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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

Demichelis & Chimento Standards Track [Page 1] RFC 3393 IP Packet Delay Variation November 2002

       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.

Demichelis & Chimento Standards Track [Page 2] RFC 3393 IP Packet Delay Variation November 2002

 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

Demichelis & Chimento Standards Track [Page 3] RFC 3393 IP Packet Delay Variation November 2002

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.

Demichelis & Chimento Standards Track [Page 4] RFC 3393 IP Packet Delay Variation November 2002

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.

Demichelis & Chimento Standards Track [Page 5] RFC 3393 IP Packet Delay Variation November 2002

 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

Demichelis & Chimento Standards Track [Page 6] RFC 3393 IP Packet Delay Variation November 2002

 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

Demichelis & Chimento Standards Track [Page 7] RFC 3393 IP Packet Delay Variation November 2002

 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.

Demichelis & Chimento Standards Track [Page 8] RFC 3393 IP Packet Delay Variation November 2002

 +  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.

Demichelis & Chimento Standards Track [Page 9] RFC 3393 IP Packet Delay Variation November 2002

 +  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

Demichelis & Chimento Standards Track [Page 10] RFC 3393 IP Packet Delay Variation November 2002

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.

Demichelis & Chimento Standards Track [Page 11] RFC 3393 IP Packet Delay Variation November 2002

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

Demichelis & Chimento Standards Track [Page 12] RFC 3393 IP Packet Delay Variation November 2002

 +  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

Demichelis & Chimento Standards Track [Page 13] RFC 3393 IP Packet Delay Variation November 2002

 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.

Demichelis & Chimento Standards Track [Page 14] RFC 3393 IP Packet Delay Variation November 2002

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

Demichelis & Chimento Standards Track [Page 15] RFC 3393 IP Packet Delay Variation November 2002

 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

Demichelis & Chimento Standards Track [Page 16] RFC 3393 IP Packet Delay Variation November 2002

 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

Demichelis & Chimento Standards Track [Page 17] RFC 3393 IP Packet Delay Variation November 2002

 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.

Demichelis & Chimento Standards Track [Page 18] RFC 3393 IP Packet Delay Variation November 2002

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.

Demichelis & Chimento Standards Track [Page 19] RFC 3393 IP Packet Delay Variation November 2002

 [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
 Philip Chimento
 Ericsson IPI
 7301 Calhoun Place
 Rockville, Maryland 20855
 Phone: +1-240-314-3597

Demichelis & Chimento Standards Track [Page 20] RFC 3393 IP Packet Delay Variation November 2002

10. Full Copyright Statement

 Copyright (C) The Internet Society (2002).  All Rights Reserved.
 This document and translations of it may be copied and furnished to
 others, and derivative works that comment on or otherwise explain it
 or assist in its implementation may be prepared, copied, published
 and distributed, in whole or in part, without restriction of any
 kind, provided that the above copyright notice and this paragraph are
 included on all such copies and derivative works.  However, this
 document itself may not be modified in any way, such as by removing
 the copyright notice or references to the Internet Society or other
 Internet organizations, except as needed for the purpose of
 developing Internet standards in which case the procedures for
 copyrights defined in the Internet Standards process must be
 followed, or as required to translate it into languages other than
 The limited permissions granted above are perpetual and will not be
 revoked by the Internet Society or its successors or assigns.
 This document and the information contained herein is provided on an


 Funding for the RFC Editor function is currently provided by the
 Internet Society.

Demichelis & Chimento Standards Track [Page 21]

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