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Network Working Group                                      C. Demichelis
INTERNET-DRAFT                                                     CSELT
Expiration Date: December 1999                               P. Chimento
                                                                    CTIT
                                                              June  1999



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


1. Status of this Memo

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

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

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

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

   The list of Internet-Draft shadow directories 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



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   reciprocal skew. Measurements performed on both directions (Two-way
   measurements) allow a better estimation of clock differences. The
   precision that can be obtained is evaluated.



3. Introduction

   This memo takes as a reference the Draft-ietf "One-Way-Delay metric   |
   for IPPM" [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.

   "Jitter" commonly has two meanings: The first meaning is the          |
   variation of a signal with respect to some clock signal, where the    |
   arrival time of the signal is expected to coincide with the arrival   |
   of the clock signal. The second meaning has to do with the variation  |
   of a metric (e.g. delay) with respect to some reference metric (e.g.  |
   average delay or minimum delay). The form of "jitter" that we talk    |
   about here has to do almost exclusively with the second meaning,      |
   rather than the first. See the section on the 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
      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 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
      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



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      stream.


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
   variations in delay, while they are not disturbed by slow variations,
   that can last a relatively long time. A specific metric for quick
   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.  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
   allows the use of the metric even if the two hosts that support the
   measurement points are not synchronized. In the latter case
   indications 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

   Everything contained in the Section 2.2. of [2] applies also in this  |
   case.

   In addition, we assume here 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 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
   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



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   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 few degrees. The total range of the
   drift is usually related to variations from 0 to 70 Celsius. These
   are important points for evaluation of precision of ipdv
   measurements, as will 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
   initial assumption is that source and destination hosts have
   synchronized clocks. The definition of a singleton of one-way ipdv
   metric is first considered, and then a definition of samples for ipdv
   will be given.

   Then the case of application to non-synchronized hosts will be
   discussed, and the precision will be compared with the one of
   synchronized clocks.

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


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

   This definition makes use of the corresponding definition of type-P-
   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










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5.2. Metric parameters


   +  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.



   Note that the packet length is an implicit parameter of both the      |
   Type-P-One-way-delay metric and the Type-P-One-way-ipdv metric, since |
   this contributes to the overall one-way delay. We assume that the     |
   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.


5.4. 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 denote the wire times 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, 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 dT1+T1 (last bit of the first packet), and at wire-time



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   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
   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.


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 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 interval T2-T1 and the
      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 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.}

   +  As with other 'type-P' metrics, the value of the metric may depend
      on such properties of the 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,
      reassembly does not occur, then the packet will be deemed lost.





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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).  Generally, for a given Type-P, the methodology would
   proceed as follows:

   +  The need of synchronized clocks for Src and Dst will be 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' 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.

   +  At the Dst host, arrange to receive the packets.

   +  At the Src host, place a timestamp in the  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 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.








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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'.

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

5.7.1. Errors/Uncertainties related to Clocks

   If, as a first approximation, the error that affects the first
   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
   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 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 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 discussed below, since they come from a statistic over a
      significant sample.  If the measurement conditions do not allow
      neglecting the drift, 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 Drift varies the skew value in the time. The limits
      in which the skew can vary are anyway limited and small, so that a



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      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  Draft on One-Way-Delay [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.

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

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


6. Definitions for Samples of One-way ipdv

   Starting from the definition of the singleton metric of one-way ipdv, |
   we define a sample of such singletons.  In the following, the two     |
   packets needed for a singleton measurement will be called a "pair".   |

   A stream of test packets is generated  where the 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 and Type-P, a  |
      sample of values of parameter T1 is defined.  To define the values |
      of 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. From the second value on, T1 value of the pair n         |
      coincides with T2 of the pair n-1, and the first packet of pair n  |
      coincides with the second packet of the pair n-1.                  |


6.1. Metric name

   Type-P-One-way-ipdv-stream







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6.2. Parameters

   +  Src, the IP address of a host

   +  Dst, the IP address of a host

   +  T0, a time

   +  Tf, a time

   +  lambda, a rate in reciprocal seconds


6.3. Metric Units:

   A sequence of triads whose elements are:

   +  T, a time

   +  Ti, a time interval.

   +  dT a real number or an undefined number of seconds


6.4. Definition

   A pseudo-random Poisson process is defined such that 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 the sample is the sequence made up of the
   resulting <time, time interval, ipdv> triple, where the time interval
   is given by T(i+1)-T(i). Each time T(i), excluding the 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 3

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

                                  Figure 3









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6.5. Discussion

   Note first that, since a pseudo-random number sequence is employed,
   the sequence of times, and hence the value of the sample, is not
   fully specified. Pseudo-random number generators of good quality will
   be needed to achieve the desired qualities.

   The sample is defined in terms of a Poisson process both to avoid the
   effects of self-synchronization and also capture a sample that is
   statistically as unbiased as possible. {Comment: there is, of course,
   no claim that real Internet traffic arrives according to a Poisson
   arrival process.}


6.6. Methodology

   Since packets can be lost or duplicated or can arrive in a different
   order than the order sent, in order to recognize the pairs of test
   packets, they should be marked with a sequence number. For duplicated
   packets only the first received copy should be considered. If a
   packet is lost, two values of ipdv will be undefined, since each
   packet is common to two pairs.

   Steps for measurement can be the following:

   +  Starting from a given time T, Src generates a test packet as for a
      singleton metrics, inserts in 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.

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

   +  On reception of the first packet, or the first packet after a
      sequence number error, Dst records sequence number and
      transmission timestamp that are contained in the packet and the
      reception time Rx as "old values".

   +  On reception of the other packets Dst verifies the seuqence number
      and if it is correct, by using the "old values" and the newly
      received ones, a value of ipdv is computed. Then Dst records the
      new sequence number, transmit and receive timestamps as "old
      values".









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6.7. Errors and uncertainties

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


6.8. Distribution of One-way-ipdv values                                 |

   The one-way-ipdv values are limited by virtue of the fact that there  |
   are upper and lower bounds on the one-way-delay values. Specifically, |
   one-way-delay is upper bounded by the value chosen as the maximum     |
   beyond which a packet is counted as lost. It is lower bounded by      |
   propagation, transmission and nodal transit delays assuming that      |
   there are no 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 one-way-ipdv can 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 non-decreasing) or of course it can vary in both   |
   directions in the interval, within the limits of the half-open        |
   interval [L,U). Accordingly, within that interval, the one-way-ipdv   |
   values can be positive, negative, or a mixture (including 0).         |

   Since the range of values is limited, the one-way-ipdv cannot         |
   increase or decrease indefinitely. Suppose, for example, that the     |
   ipdv has a positive 'run' (i.e. a long sequence of positive values).  |
   At some point in this 'run', the positive values must approach 0 (or  |
   become negative) if the one-way-delay remains finite. Otherwise, the  |
   one-way-delay bounds would be violated. If such a run were to         |
   continue infinitely long, the sample mean (assuming no packets are    |
   lost) would approach 0 (because the one-way-ipdv values must approach |
   0). Note, however, that this says nothing about the shape of the      |
   distribution, or whether it is symmetric. Note further that over      |
   significant intervals, depending on the width of the interval [L,U),  |
   that the sample mean one-way-ipdv could be positive, negative or 0.


6.9. Some statistics for One-way-ipdv

   Some statistics are suggested which can provide useful information in |
   analyzing the behavior of the packets flowing from Src to Dst. The    |
   focus is on the instantaneous behavior of the connection.  Other      |
   statistics can be defined if needed.





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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
   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.


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

   This metric was defined in [7] and is simply the absolute value of    |
   the Type-P-One-way-ipdv. This can be used to derive a number of       |
   metrics.                                                              |



7. Discussion on clock synchronization

   This section gives some considerations about the need of having
   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.


7.1. Effects of synchronization errors

   We refer here to the two components that can generate this type of
   errors that are the reciprocal "skew" and "drift" of the Src and Dst
   clocks. It is first of all noted that the variable component "drift"
   is physically limited and its effects can be interpreted by saying
   that the total reciprocal skew of the two clocks can vary, ranging
   from a min to a max. value in the time. This type of variation takes
   place very slowly being mostly connected to variations in
   temperature.

   We suppose to perform a measurement between a Src and a Dst that have
   a reciprocal, initial skew of "ts1" and a reciprocal drift such that,
   after the time T the total skew is "ts2". It is not here a limitation
   to consider that at the beginning of time T the two clocks indicate
   the same time T0.




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   In order to analyze the effects produced by this situation we suppose
   that packets are transferred, from Src to Dst, with a 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 T with two packets
   having an interval of Ti(1).Another ipdv value is measured at the end
   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 to calculate the values of the Tx and Rx
   timestamps as they are seen by the two clocks, and 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 is given by the effect of the skew during the time interval
   Ti(i) between the two packets of the pair, and a second order term
   due to the variation of that skew in the same interval.

   If, as in the most of practical cases, the drift can be considered
   close to zero, then ts1 = ts2, and the error is not depending on the
   time at which the measurement is done. In addition, this type of
   error can be corrected 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 the
   effect of the maximum reciprocal skew on the maximum interval between
   packets.

7.2. Related precision

   This means that:

   +  If the skew is constant and is = ts all the 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 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 the corresponding Ti(i)
      are collected, for each ipdv(i) value a correcting term is
      available, and a sample of "corrected" c-ipdv(i) values is
      obtained, where c-ipdv(i) = ipdv(i) - Ti(i)*st.




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   +  Considering the total skew as subdivided into a fixed part and a
      variable part (skew and drift),respectively, ts and + or - td,
      from the mean ipdv value and the 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 given by the difference between
      the actual skew at the time in which the value has been measured
      and the average skew, multiplied by the time interval between the
      packets that have generated that ipdv value. Considerations on the
      number of values in the sample affected by errors are reported in
      Appendix A.

   +  If the duration of the measurement is such that it is possible to  |
      consider that the ipdv (without skew) is close to zero, the mean
      value of the ipdv distribution will have the value of the average
      skew multiplied by the mean value of the emission interval, as
      supposed above.

   +  We observe that the displacement due to the skew does not change
      the shape of the distribution, and, for example the Standard
      Deviation remains the same. What introduces a distortion is the
      effect of the drift, also when the mean value of this effect is
      zero at the end of the measurement. The value of this distortion
      is limited to the effect of the total skew variation on the
      emission interval.

   +  In what has been said, skew and drift have been considered as
      "reciprocal". In Appendix A it will be considered that each of the
      two clocks have a skew and a drift with respect a "true time", and
      it will be observed that the difference is negligible with respect
      the situation in which one of the two clocks is taken as the "true
      time".


8. Definition for a bidirectional ipdv metric

   We now consider that the action of the skew on one direction is the
   same, with opposite sign, of the action on the other direction. The
   idea of performing at the same time two independent measurements in
   the two directions is suggested by this fact.

   If, after a long measurement, the variable conditions of the system
   under test have reached the situation of a contribution close to zero
   to the mean value of the ipdv distribution, it is expected that only
   the action of the average skew has modified the measured mean value.
   It is therefore expected that on one direction that value is equal
   and opposite to the one measured in the other direction.




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   This fact offers the possibility of defining a theoretical reference
   measurement duration in the following way:

   The reference duration of a bidirectional ipdv measurement between an
   host E and an host W is reached at time Tf such that for each time T
   > Tf the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where
   epsilon is what we can consider as zero, is always verified. This is
   one, but not the only method for verifying that the mean ipdv value
   has reached the value of the average reciprocal skew.

   At this point it is possible to evaluate the reciprocal skew.  This
   will require the knowledge of the mean value of the intervals between
   consecutive packets, that can be calculated over the transmitted
   stream, by using the collected time stamps.

   A bidirectional measurement can be defined not only as twin one-way
   independent metrics that take place (nearly) at the 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 Round Trip Delay and its variations.
   Problems will anyway arise on the characterization of emission
   intervals in the backward direction. They would be produced by the
   combination of the original Poisson arrival process and the effect of
   ipdv on the forward direction. It has to be studied if this sequence
   of intervals is still suitable for the measurement. also other
   possibilities can be envisaged for obtaining a proper backward
   sequence and still maintain the loopback concept.


9. Relationship to other standards                                       |

   The ITU definitions are based on delay variation as defined for ATM   |
   cells [5]. We will 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 different points of    |
   view. The first, called 1-point cell delay variation, is essentially  |
   a measure of how a cell stream varies from a stated cell rate (e.g.   |
   the peak cell rate). The basic idea behind the measurement is as      |
   follows: The observer at the measurement point notes cell arrival     |
   times and clock ticks. The clock ticks at a constant rate, based on   |
   the peak cell rate for the cell stream. The difference between the    |
   cell arrival times and the clock ticks is the 1-point cell delay      |
   variation. If a cell arrives later than the clock tick, the clock     |
   "restarts" at the actual cell arrival time, and continues to tick at  |



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   a constant rate from that point.                                      |

   The purpose of this measure is to identify what is called "cell       |
   clumping" and non-conforming cells. That is, to idenify cells that    |
   violate the leaky bucket parameters defined for that cell stream.     |
   That is why the clock skips when a cell is later than the normal      |
   inter-cell time defined by the peak cell rate. It is of much less     |
   interest when cells are late than when they arrive too close          |
   together.                                                             |


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

   2-Point cell delay variation, as defined in [5] is closer to what is  |
   defined here. The basic idea behind this metric is that two           |
   measurement points, whose clocks are synchronized, observe a cell     |
   stream and timestamp when each cell passes. The difference in the     |
   timestamps for a cell is essentially the one-way delay. There is also |
   assumed to be a one-way cell delay for a reference cell which we will |
   denote d0. The cell delay variation for the ith cell is then di-d0.   |
   Note that this is not an absolute value, but that the cell delay      |
   variation can be either positive or negative. [5] does not specify    |
   how to choose the reference cell delay.                               |

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

   +  Take the delay of the first packet of the sequence as the          |
      reference time.                                                    |

   +  Take the average one-way packet delay as the reference time.       |



9.3. Discussion                                                          |


9.3.1. Differences                                                       |

   Demichelis [4] points out a number of problems with the 2-point PDV   |
   definition in [3]. First of all is the issue of choosing the          |
   reference delay time. If this is chosen arbitrarily, it becomes       |
   uncertain how to compare the measurements taken from two non-         |
   overlapping periods. If it is chosen as an average, that can also be  |



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   a problem, because over long periods of time in a network, the        |
   average one-way delay can vary widely. A twenty-four hour average as  |
   the reference time can seriously overestimate the actual delay        |
   variation at a given time of day because the night-time hours, when   |
   the delay can be expected to approach the propagation and node time,  |
   is included in the average. On the other hand, there is no clear way  |
   to partition the time in order to find averages for certain periods   |
   of time and compute the delay variation with reference to these       |
   averages.                                                             |

   Another problem pointed out in [4] is the 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 metrics                                  |

   The 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 really intended to talk about the    |
   relationship of cell arrival times to a given periodic event, and     |
   consequently is more closely related to the first definition of       |
   "jitter" given in Section  3 above.                                   |

   2-point delay variation (actually, the 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 reference packet for the 2-point measurement and also as the      |
   start packet of the ipdv measurement. Denote this packet by p(0).     |
   Then given ipdv measurements for a series of packets, the 2-point     |
   delay variation for packet i is p(0) + the sum from k=1 to i of       |
   ipdv(k).                                                              |

   Similarly, given a sequence of 2-point delay variation measurements   |
   we can derive the ipdv measurement as follows: Denote the 2-point     |
   delay variation measurement for packet i as v(i). Then the ipdv value |
   for the pair of packets p(k-1), p(k) is simply v(k)-v(k-1) [6].       |


9.3.3. Summary                                                           |

   As described above, there are a number of disadvantages of the        |
   2-point packet delay variation approach. Further, the ipdv approach   |
   described here is general enough to provide the same information as   |
   the 2-point packet delay variation measurements. Because of this, and |
   because of the (possibly) looser clock synchronization requirements   |
   of ipdv, we recommend the one-way-ipdv approach for the delay         |
   variation measurement.                                                |



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10. Security Considerations                                              |

   The one-way-ipdv metric has the same security properties as the one-  |
   way-delay metric [2]. The packets contain no user information, and so |
   privacy of user data is not a concern. It is still possible that      |
   there could be an attempt at a denial of service attack by sending    |
   many measurement packets into the 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 order to avoid interfering with normal traffic  |
   in the 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 this     |
   revised draft.                                                        |


12. References                                                           |
   [1]    V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP      |
        Performance Metrics", RFC 2330  Feb. 1998                        |

   [2]    G.Almes, S.Kalidindi - "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 - IP Packet Transfer and Availability      |
        Performance Parameters"                                          |

   [4]    Demichelis, Carlo - "Packet Delay Variation Comparison between |
        ITU-T and 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>                                                       |




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13. Authors' Addresses                                                   |


   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


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



   APPENDIX A

   This Appendix considers the scenario in which two hosts have clocks
   that are both not synchronized. Between the two hosts, in an
   independent way and at the same time in both direction an ipdv
   measurement 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 the characteristics of the
   ipdv metric and its results, without considering implementation
   issues.


14. Initial positions

   The two hosts will be called West (W) and East (E). The two
   measurements start at the same time, while the end of the measurement
   it is supposed to be decided by the results of the measurement
   itself.

   At the 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 E-
   clock by an absolute skew of skw ppm.



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   The W-clock is affected by an absolute drift ranging from -drw ppm to
   +drw ppm, the 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 effect of the drift on this type of metric,
   it is necessary to consider the time in which the variation of the
   skew takes place. We consider the two extreme cases in which the
   variation takes place uniformly from the beginning to the end of the
   measurement and the variation takes place suddenly at a generic time
   along the measurement. Let TM be the measurement time.


14.1.1. Mean ipdv value

   Since the mean ipdv value, as it has been seen, is the difference of
   the last delay minus the first, divided by the number of considered
   values, we consider what, in the two cases, is measured for first and
   last delay.

   We call trueDf the true first Delay and trueDl the true last Delay.
   For the evaluation that we want to do, it is not a limitation to
   consider that they are equal and have a value of trueD. We also
   consider as time 0 the true time at which the transmission of the
   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 measurement this
   will bring the skew from a value of: skWmin = skw - drw     ;
   skEmin = ske - dre to a value 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 difference between the last and first Delay is therefore:

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



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   if TM = 10 hours drpsE is in the order of 50*10E-6 / 36000 that is
   about 10E-9 and the second term of the expression is in the order of
   10E-14 for true delays in the order of 1 sec (negligible term).  We
   consider that, with very good approximation:

   Mean emission interval (mti) = TM / number of ipdv values (N)
   Therefore:

   mean ipdv = (measured last Delay - measured first Delay) / N =
     = mti*(skEmin - skWmin + dre - drw)

   but we considered skEmin = ske - dre and skWmin = skw - drw and
   therefore:

   mean ipdv = (meas.lastD - meas.firstD) / mti*(reciprocal mean skew)

   The previous procedure is now applied to the case in which the total
   drift takes place in a very short time. Some cases are possible, and
   we consider the one in which at the beginning the West clock has
   skWmax and the East clock has skEmin, at time txW the West clock
   assumes skWmin and at time txE the East clock assumes skEmax.  What
   is measured as first Delay is now:

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

   What 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 the mean skew values will be:

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

   the difference between the two delays therefore is:

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

   and the mean ipdv value will be:

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

   the second term of the second member in the previous hypotheses is in
   the order of the nanosecond, and we neglect it. Also in this case,
   from the mean ipdv value, and knowing the mean emission interval, the



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   relative skew of the clocks can be obtained.

   More in general, independently on how the drift acts inside its
   limits, we assert that always the mean ipdv value divided by the mean
   emission interval produces the value of the mean reciprocal skew of
   the two clocks, provided that the collected number of ipdv values is
   significant for the statistics.


14.1.2. Errors and corrections

   If the drift is always close to zero, it is possible to obtain the
   true value of the reciprocal skew and correct all the ipdv values.
   Each of them is associated to an emission interval ti between the two
   packets that have produced the value itself. Then a better ipdv value
   will be: corr.ipdv(i) = meas.ipdv(i) - ti * skew This is 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:

   +  The reciprocal skew is measured as referred to the Src clock

   +  The interval ti 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 is significant 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 of variation. Some cases are considered that
   demonstrate that actually the proposed correction is not so much
   effective in this case. Only the fixed part of the total clock
   variation can be properly corrected.


14.1.3. Constant drift

   The first case is the first one considered in the preceding
   paragraph, where the drift is uniform. We suppose that a reciprocal
   skew is measured and used for correction.

   At the beginning of the measurement the actual reciprocal skew is:

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

   and at the end the actual reciprocal skew is:




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

   The correction is effective only in the central part of the
   measurement.  At the beginning and at the end a residual error will
   affect the ipdv values whose value will be:

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

   We underline here that the error 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 is a minimum and a maximum for the skew.


14.1.4. Step of drift

   In this case the error profile depends on the time at which the drift
   changes. If the change is near the beginning or near the end of the
   measurement, the calculated mean skew will be very close to the
   actual skew of the largest part of the measurement. On that part the
   correction will be effective, while over the remaining few values the
   error will be twice with respect the preceding case.  The worse
   condition is produced by a change in drift in the middle of 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 synchronized case

   In this section we consider a case in which the two hosts have
   synchronized clocks, and the synchronization is obtained by setting
   the real time each second in each of the clocks. We optimistically
   suppose that this 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 the mean ipdv value and what is the 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 case, the effect of
   synchronization is only to put to zero the offset, that does not
   appear in the calculation of ipdv values.

   Something different happens if the synchronization instant (or more



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   synchronization instants) falls inside the interval. In this case the
   error can range from + to - the error related to one second interval,
   or, more in general, from + to - the error related to an interval
   equal to the synchronization period. The (few) large intervals will
   produce a limited error while the (many) short intervals will
   continue to produce errors of the same order of magnitude of the not
   synchronized case.

   Besides, even if the drift is negligible, the mean ipdv value is no
   more suitable to calculate the skew, and it will be much more close
   to zero. Therefore it is no more possible to correct the distortion
   of the distribution.

   Finally, it is necessary to add to these errors the unavoidable
   imprecision of the synchronization process. We have to consider that
   the magnitude of errors introduced by skew and drift is in the order
   of tenth of microseconds. Not always the 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
      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 One-Way-Delay. The
      metric above presented supposes that the measurement period is
      large enough for considering this effect as tending to zero.  It
      is explicitly noted that the effect will produce a zero effect
      only on the mean ipdv value, while the effect on values ipdv(i) is
      always present. This is not a distortion of the distribution,
      since is part of the variation that is measured. This effect is
      different, and usually concordant, on the two directions.

   +  The difference between first and last instantaneous values of the
      delay variation, that tends to zero when the number 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 the drift is
   negligible, and the effect of the skew has been corrected.



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14.4. Slow variation in a given period

   The packets of the stream can be represented on a system of cartesian
   orthogonal axes with transmission time on x-axis and reception time
   on y-axis, by points localized by transmission and reception time of
   each packet. Considering an arbitrary period of time Tper, which will
   be a parameter of this procedure, it can be taken as a sliding window
   over the sample and for each position of this window, established by
   successive packets, the segment of straight line is calculated that
   best approximate the points, by means of a linear regression method.

   The slope of this segment will be one if along the period the delay
   has not changed, and different from one if that delay has increased
   (>1) or decreased (<1). For each position of the window it is
   therefore possible to find a value of "slow delay variation" with
   Tper as a parameter. This will give an indication on variations
   produced by different traffic conditions along the measurement
   period. This item can be subject for further study.

   At the same time this procedure offers a criterion for reducing the
   error introduced in the calculation of the mean ipdv by the
   instantaneous component of the difference between last and first
   delay.  Supposing that the timestamps, on which the metric is based,
   are collected and then processed, if the method of the sliding window
   is applied at the beginning and at the end of the collected sample,
   it is possible to avoid starting and ending the measurement on values
   possibly too different from the average (points too far away from the
   calculated straight line).                                            |

   Expiration date: December, 1999





















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