clock variation can be properly
corrected.

A.2.2.1 - Constant drift

The first case is the first one considered
   10E-14 for true delays in the preceding paragraph,
where the drift is uniform. order of 1 sec (negligible term).  We suppose that a reciprocal skew is measu-
-red and used for correction.

At the beginning
   consider that, with very good approximation:

   Mean emission interval (mti) = TM / number of the measurement the actual reciprocal skew is:

init.skew ipdv values (N)
   Therefore:

   mean ipdv = mean.skew (measured last Delay - rel.max.drift measured first Delay) / N =
     = mti*(skEmin - skWmin + dre - drw)

   but we considered skEmin = ske - dre and at the end the actual reciprocal skew is:

final.skew skWmin = skw - drw and
   therefore:

   mean ipdv = mean.skew + rel max.drift (meas.lastD - meas.firstD) / mti*(reciprocal mean skew)

   The correction previous procedure is effective only now applied to the case in which the central part of total
   drift takes place in a very short time. Some cases are possible, and
   we consider the measurement.
At one in which at the beginning the West clock has
   skWmax and at the end a residual error will affect East clock has skEmin, at time txW the ipdv
values whose value will be:

ipdv(i).err = ti * rel.max.drift

We underline here that West clock
   assumes skWmin and at time txE the error East clock assumes skEmax.  What
   is larger for large intervals ti and
lower for short intervals ti. For intervals derived from a poissonian
arrival process, there are many short intervals and few large intervals.
We also note that a constant drift cannot last indefinitely, since there measured as first Delay is a minimum and a maximum for the skew.

A.2.2.2 now:

   measured first Rx time - Step of drift

In this case the error profile depends on the measured first Tx time at which the drift
changes. If the change OffsetEast + trueD*(1
   + skEmin) - OffsetWest

   What is near measured as last Delay is:

   measured last Rx time - measured last Tx time + OffsetEast + txE*(1 +
   skEmin) + (TM - txE)*(1 + skEmax) + + trueD*(1 + skEmax) - -
   OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin)

   but the beginning or near mean skew values will be:

   mskw = [skWmax*txW + skWmin*(TM - txW)] / TM mske = [skEmin*txE +
   skEmax*(TM - txE)] / TM

   the end of difference between the
measurement, two delays therefore is:

   TM*(mske - mskw) + 2*trueD*dre

   and the calculated mean skew ipdv value will be very close to the actual
skew of be:

   mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TM

   the largest part second term of the measurement. On that part the correc-
-tion will be effective, while over the remaining few values the error
will be twice with respect second member in the preceding case.

I-D                          Ipdv Metric                  November 1998

The worse condition previous hypotheses is produced by a change in drift in
   the middle order of the measurement. In nanosecond, and we neglect it. Also in this case case,
   from the correction would be useful only if mean ipdv value, and knowing the drift was significantly less than mean emission interval, the skew.

A.3 - Comparison with a synchronized case

In this section we consider a case
   relative skew of the clocks can be obtained.

   More in which general, independently on how the two hosts have synchro-
-nized clocks, and drift acts inside its
   limits, we assert that always the synchronization is obtained mean ipdv value divided by setting the real
time each second in each mean
   emission interval produces the value of the clocks. We optimistically suppose mean reciprocal skew of
   the two clocks, provided that
this the collected number of ipdv values is done exactly (without any imprecision). On
   significant for the clocks, anyway
skew statistics.

14.1.2. Errors and corrections

   If the drift continue to act. We refer to reciprocal skew and drift,
having already seen that this is significant. We suppose always close to perform an
ipdv measurement and we evaluate what zero, it is measured by possible to obtain the mean ipdv
   true value and what is of the error on reciprocal skew and correct all the measured ipdv values.

We notice, first of all, that nothing changes for ipdv values measured
over intervals falling completely between two synchronization instants.
In this case, the effect
   Each of synchronization them is only to put associated to zero an emission interval ti between the
offset, two
   packets that does not appear in have produced the calculation of value itself. Then a better ipdv values.

Something different happens if value
   will be: corr.ipdv(i) = meas.ipdv(i) - ti * skew This is a better
   value but not exactly the synchronization instant (or more
synchronization instants) falls inside true one, since we supposed that both
   clocks are not synchronized to the interval. In this case true time. Two errors are
   affecting the
error can range from corrective terms which are:

   +  The reciprocal skew is measured as referred to - the error related to one second interval,
or, more in general, from Src clock

   + to - the error related to an  The interval equal
to ti is measured by the synchronization period. The (few) large intervals Src clock.

   These are second order errors since the measured skew will produce be
   affected by a limited "relative" error while in the (many) short intervals will continue to
produce errors order of the Src skew, an the
   same order of magnitude of is for the not synchronized
case.

Besides, even if error affecting the ti value.

   If the drift is negligible, significant and it can range from the mean ipdv value is no
more suitable lower to calculate the skew, and it will be much more close to
zero. Therefore it
   upper limit of its field, the measured average of the skew will
   depend on the type of variation. Some cases are considered that
   demonstrate that actually the proposed correction is no more possible to correct not so much
   effective in this case. Only the distortion fixed part of the
distribution.

Finally, it total clock
   variation can be properly corrected.

14.1.3. Constant drift

   The first case is necessary to add to these errors the unavoidable impre-
cision of first one considered in the synchronization process. preceding
   paragraph, where the drift is uniform. We have to consider suppose that a reciprocal
   skew is measured and used for correction.

   At the
magnitude beginning of errors introduced by the measurement the actual reciprocal skew is:

   init.skew = mean.skew - rel.max.drift

   and drift at the end the actual reciprocal skew is:

   final.skew = mean.skew + rel max.drift

   The correction is effective only in the order of
tenth central part of microseconds. Not always the complete synchronization process
has a better precision.

A.4 - Bidirectional measurement
   measurement.  At the beginning and components of ipdv

Three terms have been described that can displace at the end a residual error will
   affect the mean ipdv values whose value
from zero. They are:

I-D                          Ipdv Metric                  November 1998

- The total skew, already discussed above, will be:

   ipdv(i).err = ti * rel.max.drift

   We underline here that always acts in an equal
  way and opposite direction over the two directions between West error is larger for large intervals ti and
  East hosts.
- The effect of varying traffic that can increase or decrease along
  limited periods, the average value of the One-Way-Delay. The metric
  above presented supposes
   lower for short intervals ti. For intervals derived from a poissonian
   arrival process, there are many short intervals and few large
   intervals.  We also note that the measurement period a constant drift cannot last
   indefinitely, since there is large enough a minimum and a maximum for considering the skew.

14.1.4. Step of drift

   In this effect as tending to zero.
  It is explicitly noted that case the effect will produce a zero effect
  only error profile depends on the mean ipdv value, while time at which the effect on values ipdv(i) is
  always present. This is not a distortion of drift
   changes. If the distribution, since change is part of near the variation that is measured. This effect is different,
  and usually concordant, on beginning or near the two directions.
- The difference between first and last instantaneous values end of the
  delay variation, that tends
   measurement, the calculated mean skew will be very close to zero when the number
   actual skew of collected
  ipdv values becomes large.

In order to isolate the last two effects, we consider here a measurement
over a long period (e.g. 24 hours)where largest part of the drift is negligible, and measurement. On that part the effect of
   correction will be effective, while over the skew has been corrected.

A.4.1 - Slow variation in a given period

The packets of remaining few values the stream can
   error will be represented on a system of cartesian
orthogonal axes twice with transmission time on x-axis and reception time on
y-axis, by points localized respect the preceding case.  The worse
   condition is produced by transmission and reception time of each
packet. Considering an arbitrary period a change in drift in the middle of time Tper, which will the
   measurement. In this case the correction would be useful only if the
   drift was significantly less than the skew.

14.2. Comparison with a
parameter of synchronized case

   In this procedure, it can be taken as section we consider a sliding window over case in which the sample two hosts have
   synchronized clocks, and for the synchronization is obtained by setting
   the real time each second in each position of the clocks. We optimistically
   suppose that this window, established is done exactly (without any imprecision). On the
   clocks, anyway skew and drift continue to act. We refer to reciprocal
   skew and drift, having already seen that this is significant. We
   suppose to perform an ipdv measurement and we evaluate what is
   measured by suc-
-cessive packets, the segment of straight line mean ipdv value and what is calculated that best
approximate the points, by means of a linear regression method.

The slope error on the measured
   ipdv values.

   We notice, first of all, that nothing changes for ipdv values
   measured over intervals falling completely between two
   synchronization instants.  In this segment will be one if along the period case, the delay
has not changed, and different from one if that delay has increased (>1)
or decreased (<1). For each position effect of the window it
   synchronization is therefore
possible only to find a value put to zero the offset, that does not
   appear in the calculation of "slow delay variation" with Tper as a
parameter. This will give an indication on variations produced by ipdv values.

   Something different traffic conditions along happens if the measurement period. This item
can be subject for further study.

At synchronization instant (or more
   synchronization instants) falls inside the same time interval. In this procedure offers a criterion for reducing case the
   error can range from + to - the error introduced related to one second interval,
   or, more in general, from + to - the calculation of error related to an interval
   equal to the mean ipdv by synchronization period. The (few) large intervals will
   produce a limited error while the instanta-
-neous component (many) short intervals will
   continue to produce errors of the difference between last and first delay.
Supposing that the timestamps, on which same order of magnitude of the metric is based, are
collected and then processed, not
   synchronized case.

   Besides, even if the method of drift is negligible, the sliding window mean ipdv value is
applied at no
   more suitable to calculate the beginning skew, and at it will be much more close
   to zero. Therefore it is no more possible to correct the end distortion
   of the collected sample, distribution.

   Finally, it is possible necessary to avoid starting and ending add to these errors the measurement on values
possibly too different from unavoidable
   imprecision of the average (points too far away from synchronization process. We have to consider that
   the
calculated straight line).

I-D                          Ipdv Metric                  November 1998

A.5 - Symmetry magnitude of an ipdv distribution errors introduced by skew and emission intervals

It drift is demonstrated that, if in the packets order
   of tenth of microseconds. Not always the test sequence are pro-
pagated complete synchronization
   process has a better precision.

14.3. Bidirectional measurement and components of ipdv

   Three terms have been described that can displace the mean ipdv value
   from zero. They are:

   +  The total skew, already discussed above, that always acts in an independent way, in
      equal way and opposite direction over the two directions between
      West and East hosts.

   +  The effect of varying traffic that can increase or decrease along
      limited periods, the average value of the sense One-Way-Delay. The
      metric above presented supposes that none of them the measurement period is
influenced by
      large enough for considering this effect as tending to zero.  It
      is explicitly noted that the preceding packets (large emission intervals), effect will produce a zero effect
      only on the mean ipdv
distribution will be perfectly symmetrical. If value, while the variation effect on values ipdv(i) is
      always present. This is not a distortion of the
delay distribution,
      since is such part of the variation that some packets is delayed by measured. This effect is
      different, and usually concordant, on the preceding one (ideal-
-ly queued to it in a buffer), two directions.

   +  The difference between first and last instantaneous values of the related ipdv value generated will
have a lower limit,
      delay variation, that will be tends to zero when the negative value number of collected
      ipdv values becomes large.

   In order to isolate the emission
interval minus the time required for transmitting last two effects, we consider here a
   measurement over a long period (e.g. 24 hours)where the packet from drift is
   negligible, and the
buffer. If effect of the intervals were constant, this would correspond to skew has been corrected.

14.4. Slow variation in a well
defined value, that would allow to measure the bandwidth given period

   The packets of the bottle-
-neck provided stream can be represented on a system of cartesian
   orthogonal axes with transmission time on x-axis and reception time
   on y-axis, by the output points localized by transmission and reception time of that buffer. Since the intervals are
derived from
   each packet. Considering an arbitrary period of time Tper, which will
   be a poissonian arrival process, parameter of this limit is not procedure, it can be taken as a fixed
one, sliding window
   over the sample and is not immediately evident for each position of this window, established by
   successive packets, the ipdv distribution.

Another effect segment of this interference among packets straight line is calculated that also the
packet following
   best approximate the queued one will produce points, by means of a lower ipdv value since
it linear regression method.

   The slope of this segment will "gain" be one if along the time of latency in period the buffer delay
   has not changed, and different from one if that delay has increased
   (>1) or decreased (<1). For each position of the previous one.

The total effect window it is that the ipdv values will tend
   therefore possible to concentrate on
the negative side find a value of the distribution, "slow delay variation" with some limitation
   Tper as a parameter. This will give an indication on variations
   produced by different traffic conditions along the
negative maximum values. In other words, the negative side of the
distribution will measurement
   period. This item can be shorter than subject for further study.

   At the positive one, but containing more
values. Nothing changes same time this procedure offers a criterion for reducing the meaning
   error introduced in the calculation of the mean ipdv value.

This asymmetry is not a distortion, since represents the actual propa-
-gation characteristics. For by the supposed type
   instantaneous component of intervals, the dis-
-tribution difference between last and first
   delay.  Supposing that the timestamps, on which the metric is always asymmetrical, since always based,
   are present intervals
lower than the delay variability, collected and then processed, if the degree method of asymmetry will
change with the level of interference.

The relationship between asymmetry sliding window
   is applied at the beginning and at the combination end of average emis-
-sion interval and available bandwidth can be investigated the collected sample,
   it is possible to avoid starting and could
provide information about ending the level of congestion of measurement on values
   possibly too different from the average (points too far away from the network
   calculated straight line).                                            |

   Expiration date: December, 1999