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RFC 3393 - IP Packet Delay Variation Metric for IP Performance M

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Network Working Group                                      C. Demichelis
Request for Comments: 3393                             Telecomitalia Lab
Category: Standards Track                                    P. Chimento
                                                            Ericsson IPI
                                                           November 2002

                    IP Packet Delay Variation Metric
                   for IP Performance Metrics (IPPM)

Status of this Memo

   This document specifies an Internet standards track protocol for the
   Internet community, and requests discussion and suggestions for
   improvements.  Please refer to the current edition of the "Internet
   Official Protocol Standards" (STD 1) for the standardization state
   and status of this protocol.  Distribution of this memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (2002).  All Rights Reserved.


   This document refers to a metric for variation in delay of packets
   across Internet paths.  The metric is based on the difference in the
   One-Way-Delay of selected packets.  This difference in delay is
   called "IP 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.  We discuss both in this document.

Table of Contents

   1 Introduction..................................................... 2
     1.1 Terminology.................................................. 3
     1.2 Definition................................................... 3
     1.3 Motivation................................................... 4
     1.4 General Issues Regarding Time................................ 5
   2 A singleton definition of a One-way-ipdv metric.................. 5
     2.1 Metric name.................................................. 6
     2.2 Metric parameters............................................ 6
     2.3 Metric unit.................................................. 6
     2.4 Definition................................................... 6
     2.5 Discussion................................................... 7
     2.6 Methodologies................................................ 9
     2.7 Errors and Uncertainties.....................................10

         2.7.1 Errors/Uncertainties related to Clocks.................11
         2.7.2 Errors/uncertainties related to Wire-time vs Host-time.12
   3 Definitions for Samples of One-way-ipdv..........................12
     3.1 Metric name..................................................12
     3.2 Parameters...................................................12
     3.3 Metric Units.................................................13
     3.4 Definition...................................................13
     3.5 Discussion...................................................13
     3.6 Methodology..................................................14
     3.7 Errors and uncertainties.....................................14
   4 Statistics for One-way-ipdv......................................14
     4.1 Lost Packets and ipdv statistics.............................15
     4.2 Distribution of One-way-ipdv values..........................15
     4.3 Type-P-One-way-ipdv-percentile...............................16
     4.4 Type-P-One-way-ipdv-inverse-percentile.......................16
     4.5 Type-P-One-way-ipdv-jitter...................................16
     4.6 Type-P-One-way-peak-to-peak-ipdv.............................16
   5 Discussion of clock synchronization..............................17
     5.1 Effects of synchronization errors............................17
     5.2 Estimating the skew of unsynchronized clocks.................18
   6 Security Considerations..........................................18
     6.1 Denial of service............................................18
     6.2 Privacy/Confidentiality......................................18
     6.3 Integrity....................................................19
   7 Acknowledgments..................................................19
   8 References.......................................................19
      8.1 Normative References........................................19
      8.2 Informational References....................................19
   9 Authors' Addresses...............................................20
   10 Full Copyright Statement........................................21

1. Introduction

   This memo defines a metric for the variation in delay of packets that
   flow from one host to another through an IP path.  It is based on "A
   One-Way-Delay metric for IPPM", RFC 2679 [2] and part of the text in
   this memo is taken directly from that document; the reader is assumed
   to be familiar with that document.

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in BCP 14, RFC 2119 [3].
   Although BCP 14, RFC 2119 was written with protocols in mind, the key
   words are used in this document for similar reasons.  They are used
   to ensure the results of measurements from two different
   implementations are comparable and to note instances where an
   implementation could perturb the network.

   The structure of the memo is as follows:

   +  A 'singleton' analytic metric, called Type-P-One-way-ipdv, will be
      introduced to define a single instance of an ipdv measurement.

   +  Using this singleton metric, a 'sample', called Type-P-one-way-
      ipdv-Poisson-stream, will be introduced to make it possible to
      compute the statistics of sequences of ipdv measurements.

   +  Using this sample, several 'statistics' of the sample will be
      defined and discussed

1.1. Terminology

   The variation in packet delay is sometimes called "jitter".  This
   term, however, causes confusion because it is used in different ways
   by different groups of people.

   "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.  This meaning is used with reference to
   synchronous signals and might be used to measure the quality of
   circuit emulation, for example.  There is also a metric called
   "wander" used in this context.

   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).  This meaning is frequently used by computer
   scientists and frequently (but not always) refers to variation in

   In this document we will avoid the term "jitter" whenever possible
   and stick to delay variation which is more precise.

1.2. Definition

   A definition of the IP Packet Delay Variation (ipdv) can be given for
   packets inside a stream of packets.

   The ipdv of a pair of packets within a stream of packets is defined
   for a selected pair of packets in the stream going from measurement
   point MP1 to measurement point MP2.

   The ipdv is the difference between the one-way-delay of the selected

1.3. Motivation

   One important use of delay variation is the sizing of play-out
   buffers for applications requiring the regular delivery of packets
   (for example, voice or video play-out).  What is normally important
   in this case is the maximum delay variation, which is used to size
   play-out buffers for such applications [7].  Other uses of a delay
   variation metric are, for example, to determine the dynamics of
   queues within a network (or router) where the changes in delay
   variation can be linked to changes in the queue length process at a
   given link or a combination of links.

   In addition, this type of metric is particularly robust with respect
   to 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.

   The scope of this document is to provide a way to measure the ipdv
   delivered on a path.  Our goal is to provide a metric which can be
   parameterized so that it can be used for various purposes.  Any
   report of the metric MUST include all the parameters associated with
   it so that the conditions and meaning of the metric can be determined
   exactly.  Since the metric does not represent a value judgment (i.e.,
   define "good" and "bad"), we specifically do not specify particular
   values of the metrics that IP networks must meet.

   The flexibility of the metric can be viewed as a disadvantage but
   there are some arguments for making it flexible.  First, though there
   are some uses of ipdv mentioned above, to some degree the uses of
   ipdv are still a research topic and some room should be left for
   experimentation.  Secondly, there are different views in the
   community of what precisely the definition should be (e.g.,
   [8],[9],[10]).  The idea here is to parameterize the definition,
   rather than write a different document for each proposed definition.
   As long as all the parameters are reported, it will be clear what is
   meant by a particular use of ipdv.  All the remarks in the document
   hold, no matter which parameters are chosen.

1.4. General Issues Regarding Time

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

   To summarize: As in [1] we define "skew" as the first derivative of
   the offset of a clock with respect to "true time" and define "drift"
   as the second derivative of the offset of a clock with respect to
   "true time".

   From there, we can construct "relative skew" and "relative drift" for
   two clocks C1 and C2 with respect to one another.  These are natural
   extensions of the basic framework definitions of these quantities:

   +  Relative offset = difference in clock times

   +  Relative skew = first derivative of the difference in clock times

   +  Relative drift = second derivative of the difference in clock

   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
   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 a 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.

2. A singleton definition of a One-way-ipdv metric

   The purpose of the singleton metric is to define what a single
   instance of an ipdv measurement is.  Note that it can only be
   statistically significant in combination with other instances.  It is
   not intended to be meaningful as a singleton, in the sense of being
   able to draw inferences from it.

   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.

2.1. Metric name


2.2. Metric parameters

   +  Src, the IP address of a host

   +  Dst, the IP address of a host

   +  T1, a time

   +  T2, a time

   +  L, a packet length in bits.  The packets of a Type P packet stream
      from which the singleton ipdv metric is taken MUST all be of the
      same length.

   +  F, a selection function defining unambiguously the two packets
      from the stream selected for the metric.

   +  I1,I2, times which mark that beginning and ending of the interval
      in which the packet stream from which the singleton measurement is
      taken occurs.

   +  P, the specification of the packet type, over and above the source
      and destination addresses

2.3. 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.

2.4. Definition

   We are given a Type P packet stream and I1 and I2 such that the first
   Type P packet to pass measurement point MP1 after I1 is given index 0
   and the last Type P packet to pass measurement point MP1 before I2 is
   given the highest index number.

   Type-P-One-way-ipdv is defined for two packets from Src to Dst
   selected by the selection function F, as the difference between the
   value of the type-P-One-way-delay from Src to Dst at T2 and the value

   of the type-P-One-Way-Delay from Src to Dst at T1.  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 derived from the One-Way-Delay metric.

   Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to
   Dst at T1, T2 is ddT" means that Src sent two 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 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 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.

   Figure 1 illustrates this definition.  Suppose that packets P(i) and
   P(k) are selected.

     I1  P(i)       P(j)                  P(k)                     I2

   MP1 |--------------------------------------------------------------|
           |\        |\                    |\
           | \       | \                   | \
           |  \      |  \                  |  \
           |   \     |   \                 |   \
           |dTi \    |dTj \                |dTk \
           |<--->v   |<--->v               |<--->v

   MP2 |--------------------------------------------------------------|

    I1          P(i)       P(j)                 P(k)               I2

                     Figure 1: Illustration of the definition

   Then ddT = dTk - dTi as defined above.

2.5. Discussion

   This metric definition depends on a stream of Type-P-One-Way-Delay
   packets that have been measured.  In general this can be a stream of
   two or more packets, delimited by the interval endpoints I1 and I2.
    There must be a stream of at least two packets in order for a
   singleton ipdv measurement to take place.  The purpose of the
   selection function is to specify exactly which two packets from the
   stream are to be used for the singleton measurement.  Note that the

   selection function may involve observing the one-way-delay of all the
   Type P packets of the stream in the specified interval.  Examples of
   a selection function are:

   +  Consecutive Type-P packets within the specified interval

   +  Type-P packets with specified indices within the specified

   +  Type-P packets with the min and max one-way-delays within the
      specified interval

   +  Type-P packets with specified indices from the set of all defined
      (i.e., non-infinite) one-way-delays Type-P packets within the
      specified interval.

      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 5 of this memo.  It is pointed out that, if
      the relative clock conditions change in time, the accuracy of the
      measurement will depend on the time interval I2-I1 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).

   +  ddT is derived from the start of the first bit out from a packet
      sent out by Src to the reception of the last bit received by Dst.
      Delay is correlated to the size of the packet.  For this reason,
      the packet size is a parameter of the measurement and must be
      reported along with the measurement.

   +  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,
      re-assembly does not occur, then the packet will be deemed lost.

   In this document it is assumed that the Type-P packet stream is
   generated according to the Poisson sampling methodology described in

   The reason for Poisson sampling is that it ensures an unbiased and
   uniformly distributed sampling of times between I1 and I2.  However,
   alternate sampling methodologies are possible.  For example,
   continuous sampling of a constant bit rate stream (i.e., periodic
   packet transmission) is a possibility.  However, in this case, one
   must be sure to avoid any "aliasing" effects that may occur with
   periodic samples.

2.6. 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,

   The measurement methodology described in this section assumes the
   measurement and determination of ipdv in real-time as part of an
   active measurement.  Note that this can equally well be done a
   posteriori, i.e., after the one-way-delay measurement is completed.

   Generally, for a given Type-P, the methodology would proceed as
   follows: Note that this methodology is based on synchronized clocks.
   The need for synchronized clocks for Src and Dst will be discussed

   +  Start after time I1.  At the Src host, select Src and Dst IP
      addresses, and form test packets of Type-P with these addresses
      according to a given technique (e.g., the Poisson sampling
      technique).  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

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

   +  At the Src host, place a time stamp in the Type-P packet, and send
      it towards Dst.

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

   +  If the packet meets the selection function criterion for the first
      packet, record this first delay value.  Otherwise, continue
      generating the Type-P packet stream as above until the criterion
      is met or I2, whichever comes first.

   +  At the Src host, packets continue to be generated according to the
      given methodology.  The Src host places a time stamp in the Type-P
      packet, and send it towards Dst.

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

   +  If the packet meets the criterion for the second packet, then by
      subtracting the first value of One-Way-Delay from the second value
      the ipdv value of the pair of packets is obtained.  Otherwise,
      packets continue to be generated until the criterion for the
      second packet is fulfilled or I2, whichever comes first.

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

2.7. Errors and Uncertainties

   In the singleton metric of ipdv, factors that affect the measurement
   are the same as those affecting 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 following

2.7.1. Errors/Uncertainties related to Clocks

   If, as a first approximation, the error that affects the first
   measurement of One-Way-Delay were the same as 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 time T1, at which the first
   measurement is performed, to time T2 at which the second measurement
   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.

   +  The effect of drift and skew errors on ipdv measurements can be
      quantified as follows: Suppose that the skew and drift functions
      are known.  Assume first that the skew function is linear in time.
      Clock offset is then also a function of time and the error evolves
      as e(t) = K*t + O, where K is a constant and O is the offset at
      time 0.  In this case, the error added to the subtraction of two
      different time stamps (t2 > t1) is e(t2)-e(t1) = K*(t2 - t1) which
      will be added to the time difference (t2 - t1).  If the drift
      cannot be ignored, but we assume that the drift is a linear
      function of time, then the skew is given by s(t) = M*(t**2) + N*t
      + S0, where M and N are constants and S0 is the skew at time 0.
      The error added by the variable skew/drift process in this case
      becomes e(t) = O + s(t) and the error added to the difference in
      time stamps is e(t2)-e(t1) = N*(t2-t1) + M*{(t2-t1)**2}.

      It is the claim here (see remarks in section 1.3) that the effects
      of skew are rather small over the time scales that we are
      discussing here, since temperature variations in a system tend to
      be slow relative to packet inter-transmission times and the range
      of drift is so small.

   +  As far as accuracy and resolution are concerned, what is noted in
      the one-way-delay document [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.

2.7.2. 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.

   However, in most cases, the fixed and variable components are not
   known exactly.

3. Definitions for Samples of One-way-ipdv

   The goal of the sample definition is to make it possible to compute
   the statistics of sequences of ipdv measurements.  The singleton
   definition is applied to a stream of test packets generated according
   to a pseudo-random Poisson process with average arrival rate lambda.
   If necessary, the interval in which the stream is generated can be
   divided into sub-intervals on which the singleton definition of ipdv
   can be applied.  The result of this is a sequence of ipdv
   measurements that can be analyzed by various statistical procedures.

   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".

3.1. Metric name


3.2. 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

   +  L, a packet length in bits.  The packets of a Type P packet stream
      from which the sample ipdv metric is taken MUST all be of the same

   +  F, a selection function defining unambiguously the packets from
      the stream selected for the metric.

   +  I(i),I(i+1), i >=0, pairs of times which mark the beginning and
      ending of the intervals in which the packet stream from which the
      measurement is taken occurs.  I(0) >= T0 and assuming that n is
      the largest index, I(n) <= Tf.

   +  P, the specification of the packet type, over and above the source
      and destination addresses

3.3. Metric Units:

   A sequence of triples whose elements are:

   +  T1, T2,times

   +  dT a real number or an undefined number of seconds

3.4. 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 for packet generation times.

   Each packet falling within one of the sub-intervals I(i), I(i+1) is
   tested to determine whether it meets the criteria of the selection
   function F as the first or second of a packet pair needed to compute
   ipdv.  The sub-intervals can be defined such that a sufficient number
   of singleton samples for valid statistical estimates can be obtained.

   The triples defined above consist of the transmission times of the
   first and second packets of each singleton included in the sample,
   and the ipdv in seconds.

3.5. 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.  There is, of course, no claim
   that real Internet traffic arrives according to a Poisson arrival

   The sample metric can best be explained with a couple of examples:
   For the first example, assume that the selection function specifies
   the "non-infinite" max and min one-way-delays over each sub-interval.
   We can define contiguous sub-intervals of fixed specified length and
   produce a sequence each of whose elements is the triple <transmission
   time of the max delay packet, transmission time of the min delay
   packet, D(max)-D(min)> which is collected for each sub-interval.  A
   second example is the selection function that specifies packets whose
   indices (sequence numbers) are just the integers below a certain
   bound.  In this case, the sub-intervals are defined by the
   transmission times of the generated packets and the sequence produced
   is just <T(i), T(i+1), D(i+1)-D(i)> where D(i) denotes the one-way-
   delay of the ith packet of a stream.

   This definition of the sample metric encompasses both the definition
   proposed in [9] and the one proposed in [10].

3.6. Methodology

   Since packets can be lost or duplicated or can arrive in a different
   order than the order sent, the pairs of test packets should be marked
   with a sequence number.  For duplicated packets only the first
   received copy should be considered.

   Otherwise, the methodology is the same as for the singleton
   measurement, with the exception that the singleton measurement is
   repeated a number of times.

3.7. Errors and uncertainties

   The same considerations apply that have been made about the singleton
   metric.  Additional error can be introduced by the pseudo-random
   Poisson process as discussed in [2].  Further considerations will be
   given in section 5.

4. 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
   statistics are assumed to be computed from an ipdv sample of
   reasonable size.

   The purpose is not to define every possible statistic for ipdv, but
   ones which have been proposed or used.

4.1. Lost Packets and ipdv statistics

   The treatment of lost packets as having "infinite" or "undefined"
   delay complicates the derivation of statistics for ipdv.
   Specifically, when packets in the measurement sequence are lost,
   simple statistics such as sample mean cannot be computed.  One
   possible approach to handling this problem is to reduce the event
   space by conditioning.  That is, we consider conditional statistics;
   namely we estimate the mean ipdv (or other derivative statistic)
   conditioned on the event that selected packet pairs arrive at the
   destination (within the given timeout).  While this itself is not
   without problems (what happens, for example, when every other packet
   is lost), it offers a way to make some (valid) statements about ipdv,
   at the same time avoiding events with undefined outcomes.

   In practical terms, what this means is throwing out the samples where
   one or both of the selected packets has an undefined delay.  The
   sample space is reduced (conditioned) and we can compute the usual
   statistics, understanding that formally they are conditional.

4.2. 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.

   There are basically two ways to represent the distribution of values
   of an ipdv sample: an empirical pdf and an empirical cdf.  The
   empirical pdf is most often represented as a histogram where the
   range of values of an ipdv sample is divided into bins of a given
   length and each bin contains the proportion of values falling between
   the two limits of the bin.  (Sometimes instead the number of values
   falling between the two limits is used).  The empirical cdf is simply
   the proportion of ipdv sample values less than a given value, for a
   sequence of values selected from the range of ipdv values.

4.3. Type-P-One-way-ipdv-percentile

   Given a Type-P One-Way-ipdv sample and a given percent X between 0%
   and 100%.  The Xth percentile of all ipdv values is in the sample.
   Therefore, then 50th percentile is the median.

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

   Given a Type-P-One-way-ipdv sample and a given value Y, the percent
   of ipdv sample values less than or equal to Y.

4.5. Type-P-One-way-ipdv-jitter

   Although the use of the term "jitter" is deprecated, we use it here
   following the authors in [8].  In that document, the selection
   function specifies that consecutive packets of the Type-P stream are
   to be selected for the packet pairs used in ipdv computation.  They
   then take the absolute value of the ipdv values in the sample.  The
   authors in [8] use the resulting sample to compare the behavior of
   two different scheduling algorithms.

   An alternate, but related, way of computing an estimate of jitter is
   given in RFC 1889 [11].  The selection function there is implicitly
   consecutive packet pairs, and the "jitter estimate" is computed by
   taking the absolute values of the ipdv sequence (as defined in this
   document) and applying an exponential filter with parameter 1/16 to
   generate the estimate (i.e., j_new = 15/16* j_old + 1/16*j_new).

4.6. Type-P-One-way-peak-to-peak-ipdv

   In this case, the selection function used in collecting the Type-P-
   One-Way-ipdv sample specifies that the first packet of each pair to
   be the packet with the maximum Type-P-One-Way-Delay in each
   subinterval and the second packet of each pair to be the packet with

   the minimum Type-P-One-Way-Delay in each sub-interval.  The resulting
   sequence of values is the peak-to-peak delay variation in each
   subinterval of the measurement interval.

5. Discussion of clock synchronization

   This section gives some considerations about the need for having
   synchronized clocks at the source and destination, although in the
   case of unsynchronized clocks, data from the measurements themselves
   can be used to correct error.  These considerations are given as a
   basis for discussion and they require further investigation.

5.1. Effects of synchronization errors

   Clock errors can be generated by two processes: the relative drift
   and the relative skew of two given clocks.  We should note that drift
   is physically limited and so the total relative skew of two clocks
   can vary between an upper and a lower bound.

   Suppose then that we have a measurement between two systems such that
   the clocks in the source and destination systems have at time 0 a
   relative skew of s(0) and after a measurement interval T have skew
   s(T).  We assume that the two clocks have an initial offset of O
   (that is letter O).

   Now suppose that the packets travel from source to destination in
   constant time, in which case the ipdv is zero and the difference in
   the time stamps of the two clocks is actually just the relative
   offset of the clocks.  Suppose further that at the beginning of the
   measurement interval the ipdv value is calculated from a packet pair
   and at the end of the measurement interval another ipdv value is
   calculated from another packet pair.  Assume that the time interval
   covered by the first measurement is t1 and that the time interval
   covered by the second measurement is t2.  Then

   ipdv1 = s(0)*t1 + t1*(s(T)-s(0))/T

   ipdv2 = s(T)*t2 + t2*(s(T)-s(0))/T

   assuming that the change in skew is linear in time.  In most
   practical cases, it is claimed that the drift will be close to zero
   in which case the second (correction) term in the above equations

   Note that in the above discussion, other errors, including the
   differences between host time and wire time, and externally-caused
   clock discontinuities (e.g., clock corrections) were ignored.  Under
   these assumptions the maximum clock errors will be due to the maximum
   relative skew acting on the largest interval between packets.

5.2. Estimating the skew of unsynchronized clocks

   If the skew is linear (that is, if s(t) = S * t for constant S), the
   error in ipdv values will depend on the time between the packets used
   in calculating the value.  If ti is the time between the packet pair,
   then let Ti denote the sample mean time between packets and the
   average skew is s(Ti) = S * Ti.  In the event that the delays are
   constant, the skew parameter S can be estimated from the estimate Ti
   of the time between packets and the sample mean ipdv value.  Under
   these assumptions, the ipdv values can be corrected by subtracting
   the estimated S * ti.

   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.

6. Security Considerations

   The one-way-ipdv metric has the same security properties as the one-
   way-delay metric [2], and thus they inherit the security
   considerations of that document.  The reader should consult [2] for a
   more detailed treatment of security considerations.  Nevertheless,
   there are a few things to highlight.

6.1. Denial of service

   It is still possible that there could be an attempt at a denial of
   service attack by sending many measurement packets into the network.
   In general, legitimate measurements must have their parameters
   carefully selected in order to avoid interfering with normal traffic.

6.2. Privacy/Confidentiality

   The packets contain no user information, and so privacy of user data
   is not a concern.

6.3. Integrity

   There could also be attempts to disrupt measurements by diverting
   packets or corrupting them.  To ensure that test packets are valid
   and have not been altered during transit, packet authentication and
   integrity checks may be used.

7. Acknowledgments

   Thanks to Merike Kaeo, Al Morton and Henk Uiterwaal for catching
   mistakes and for clarifying re-wordings for this final document.

   A previous major revision of the document resulted from e-mail
   discussions with and suggestions from Mike Pierce, Ruediger Geib,
   Glenn Grotefeld, and Al Morton.  For previous revisions of this
   document, discussions with Ruediger Geib, Matt Zekauskas and Andy
   Scherer were very helpful.

8. References

8.1 Normative References

   [1]  Paxon, V., Almes, G., Mahdavi, J. and M. Mathis, "Framework for
        IP Performance Metrics", RFC 2330, February 1998.

   [2]  Almes, G. and S. Kalidindisu, "A One-Way-Delay Metric for IPPM",
        RFC 2679, September 1999.

   [3]  Bradner, S., "Key words for use in RFCs to indicate requirement
        levels", BCP 14, RFC 2119, March 1997.

8.2 Informational References

   [4]  ITU-T Recommendation Y.1540 (formerly numbered I.380) "Internet
        Protocol Data Communication Service - IP Packet Transfer and
        Availability Performance Parameters", February 1999.

   [5]  Demichelis, Carlo - "Packet Delay Variation Comparison between
        ITU-T and IETF Draft Definitions" November 2000 (in the IPPM
        mail archives).

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

   [7]  S. Keshav - "An Engineering Approach to Computer Networking",
        Addison-Wesley 1997, ISBN 0-201-63442-2.

   [8]  Jacobson, V., Nichols, K. and Poduri, K. "An Expedited
        Forwarding PHB", RFC 2598, June 1999.

   [9]  ITU-T Draft Recommendation Y.1541 - "Internet Protocol
        Communication Service - IP Performance and Availability
        Objectives and Allocations", April 2000.

   [10] Demichelis, Carlo - "Improvement of the Instantaneous Packet
        Delay Variation (IPDV) Concept and Applications", World
        Telecommunications Congress 2000, 7-12 May 2000.

   [11] Schulzrinne, H., Casner, S., Frederick, R. and V. Jacobson,
        "RTP: A transport protocol for real-time applications", RFC
        1889, January 1996.

9. Authors' Addresses

   Carlo Demichelis
   Telecomitalia Lab S.p.A
   Via G. Reiss Romoli 274
   10148 - TORINO

   Phone: +39 11 228 5057
   Fax:   +39 11 228 5069
   EMail: carlo.demichelis@tilab.com

   Philip Chimento
   Ericsson IPI
   7301 Calhoun Place
   Rockville, Maryland 20855

   Phone: +1-240-314-3597
   EMail: chimento@torrentnet.com

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