Network Working Group                                      C. Demichelis
INTERNET-DRAFT                                                     CSELT
Expiration Date: December 2000 August 2001                                 P. Chimento
                                                                    CTIT
                                                              July  2000

          Instantaneous
                                                            Ericsson IPI
                                                         February   2001

               IP Packet Delay Variation Metric for IPPM
                     <draft-ietf-ippm-ipdv-05.txt>
                     <draft-ietf-ippm-ipdv-06.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 the One-Way-
   Delay of consecutive selected packets. This particular definition
   of variation difference in delay is called "Instantaneous "IP
   Packet Delay Variation (ipdv)". variation."

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

3. Introduction

   This memo is based on "A One-way-Delay One-Way-Delay metric for IPPM", RFC 2679     |
   [2].

   Part of the text in this memo is taken directly from that document.

   This memo defines a metric for variation in delay of packets that     >
   flow from one host to another one through an IP path. This quantity   >
   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. 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 first 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,      |
   rather than meaning is frequently used by computer scientists and
   frequently (but not always) refers to variation in delay.

   In this document we will avoid the first. For term "jitter" whenever possible
   and stick to delay variation which is more information see the section on the    |
   relationship with other standards. precise.

3.1. Definition

   A definition of the Instantaneous IP 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 IP Packet Delay Variation (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 packets within a
   stream of packets:

   +  The Instantaneous Packet Delay Variation of an IP packet, inside packets is defined for a
      stream selected pair of packets, packets in the
   stream going from the measurement point MP1 to the measurement point MP2, MP2 is
   the difference between the one-way-delay of the One-way-Delay first of
      that packet the selected
   packets and the One-way-Delay one-way-delay of the preceding packet in second of the
      stream. selected packets.

3.2. Motivation

   A number

   One important use of services that can be supported by IP are sensitive to delay variation is the sizing of playout buffers
   for applications requiring the regular delivery of packets and can be disturbed by instantaneous
   variations (for
   example, voice or video playout). What is normally important in delay, while they are not disturbed by slow variations,
   that can last this
   case is the maximum delay variation, which is used to size playout
   buffers for such applications [6]. Other uses of a relatively long time. A specific delay variation
   metric are, for quick
   variations is therefore desirable. Metrics that can be derived from example, to determine the analysis dynamics of statistics of ipdv queues within a
   network (or router) where the changes in delay variation can also be used, for example, for |
   buffer dimensioning.  The scope of this metric is
   linked to provide a way
   for measurement of changes in the quality delivered by queue length process at a path. given link or a
   combination of links.

   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.

   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. 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. [7],[8],[9]). The
   idea here is to parameterize the definition, rather than write a
   different draft 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 draft hold, no matter
   which parameters are chosen.

3.3. General Issues Regarding Time

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

   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      >
      times                                                              >

   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
   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 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 A singleton definition of this memo

   The a One-way ipdv 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 purpose of a the singleton of one-way ipdv metric is first considered, and then to define what a definition single
   instance of samples for an ipdv
   will be given.

   Then the case of application to non-synchronized hosts will be
   discussed, and the precision will measurement is. Note that it can only be compared
   statistically significant in combination with the one of
   synchronized clocks.

   A bidirectional ipdv metric will be defined, as well as the           >
   methodology for error corrections. This will other instances. It is
   not intended to be meaningful as a two-way metric, >
   but a "paired" one-way singleton, in opposite directions.

5. A singleton definition the sense of a One-way ipdv metric                       | being
   able to draw inferences from it.

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

5.1.

4.1. Metric name

   Type-P-One-way-ipdv

5.2.

4.2. 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 time

   +  L, a parameter packet length in bits. The packets of a Type P packet stream
      from which the measurement though this singleton ipdv metric is already implicit,
      since 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 T1 which mark that beginning and T2 exactly define ending of the time conditions interval
      in which the measurement takes place.

   Note that the packet length stream from which the singleton measurement is an implicit parameter
      taken occurs.

   +  P, the specification of both the      |
   Type-P-One-way-delay metric packet type, over and above 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. source
      and destination addresses

4.3. 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.

4.4. Definition

   Type-P-One-way-ipdv is defined for two (consecutive) packets from Src
   to Dst, as the difference between

   We are given a Type P packet stream and I1 and I2 such that the first
   Type P packet to pass measurement point MP2 after I1 is given index 0
   and the last Type P packet to pass measurement point MP2 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- type-P-One-way- delay from Src to Dst at T2 and the
   value of the Type-P-One-way-Delay 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 therefore
   ideally derived from the One-way-Delay 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 type-P-one-way-ipdv from Src to
   Dst at T1, T2 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 dT2+T2 (last bit of the second
   packet), and that dT2-dT1=ddT.

   "The Type-P-one-way-ipdv 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.

5.5.

4.5. Discussion

   Type-P-One-way-ipdv is a

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

   +  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 7 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 T2-T1 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:
      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.} 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. One-Way-Delay.

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

5.6.

   It is assumed that the Type-P packet stream is generated according to
   the Poisson sampling methodology described in [1].

4.6. 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).

   The measurement methodology described in this section asssumes 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:

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

   +  After time I1, start.  At the Src host, select Src and Dst IP
      addresses, and form two test packets of Type-P with these addresses. Any 'padding' portion 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
      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.

   +  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 One-Way-Delay can
      be computed.

   +  Record  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, place packets continue to be generated according to the
      given methodology. The Src host places a timestamp in the second Type-P
      packet, and send it towards Dst.

   +  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 One-Way-Delay can
      be computed.

   +  By  If the packet meets the criterion for the second packet for the
      second packet, then by subtracting the second value of One-way-Delay One-Way-
      Delay from the first 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.

5.7.

4.7. Errors and Uncertainties

   In the singleton metric of ipdv, factors that affect the measurement
   are the same that can affect as those affecting the One-way-Delay 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 following
   paragraphs.

5.7.1.

4.7.1. Errors/Uncertainties related to Clocks

   If, as a first approximation, the error that affects the first
   measurement of One-way-Delay One-Way-Delay were the same of 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 the time T1, at which the first
   measurement is performed, to the time T2 at which the second
   measure ment 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 if 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 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 3.3) 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.

5.7.2.

4.7.2. 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.

6.

5. 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".   |

   A stream of test packets is generated  where

5.1. Metric name

   Type-P-One-way-ipdv-stream

5.2. Parameters

   +  Src, the second packet IP address of a   |
   pair is, at the same time, the first packet of the next pair.         | host

   +  Given particular binding of the parameters Src, Dst and Type-P, a  |
      sample of values of parameter T1 is defined.  To define  Dst, the values | IP address of T1, select a beginning time host

   +  T0, a final time

   +  Tf, and an average |
      rate lambda, then define a pseudo-random Poisson arrival process   |
      of rate time

   +  lambda, whose values fall between T0 and Tf. a rate in reciprocal seconds

   +  L, a packet length in bits. The time      |
      interval between successive values packets of T1 will then average         |
      1/lambda. From a Type P packet stream
      from which the second value on, T1 value sample ipdv metric is taken MUST all be of the pair n         |
      coincides with T2 same
      length.

   +  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 pair n-1, beginning and the first packet
      ending of pair n  |
      coincides with the second intervals in which the packet of stream from which the pair n-1.                  |

6.1. Metric name

   Type-P-One-way-ipdv-stream

6.2. Parameters

   +  Src,
      measurement is taken occurs. I(0) >= T0 and assuming that n is the IP address of a host
      largest index, I(n) <= Tf.

   +  Dst,  P, the IP address specification of a host

   +  T0, a time

   +  Tf, a time

   +  lambda, a rate in reciprocal seconds

6.3. the packet type, over and above the source
      and destination addresses

5.3. Metric Units:

   A sequence of triads triples whose elements are:

   +  T, a time

   +  Ti, a time interval.  T1, T2,times

   +  dT a real number or an undefined number of seconds

6.4.

5.4. 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 selected for packet generation times.

   Each packet falling within one of
   times T(i), T(i+1) 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 this process a value packet pair needed to compute
   ipdv. The sub-intervals can be defined such that a sufficient number
   of Type-P-One-way-ipdv is singleton samples for valid statistical estimates can be obtained.

   The value triples defined above consist of the sample is the sequence made up transmission times 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 packets of pair i each singleton included in the sample,
   and the first time of pair i+1. The result is shown ipdv in figure 3

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

                                  Figure 3

6.5. seconds.

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

6.6.
   process.

   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 specifiec 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)-D(i+1)> 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 [9].

5.6. 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

   Otherwise, the methodology is common to two pairs.

   Steps for measurement can be the following:

   +  Starting from a given time T, Src generates a test packet same 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 singleton
   measurement, with the first packet after a
      sequence number error, Dst records sequence number and
      transmission timestamp exception 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 singleton measurement is correct, by using the "old values" and the newly
      received ones,
   repeated a value number of ipdv is computed. Then Dst records the
      new sequence number, transmit and receive timestamps as "old
      values".

6.7. times.

5.7. 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 7.                                                   |

6.8.

6. 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.

6.1. 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.

6.2. 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.

6.9. Some statistics for One-way-ipdv

   Some statistics

   There are suggested which can provide useful information in |
   analyzing basically two ways to represent the behavior distribution of the packets flowing from Src to Dst. values
   of an ipdv sample: an empirical pdf and an empirical cdf. The    |
   focus
   empirical pdf is on most often represented as a histogram where the instantaneous behavior
   range of the connection.  Other      |
   statistics can be defined if needed.

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

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

   Given a Type-P-One-way-ipdv-Stream Type-P One-Way-ipdv sample and a time threshold, that can be
   either positive or negative, percent X between 0% and
   100%, the fraction Xth percentile of all the ipdv values in the Stream sample. The 50th
   percentile is the median.

6.4. 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.

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

   Although the threshold, if use of the threshold term "jitter" is
   positive, or greater or equal to the threshold if deprecated, we use it here
   following the threshold is
   negative.

   For many real-time services authors in [7]. In that require a regular delivery of the
   packets, these statistics provide document, the number of selection
   function specifies that consecutive packets exceeding a
   given limit.

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

   This metric is of the same as Type-P stream are
   to be selected for the definition of "jitter" packet pairs used in  [7], and is |
   simply ipdv computation. They
   then take the absolute value of the Type-P-One-way-ipdv.                 |

6.9.3.  The treatment of lost packets as having "infinite" or            >
   "undefined" delay complicates ipdv values in the derivation of statistics for ipdv.  >
   Specifically, when packets sample. The
   authors in [7] use the measurement sequence are lost,      >
   simple statistics such as resulting sample mean cannot be computed. One         >
   possible approach to handling this problem is to reduce compare the event     >
   space by conditioning. That is, we consider conditional statistics;   >
   namely we estimate behavior of
   two different scheduling algorithms.

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

   In this case, the mean ipdv (or jitter or other derivative       >
   statistic) conditioned on selection function used in collecting the event Type-P-
   One-Way-ipdv sample specifies that successive packet pairs      >
   arrive at the destination (within the given timeout). While this      >
   itself is not without problems (what happens, for example, when every >
   other first packet is lost), it offers a way of each pair to make some (valid)           >
   statements about ipdv, at
   be the same time avoiding events packet with          >
   undefined outcomes. We suggest that this the maximum Type-P-One-Way-Delay in each sub-
   interval and the second packet of each pair to be a topic for further       >
   study. 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 sub-
   interval of the measurement interval.

7. Discussion of clock synchronization

   This section gives some considerations about the need of having
   synchronized clocks at the source and destination. These
   considerations are given as a basis for discussion and they require
   further investigation.                                                >

7.1. 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 timestamps 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 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 is 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 disappears.  >

   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.         >

7.2. 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 ith and       >
   (i+1)st packet, packet pair,
   then let Ti denote the sample mean time between       > packets and the
   average skew is s(Ti) = S * Ti. Note that E[Ti]       >
   should equal 1/lambda.  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.          >

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 in one direction that value is equal
   and opposite to the one measured in the other direction.

   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 relative skew.

   At this point it is possible to evaluate the relative 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, 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  |
   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  |
   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   | are
   constant, the reference packet for skew parameter S can be estimated from the 2-point measurement estimate Ti
   of the time between packets and also as the      |
   start packet of sample mean ipdv value. Under
   these assumptions, the ipdv measurement. Denote this packet values can be corrected by p(0).     |
   Then given ipdv measurements for a series of packets, subtracting
   the 2-point     |
   delay variation for packet i is p(0) + estimated S * ti.

   We observe that the sum from k=1 displacement due to i of       |
   ipdv(k).                                                              |

   Similarly, given a sequence of 2-point delay variation measurements   |
   we can derive the ipdv measurement as follows: Denote skew does not change the 2-point     |
   delay variation measurement for packet i as v(i). Then
   shape of the ipdv value | distribution, and, for example 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 Standard Deviation
   remains the same. What introduces a number of disadvantages distortion is the effect of the        |
   2-point packet delay variation approach. Further,
   drift, also when the ipdv approach   |
   described here mean value of this effect is general enough to provide the same information as   | zero at the 2-point packet delay variation measurements. Because of this, and |
   because end of
   the (possibly) looser clock synchronization requirements   | measurement. The value of ipdv, we recommend this distortion is limited to the one-way-ipdv approach for
   effect of the delay         | total skew variation measurement.                                                |

10. on the emission interval.

8. 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.

9. Acknowledgements                                                     |

   Thanks to Matt Zekauskas

   This major revision of the draft resulted from Advanced e-mail discussions
   with and Ruediger Geib suggestions from         |
   Deutsche Telekom for discussions relating to the contents of this     |
   revised draft. Mike Pierce, Ruediger Geib, Glenn
   Grotefeld, and Al Morton.  For previous revisions of this additional revision, document,
   discussions by e-mail   > with Ruediger Geib, Matt Zekaukas and Andy Scherrer Scherer were
   very helpful.

12.

10. 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 One-Way-Delay Metric for IPPM", RFC
        2679, September 1999

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

   [4]    Demichelis, Carlo - "Packet Delay Variation Comparison between
        ITU-T and IETF Draft Definitions" March 1999 November 2000 (in the IPPM
        mail archives)

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

   [6]    e-mail exchanges with Ruediger Geib    S. Keshav - "An Engineering Approach to Computer Networking",
        Addison-Wesley 1997, ISBN 0-201-63442-2

   [7]    V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding
        PHB", RFC 2598, June 1999

13.

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

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

11. 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 <chimento@torrentnet.com>
   Ericsson IPI
   7301 Calhoun Place
   Rockville, Maryland
   20855
   USA
   Phone +31 53 489 4331
   FAX   +31 53 489 4524 +1-240-314-3597

   Expiration date: December 2000 August 2001