Network Working Group                                 C.Demichelis CSELT

Internet Draft                                                March 1998

expires 16 August 1998

           Instantaneous Packet Delay Variation Metric for IPPM


1. Status of this Memo

   This document is an Internet Draft.  Internet Drafts are working doc-

   uments  of the Internet Engineering Task Force (IETF), its areas, and

   its working groups.  Note that other groups may also distribute work-

   ing 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''.

   To learn the current status of any Internet Draft, please  check  the

   ``1id-abstracts.txt'' listing contained in the Internet Drafts shadow

   directories  on   (Africa),   (Europe),  (Pacific  Rim),  (US  East Coast), or (US West Coast).

   This memo provides information for the Internet community.  This memo

   does  not  specify an Internet standard of any kind.  Distribution of

   this memo is unlimited.

2. Abstract

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

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

   This memo is intended to have, as much as possible, the  structure of
   the ippm draft on one-way delay metric.

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3. Introduction

   This memo defines a metric for variation in delay of  packets that go

   from one host to another one through an IP path.  Since the metric is

   related to a variation,  different definitions are possible according

   to what the variation is measured against.

[Editor's Note: This memo refers to the Draft-ietf "One-way-delay metric

for IPPM" that supposes as known. For sake  of readability, some text is

directly taken from that Draft. Text taken without modification is mark-

ed with trailing "TTTTTTT" and ending "EEEEEEE". These marks will be re-

moved in next versions]

3.1. Definition

   The  Instantaneous Packet Delay Variation  of an  IP packet, inside a

   stream of packets, going from the measurement point MP1 to the measu-

   rement point MP2, is the difference of the One-Way Delay of that pac-

   ket and the One-Way Delay of preceding packet in the stream.

3.2. Motivation

   A number of services that can be supported by IP are sensitive to the

   regular delivery of packets and can be disturbed by instantaneous va-

   riations in delay, while they are not  disturbed  by slow variations,

   that can last a relatively long time. A specific metric for quick va-

   riations is therefore desirable.

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

   differences and variations of the clocks of the two hosts. This allow

   the use of the metric even if the two hosts that support the measure-

   ment points are not synchronized. The related precision is comparable

   with the one that can be achieved with synchronized clocks. This will

   be discussed below.

3.3. General Issues Regarding Time

   All what is contained in the paragraph 2.2. of the Draft ippm on one-

   way delay metric (2.2. General Issues Regarding Time) applies also in

   this case.

   In addition, it is here considered that  the relative skew of the two

   clocks can be decomposed into two parts:

   * A fixed one, called in this context "skew",  given, for example, by

     tolerances in physical dimension of crystals.

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   * A variable one, called in this context "drift", given, for example,

     by changes in temperature or other conditions of operation.

   Both of this components are part of the term "skew" as defined in the

   referenced Draft and in the Framework document.

4. Structure of this memo

   The metric will be defined  as applicable to a stream of packets that

   flow from a source host to a destination host (one-way ipdv). The ini

   -tial assumption is that source and destination hosts have synchroni-

   zed clocks.

   The definition of a singleton of one-way ipdv metric  is first consi-

   dered, and then a definition of samples for ipdv will be given.

   Then the case of application  to not synchronized hosts  will be dis-

   cussed, and the precision  will be compared with  the one of the pre-

   vious case.

   A bidirectional ipdv metric will be defined,  and the methodology for

   error corrections. This will not be a two-ways metric, but a "paired"

   one-way in opposite directions.    Some statistics  describing the IP

   path behavior will be proposed.

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

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

   One-way-delay, that is supposed to  be known.  This section makes use

   of those parts of the One-way-delay Draft that  directly apply to the

   One-way-ipdv metric, or makes direct references to that Draft.

5.1. Metric name


5.2. Metric parameters

   +   Scr, the IP address of a host

   +   Dst, the IP address of a host

   +   T1, a time

   +   T2, a time


   +   Path, the path from Src to Dst; in cases where there is only  one

       path from Src to Dst, this optional parameter can be omitted.

   {Comment:  the  presence  of  path is motivated by cases such as with

   Merit's NetNow setup, in which a Src on one NAP can reach  a  Dst  on

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   another NAP by either of several different backbone networks.  Gener-

   ally, this optional parameter is useful only when  several  different

   routes are possible from Src to Dst.  Using the loose source route IP

   option is avoided since it would often artificially worsen  the  per-

   formance  observed,  and  since  it might not be supported along some



5.2. Metric unit

   The value of a Type-P-One-way-ipdv is either a real number of seconds

   or an undefined number of seconds

5.3. Definition

   Type-P-One-way-ipdv is defined  for two consecutive  packets from Src

   to Dst, as the  difference between  the value of  the type-P-One-way-

   delay from Src to Dst at T2 [via path]  and the value of  the type-P-

   One-way-delay  from Src to Dst at T1 [via path].  T1 is the wire-time

   at which Scr sent the  first bit  of the first packet,  and T2 is the

   wire-time at which Src sent the first bit of the second packet.

   Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to

   Dst at T1, T2 [via path] is ddT"  means that Src sent two consecutive

   packets whose the first  at wire-time T1 (first bit),  and the second

   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 [via path] is unde-

   fined" 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.

5.4. Discussion

   Type-P-One-way-ipdv is a metric  that makes use of the  same measure-

   ment methods provided for delay metrics.

   The following practical issues have to be considered:

   +    Being a differential measurement, this  metric is less sensitive

                to clock synchronization problems. This issue will be more care-

                fully  examined  in section 6.  of this memo. It is  pointed out

                that, if the reciprocal clock conditions change in time, the ac-

                curacy of the measurement will depend on the time interval T2-T1

                and the amount of possible errors will be discussed below.

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   +    A  given  methodology  will  have  to  include  a way to  deter-

            mine whether a delay value is infinite or whether  it  is  mere-

                ly  very large  (and the packet is yet to arrive at Dst).

                As noted by Mahdavi and Paxson, simple upper bounds (such as the

                255 seconds   theoretical  upper  bound   on the lifetimes of IP

                packets [Postel: RFC 791]) could be used, but good  engineering,

                including  an  understanding  of  packet lifetimes, will be nee-

                ded 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 de-

        pend on such properties of the packet as protocol,(UDP  or  TCP)

                port number,  size,  and  arrangement for special  treatment (as

                with IP precedence or with RSVP).

   +    If the packet is duplicated along the path  (or  paths!) so that

        multiple non-corrupt copies arrive at the destination,  then the

        packet is  counted  as received, and the  first  copy  to arrive

                determines the packet's one-way delay.

   +    If  the packet is fragmented and if, for whatever  reason, reas-

        sembly does not occur, then the packet will be deemed lost.


5.5. 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,


   Generally, for a given Type-P, the methodology would proceed as  fol-



   +    The need of synchronized clocks  for Src and Dst will be discus-

        sed later.  Here  a methodology  is  supposed  that is bases  on

                synchronized clocks.


   +    At the  Src  host, select  Src and  Dst IP addresses, and form a

        test packet of Type-P with these addresses.  Any  'padding' por-

                tion  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.

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   +    Optionally, select a specific path  and arrange  for Src to send

        the packet  to  that path.     {Comment: This could be done, for

                example, by installing a temporary host-route  for  Dst in Src's

                routing table.}

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

   +    At  the Src host, place a  timestamp in the prepared Type-P pac-

        ket, and send it towards Dst [via path].

   +    If the packet arrives within a reasonable period of time, take a

        timestamp as soon as possible upon the receipt of the packet. By

                subtracting the two timestamps, an estimate of one-way delay can

                be computed.


        Record this first delay value.

   +    Repeat the procedure with the same parameters and record the se-

        cond delay value. By subtracting the second value from the first

                the ipdv value is obtained.

   +    If one or both packets fail to arrive within a reasonable period

        ot time, the ipdv is taken to be undefined.

5.6. Errors and Uncertainties

   In the singleton metric of ipdv,  factors that affect the measurement

   are the same that can affect the one-way delay measurement,  even if,

   in this case, the influence is different.


   The Framework document 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 are discussed in more detail below.


5.6.1. Errors/Uncertainties related to Clocks

   If, as a first approximation, the error that affects the first measu-

   rement of one-way delay were the same of the one affecting the second

   measurement, they will cancel each other when calculating ipdv.   The

   residual error related to clocks is the difference of the said errors

   that  are supposed to change  from  the time T1, at which   the first

   measurement is performed, to the time T2 at which the second measure-

   ment is performed. Synchronization, skew, accuracy and resolution are

   here considered with the following notes:

   +    Errors in synchronization  between source and destination clocks

        contribute to errors in both of the delay measurements  required

                for calculating ipdv.

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   +    If the  synchronization error is Tsync, and it is a linear func-

        tion of time, through the skew value, at time T1 the error  will

                be Tsync1 and at time T2 the error will be Tsync2. The ipdv mea-

                surement will be affected by  the error Tsync2-Tsync1, depending

                from skew and T2-T1.  To minimize  this error  it is possible to

                reduce the time interval T2-T1, but this could limit the genera-

                lity of the metric. Methods for  evaluating the  synchronization

                error will be discussed below, since they come from  a statistic

                of a significant sample.

   +    As far as accuracy and  resolution are concerned,  what is noted

        in the above referenced Draft on one-way delay at 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.

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

   The content of sec. 3.7.2 of the above referenced  Draft applies also

   in this case, with the following further consideration:

   The difference between Host-time and Wire-time can be in general  de-

   composed into two components,  whose one is constant and the other is

   variable aroud zero. Only the variable components will produce measu-

   rement errors, while the constant one will be cancelled while  calcu-

   lating ipdv.

6. Definitions for Samples of One-way ipdv

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

   some ways of building  a sample of such singletons are here described

   that have to be further anlyzed in order to find the best way of con-

   sidering all the related problems.  In the following, the two packets

   needed for a singleton measurement will be called a "pair".

6.1. A "discontinuous" definition

   A general definition can be the following:

        Given particular binding of the parameters  Src,  Dst, path, and

        Type-P, a sample  of values of  parameters T1 and T2 is defined.

                The means for defining the values of T1 is to select a beginning

                time  T0, a  final time  Tf, and  an  average  rate lambda, then

                define a pseudo-random Poisson  arrival  process of rate lambda,

                whose values fall between  T0 and  Tf. The time interval between

                successive  values of T1 will then average 1/lambda. Another si-

                milar, but independent, pseudo-random  Poisson  arrival  process

                based  on T0', Tf' and lambda', for each T1  value that has been

                obtained by the first process, is used  for obtaining the inter-

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                val T2-T1, that falls  between  T0' and  Tf'  with an average of


   This general  definition is likely go give problems, if no limits are

   considered for the values T0, Tf, T0', Tf'. For example, the emission

   time of the  first packet of a pair, could  fall  before the emission

   time of the second packet of the preceding pair.  Probably this could

   be acceptable (provided that there are means to recognize pairs -e.g.

   use of sequence numbers-), but the concept itself of ipdv would be,at

   least, slightly changed.  A way for avoiding problems  can be to give

   some rules  on the  values T0, Tf, lambda, T0', Tf', lambda', without

   changing  the meaning  of the metric.  For example it can be required

   that Tf'<T0 in order to assure that pairs of  packets consist  of two

   consecutive packets.

6.2. A "continuous" definition

   A continuous stream of test packets can be supposed, where the second

   packet of a pair is,  at the same time,  the first packet of the next

   pair. Therefore the preceding definition becomes:

   +    Given particular binding of the parameters  Src,  Dst, path, and

        Type-P, a sample  of values of  parameter T1 is defined.

                The means for defining the values of T1 is to select a beginning

                time  T0, a  final time  Tf, and  an  average  rate lambda, then

                define a pseudo-random Poisson  arrival  process of rate lambda,

                whose values fall between  T0 and  Tf. The time interval between

                successive  values of  T1 will then  average 1/lambda.  From the

                second value on, T1 value of the pair n coincides with T2 of the

                pair n-1, and the first packet of pair n  coincides with the se-

                cond packet of the pair n-1.

   For the moment, in the following, this second definition will be con-

   sidered. Further refinement is required and is for further discussion

6.3. Metric name


6.4. Parameters

   +    Src, the IP address of a host

   +    Dst, the IP address of a host

   +    Path, the path* from Src to Dst;   in cases where there  is only

        one path from Src to Dst, this optional parameter can be omitted

   +    T0, a time

   +    Tf, a time

   +    lambda, a rate in reciprocal seconds

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6.5. Metric Units:

   A sequence of triads whose elements are:

   +    T, a time

   +    Ti,  a time interval.

   +    dT a real number or an undefined number of seconds

6.6. Definition

   A pseudo-random  Poisson process is defined such that ir begins at or

   before T0, with average arrival rate lambda, and ends at or after Tf.

   Those time values Ti greater  than  or  equal to T0  and less than or

   equal to Tf are then selected. Starting from time T,  at each time Ti

   of this process a value of  Type-P-One-way-ipdv  is obtained, and the

   time T becomes T = T+Ti. The value of the sample is the sequence made

   up of the resulting <time, time interval, ipdv> triad.

6.7. Discussion


   Note  first  that, since a pseudo-random number sequence is employed,

   the sequence of times, and hence the value  of  the  sample,  is  not

   fully  specified.   Pseudo-random  number  generators of good quality

   will be needed to achieve the desired qualities.

   The sample is defined in terms of a Poisson process both to avoid the

   effects  of  self-synchronization  and  also capture a sample that is

   statistically as  unbiased  as  possible.   {Comment:  there  is,  of

   course,  no  claim  that real Internet traffic arrives according to a

   Poisson arrival process.}


6.8. Methodology

   Since packets can be lost or duplicated or  can arrive in a different

   order  with  respect  the one of emission, in order to  recognize the

   pairs of test packets, they should  be marked  with a Sequence Number

   or make  use of any other tool suitable to the scope.  For duplicated

   packets only the first received copy should be  considered. If a pac-

   ket is lost, two values of ipdv will be undefined, since each packet,

   in the supposed "continuous" definition, is common to two pairs.

   Steps for measurement can be the following:

   +    Starting from a given time T, Src generates a test packet as for

        a singleton metrics, adding also a Sequence Number, and  sorts a

                Ti interval to determine the time at wich the next packet has to

                be sent.

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   +    On reception of the packet, Dst verifies the Sequence Number SN,

        and records SN and Tx timestamp that are contained in the packet

                and the Rx timestamp.

   +    if the  packet is not the first received and the SN is  correct,

        ipdv is computed  and Ti is  recorded.  Then Dst  records SN, Tx

                and Rx timestamps as "old" values.

6.9. Errors and uncertainties

   The same considerations apply  that  have been made about the single-

   ton metric. An additional error can  be introduced by the pseudo-ran-

   dom Poisson process as focushed in the above referenced Draft.

   Further considerations will be made in section 7.

6.10 Some statistics for One-way-ipdv

   Some statistics are here considered, that can provide useful informa-

   tion in analyzing the behavior of the packets flowing from Src to Dst

   These statistics  are given having  in mind a  practical use of them.

   Other statistics can be defined if needed.

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

   Given  a Type-P-One-way-ipdv-Stream and a time threshold, that can be

   either positive or negative, the fraction of all the dT values in the

   Stream less  than or  equal to the threshold, if the threshold is po-

   sitive, or greater or equal to the threshold if the threshold is  ne-


   For many real-time  services  that require a  regular delivery of the

   packets, this statistics can give the amount of packets beyond accep-

   table limits.

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

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

   is   considered and  the Standard  Deviation can be  calculated as an

   indication of regularity of delivery. For  practical  purposes it can

   useful to define a total  standard deviation, computed over  the com-

   plete set of value, and a  standard deviation  computed over the sub-

   set of those values that do not exceede given  positive  and negative

   thresholds. This allows a more accurate description of the performan-

   ce experienced by packets.

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

   This statistic  should tend to a value of ZERO  for a  number of ipdv

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   values  that tend to infinite. The  behavior of  Type-P-One-way-ipdv-

   average is an issue for the next section 7.

7. Discussion on clock synchronization

   This section gives some considerations  about the need of having syn-

   chronized clocks at Src and  Dst. These considerations are given as a

   basis for discussion, they  require further  investigation.  We start

   from the analysis of the mean value of the ipdv  distribution related

   to a "continuous" sample.

7.1. Mean value of ipdv distribution.

   If D(i) is the delay of packet "i", and ipdv(i) is the i-th  value of

   ipdv in the distribution of a sample  of "n" values,  collected  with

   the described methodology, we can write:

   ipdv(1) = D1 - D0


   ipdv(i) = D(i) - D(i-1)


   ipdv(n) = D(n) - D(n-1)

   The mean value of ipdv distribution will result in

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

   If an actual  measurement is  performed, that lasts a  period of time

   long enough to contain a number "n" sufficiently large and, supposing

   synchronized clocks, such that the network conditions (traffic) allow

   to  find a D(n) not too  diferent from D(0), e.g. a time of 24 hours,

   E(ipdv) will tend to zero.

7.2. Effects of a varying traffic

   If the mean values of delay D are changing inside  a given  period of

   time, for example they are increasing due to an increment of traffic,

   we can consider, as a first approximation, the  ipdv values as decom-

   posed into two components, one being  instantaneous  and  another one

   as having a constant rate dD  and corresponding to the increment "per

   interval" of  the mean value of D. The mean value of the distribution

   will be  shifted of  the value dD  corresponding to the mean value of

   the interval between test packets. When the conditions will come back

   to the initial ones, the distribution will resume a mean value around

   zero.   At any  time the distribution  will  correctly  describe  the

   behavior of the packet flow.

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7.3. Effects of syncronization errors

   We refer here to  the two  components that can  generate this type of

   errors that are  the relative  "skew" and "drift" of the  Src and Dst

   clocks. It is first of all  noted that the variable component "drift"

   is physically  limited  and  its effects can be interpreted by saying

   that the total  skew of the two  clocks can  vary, ranging from a min

   to a max value in the time. This type of   variation takes place very

   slowly being most connected to variations in temperature.

   We suppose to perform a measurement between a Src and a Dst that have

   a reciprocal, initial skew of "ts1" and a reciprocal drift such that,

   after the time T the total skew is "ts2". It is not here a limitation

   to consider that at the beginning of time T the  two clocks  indicate

   the same time T0.   In order  to analyze the effects produced by this

   situation we  suppose that packets  are transferred, from Src to Dst,

   with a consatant delay D. In this conditions the measured ipdv should

   always be zero, and what is  actually  measured is  the error.

   An ipdv value is measured at the beginning of time T with two packets

   having an interval of Ti(1).Another ipdv value is measured at the end

   of T with two packets having a time interval Ti(2).

   On our  purposes other  errors (like wire-time vs host-time)  are not

   considered since they are not relevant in this analysis.

   It is then  possible to  calculate the values  of the Tx and Rx time-

   stamps  as they are seen by the two clocks, and the related values of

   the two ipdv values.

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

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

   The error is given by the amount of variation during the  time inter-

   val Ti(i) between  the  two  packets of  the pair, and a second orded

   term due to the variation of that variation in the same interval.

7.4. Related precision

   This means that:

   1) + If the skew is constant and is = ts all the  ipdv(i)  values are

      increased  by the quantity Ti(i)*ts with respect the actual value.

   2) + Considering the total skew as subdivided into a fixed part and a

      variable part (skew and drift),respectively, ts and + or - td, and

          a minimum time T in which the drift can go from -td to +td or vice

          -versa, each ipdv(i) value will be increased of the fixed quantity

          Ti(i)*ts plus or minus, as a maximum, the quantity 2*td*Ti(i)/T

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    3) + If the duration of the measurement  is such that it  is possible

      to consider that  the effect  of the items  at points 7.1 and 7.2,

          and the effect of the drift are negligeables (related average ten-

      ding to zero),  the mean value  of the ipdv distribution will have

          the value of the skew multiplied by the mean value of the emission


   4) + We observe that the displacemet due to the skew does not  change

      the shape of the distribution, and, for example the Standard Devi-

          ation remains the same. What introduces a distortion is the effect

          of the drift, even if the mean value of this effect is zero at the

          end of the measurement. This is, anyway, a "second order"  effect.

          If, for example, a drift of 30 parts per million (ppm) takes place

          along a time of 4  hours, and the used Ti(i) interval ranges  from

          200 ms to 1200 ms, with an average of 700 ms, the maximum error on

          ipdv(i) values will be in the order of:

          Ti(i)*td/(4*3600)= 2.25 E -9 seconds

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 fixed action of the skew has modified the measured mean value. It

   is therefore expected that on one  direction that value is  equal and

   opposite to the one measured in the other direction.

   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-ways  metric making use of packets  looped back at one

   end. This metric, that can be object of further study/Draft, would be

   able to measure also the Round Trip Delay and its variations.

9. References

   V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP Performance

   Metrics", Internet Draft <draft-ietf-ippm-framework-01.txt> Feb. 1998

   G.Almes, S.Kalidindi  -  "A One-way Delay Metric for IPPM",  Internet

   Draft <draft-ietf-ippm-delay-01.txt>  Nov. 1997

Demichelis                                                     [Page 13]

I-D                          Ipdv Metric                      March 1998

10. Author's Address

   Carlo Demichelis <>

   CSELT - Centro Studi E Laburatori Telecomunicazioni S.p.A

   Via G. Reiss Romoli 274

   10148 - TORINO


   Phone +39 11 228 5057

   Fax.  +39 11 228 5069

Demichelis                 expires 16 August 1998              [Page 14]