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Network Working Group                                          A.Morton
Internet Draft                                             L.Ciavattone
Document: <draft-ietf-ippm-reordering-02.txt>            G.Ramachandran
Category: Standards Track                                     AT&T Labs
                                                             S.Shalunov
                                                              Internet2
                                                               J.Perser
                                                                Spirent


                   Packet Reordering Metric for IPPM


Status of this Memo

   This document is an Internet-Draft and is in full conformance with
   all provisions of Section 10 of RFC2026 [1].

   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 made obsolete 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.


   Abstract

   This memo defines a simple metric to determine if a network has
   maintained packet order. It provides motivations for the new metric,
   suggests a metric definition, and discusses the issues associated
   with measurement. The memo includes sample metrics to quantify the
   extent of reordering in several useful dimensions. Some examples of
   evaluation using the various sample metrics are included.

1. Conventions used in this document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [2].
   Although 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 when an
   implementation could perturb the network.


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2. Introduction

   Ordered delivery is a property of successful packet transfer
   attempts, where the packet sequence ascends for each arriving packet
   and there are no backward steps.

   An explicit sequence number, such as an incrementing message number
   or the packet sending time carried in each packet, establishes the
   Source Sequence.

   The presence of reordering at the Destination is based on arrival
   order.

   This metric is consistent with RFC 2330 [3], and classifies arriving
   packets with sequence numbers smaller than their predecessors as
   out-of-order, or reordered. For example, if arriving packets are
   numbered 1,2,4,5,3, then packet 3 is reordered. This is equivalent
   to Paxon's reordering definition in [4], where "late" packets were
   declared reordered. The alternative is to emphasize "premature"
   packets instead (4 and 5 in the example), but only the arrival of
   packet 3 distinguishes this circumstance from packet loss. Focusing
   attention on late packets allows us to maintain orthogonality with
   the packet loss metric. The metric's construction is very similar to
   the sequence space validation for received segments in RFC793 [5].
   Earlier work to define ordered delivery includes [6], [7], [8 and
   more ???.

2.1 Motivation

   A reordering metric is relevant for most applications, especially
   when assessing network support for Real-Time media streams. The
   extent of reordering may be sufficient to cause a received packet to
   be discarded by functions above the IP layer.

   Packet order is not expected to change during transfer, but several
   specific path characteristics can cause their order to change.

   Examples are:
   * When two paths, one with slightly longer transfer time, support a
     single packet stream or flow, then packets traversing the longer
     path may arrive out-of-order. Multiple paths may be used to
     achieve load balancing, or may arise from route instability.
   * To increase capacity, a network device designed with multiple
     processors serving a single port may reorder as a byproduct.
   * A layer 2 retransmission protocol that compensates for an error-
     prone link may cause packet reordering.
   * If for any reason, the packets in a buffer are not serviced in the
     order of their arrival, their order will change.
   * If packets in a flow are assigned to multiple buffers (following
     evaluation of traffic characteristics, for example), and the


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     buffers have different occupations and/or service rates, then
     order will likely change.

   The ability to restore order at the destination will likely have
   finite limits.  Practical hosts have receiver buffers with finite
   size in terms of packets, bytes, or time (such as de-jitter
   buffers). Once the initial determination of reordering is made, it
   is useful to quantify the extent of reordering, or lateness, in all
   meaningful dimensions.

2.2 Goals and Objectives

   The definitions below intend to satisfy the goals of:
     1. Determining whether or not packet order is maintained.
     2. Quantifying the extent (achieving this second goal requires
        assumptions of upper layer functions and capabilities to
        restore order, and therefore several solutions).

   Reordering Metrics MUST:

   +  be relevant to one or more known applications
   +  be computable "on the fly"
   +  work with Poisson and Periodic test streams
   +  work even if the stream has duplicate or lost packets

   Reordering Metrics SHOULD:

   +  have concatenating results for segments measured separately
   +  have simplicity for easy consumption and understanding
   +  have relevance to TCP performance
   +  have relevance to Real-time application performance


3. An Ordered Arrival Singleton Metric

   The IPPM framework RFC 2330 [3] gives the definitions of singletons,
   samples, and statistics.

   The evaluation of packet order requires several supporting concepts.
   The first is a sequence number applied to packets at the source to
   uniquely identify the order of packet transmission.  The sequence
   number may be established by a simple message number, a byte stream
   number, or it may be the actual time when each packet departs from
   the Src.

   The second supporting concept is a stored value which is the "next
   expected" packet number. Under normal conditions, the value of Next
   Expected (NextExp) is the sequence number of the previous packet
   (plus 1 for message numbering).  In byte stream numbering, NextExp
   is a value 1 byte greater than the last in-order packet sequence
   number + payload. If Src time is used as the sequence number,


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   NextExp is the Src time from the last in-order packet + 1 clock
   tick.

   Each packet within a packet stream can be evaluated for its order
   singleton metric.

3.1 Metric Name:

   Type-P-Non-Reversing-Order

3.2 Metric Parameters:

   +  Src, the IP address of a host

   +  Dst, the IP address of a host

   +  SrcTime, the time of packet emission from the Src (or wire time)

   +  s, the packet sequence number applied at the Src, in units of
     messages.

   +  SrcByte, the packet sequence number applied at the Src, in units
      of payload bytes.

   +  NextExp, the Next Expected Sequence number at the Dst, in units
      of messages, time, or bytes.

   +  PayloadSize, the number of bytes contained in the information
      field and referred to when the SrcByte sequence is based on byte
      transfer.

3.3 Definition:

   In-order packets have sequence numbers (or Src times) greater than
   or equal to the value of Next Expected. Each new in-order packet
   will increase the Next Expected (typically by 1 for message
   numbering, or the payload size plus 1 for byte numbering).  The Next
   Expected value cannot decrease, thereby specifying non-reversing
   order as the basis to identify reordered packets.

   A reordered packet outcome occurs when a single IP packet at the Dst
   Measurement Point results in the following:
   The packet has a Src sequence number lower than the Next Expected
   (NextExp), and therefore the packet is reordered. The Next Expected
   value does not change on the arrival of this packet.

   This definition can also be specified in pseudo-code.
   On successful arrival of a packet with sequence number s:
        if s >= NextExp, /* s is in-order */
                then
                NextExp = s + PayloadSize + 1;
        else            /* when s < NextExp */

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                designate packet s as reordered;

   The sequence number s may be replaced by SrcTime or SrcByte. When
   using s (message-based sequence numbering) or Src time,
   PayloadSize=0.

3.4 Discussion

   Any arriving packet bearing a sequence number from the sequence that
   establishes the Next Expected value can be evaluated to determine if
   it is in-order, or reordered, based on a previous packet's arrival.
   In the case where Next Expected is Undefined (because the arriving
   packet is the first successful transfer), the packet is designated
   in-order.

   If duplicate packets (multiple non-corrupt copies) arrive at the
   destination, they MUST be noted and only the first to arrive is
   considered for further analysis (additional copies would be declared
   reordered according to the definition above). This requirement has
   the same storage requirements as earlier IPPM metrics, and follows
   the precedent of RFC 2679.

   Packets with s > NextExp are a special case of in-order delivery.
   This condition indicates a sequence discontinuity, either because of
   packet loss or reordering. Reordered packets must arrive for the
   sequence discontinuity to be part of a reordering event (defined in
   the next section). Discontinuities are easiest to detect with
   message numbering or payload byte numbering where payload size is
   constant, and may be possible with Periodic Streams and Src Time
   numbering.

4. Sample Metrics

   In this section, we define metrics applicable to a sample of packets
   from a single Src sequence number system. We begin with a simple
   ratio metric indicating the reordered portion of the sample. When
   this ratio is zero, no further reordering metrics are needed for
   that sample.

   When reordering occurs, it is highly desirable to assert the degree
   to which a packet is out-of-order, or reordered with respect to a
   sample of packets. This section defines several metrics that
   quantify the extent of reordering in various units of measure. Each
   "extent" metric highlights a relevant application.

4.1 Reordered Packet Ratio

4.1.1 Metric Name:

   Type-P-Reordered-Ratio-Poisson/Periodic-Stream

4.1.2 Metric Parameters:

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   The parameter set includes Type-P-Non-Reversing-Order singleton
   parameters, the parameters unique to Poisson or Periodic Streams,
   plus the following:

   + T0, a start time

   + Tf, an end time

   + dT, a waiting time for each packet to arrive

4.1.3 Definition:

   For the packets arriving successfully between T0 and Tf+dT, the
   ratio of reordered packets in the sample is

   (Total of Reordered packets) / (Total packets received)

   This fraction may be expressed as a percentage (multiply by 100%).
   Note that in the case of duplicate packets, only the first copy is
   used.

4.2 Reordering Events and their Extent
   Note: This section is expected to evolve further as we integrate the
   various metrics of reordering extent (n-reordering and other
   distance metrics used in earlier drafts). The co-authors are not yet
   satisfied with all aspects of this section, and comments are
   welcome.

4.2.1 Metric Name:

   Type-P-packet-n-Reordering-Event-Poisson/Periodic-Stream

4.2.2 Parameter Notation:

   Let n be a positive integer (a parameter).  Let k be a positive
   integer (sample size, the number of packets sent).  Let l be a non-
   negative integer representing the number of packets that were
   received out of the k packets sent.  (Note that there is no
   relationship between k and l: on one hand, losses can make l less
   than k; on the other hand, duplicates can make l greater than k.)
   Assign each sent packet a sequence number, 1 to k.

   Let s[1], s[2], ..., s[l] be the original sequence numbers of the
   received packets, in the order of arrival.

4.2.3 Definition 1:

   Received packet number i (n < i <= l), with Src sequence number s
   (s[i]), is reordered to the extent n if and only if for all j such
   that i-n <= j < i we have s[j] > s[i].


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   Claim: If by this definition, the extent of a packet's reordering is
   n and 0 < n' < n, then the packet is also reordered to the n'
   extent.

   Note: This definition is illustrated by C code in Appendix A.  It
   determines the presence of n-reordering events for a particular
   value of n (when actually writing applications that would report the
   metric, one would probably report it for several values of n, such
   as 1, 2, 3, 4 -- and maybe a few more consecutive values).
   Also, this definition does not assign an extent to all reordered
   packets as defined by the singleton metric, in particular when
   blocks of successive packets are reordered. (In the arrival sequence
   s={1,2,3,7,8,9,4,5,6}, packets 4, 5, and 6 are reordered, but only 4
   is assigned a reordering extent according to Definition 1.) All
   reordered packets are assigned a reordering extent by associating
   them with a specific reordering event, as defined below.

4.2.4 Definition 2:
   Note: The intent of this section is to assign a reordering extent to
   all reordered packets, not just the ones identified by Definition 1.
   This definition is new in this version and needs more study.

   A packet s[i] that satisfies Definition 1 constitutes an n-
   Reordering Event with the following characteristics:

   1. The maximum value of n that satisfies Definition 1 is the extent
   of the reordering event. (Extent n is assigned to all packets
   associated with this event in part 3 below.)

   2. The in-order packet arrival defined as beginning the event
   (having indicated a sequence discontinuity) is s[j] for j that
   satisfies the following:

           min{j|1<=j<i} for which s[j]> s[i]

   Typically i-n=j. This aspect of a reordering event is used later in
   the definition of the gap between successive events.

   3. The arrival of any subsequent reordered packets with sequence
   number s meeting the following condition:

                      s[j] > s[*] > s[i], or
   (s at beginning of event) > s > (lowest s in the reordering event)

   are associated with the reordering event first identified by s[i],
   the sequence discontinuity that starts the event at s[j], and are
   assigned the same reordering extent, n.
   >>>
   Comment on Part 3.:  For some arrival orders, the assignment of the
   same extent to all packets in a reordering event will tend to
   underestimate their true extent.  However, a pure position/distance
   metric (as appeared in earlier versions of this draft) would tend to

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   overestimate the receiver storage needed. We need to weigh the value
   of adding more complexity in this definition against the accuracy it
   would provide.
   A more accurate and complex procedure would be to count any
   additional in-order packets that arrive after a reordering event is
   identified, and add them to the extent of the first reordered packet
   (up to some counter limit of interest) for packets in the interval
   s[i] < s[*] < s[j].
   Those who desire "on-the-fly" calculation must assess whether such a
   procedure is feasible.

   Discussion:

   A receiver must perform some amount of "work" to restore order to
   all packets that are part of an n-reordering event. The extent n
   gives the number of packets that must be held in the receiver's
   buffer while waiting for the reordered packets in the sequence. As
   reordered packets arrive, the amount of work stays the same if they
   are all part of the same reordering event. If new reordering events
   occur, the work in terms of buffer size can increase.  See Examples
   section (specific example to be provided).

   Knowledge of the reordering extent n is particularly useful for
   determining the portion of reordered packets that can or cannot be
   restored to order in a typical TCP receiver buffer based on their
   arrival order alone (and without the aid of retransmission).

   Important special cases are n=1 and n=3:

   - For n=1, absence of 1-reordering events means the sequence numbers
   that the receiver sees are monotonically increasing with respect to
   the previous arriving packet.

   - For n=3, a NewReno TCP sender would retransmit 1 packet in
   response to a 3-reordering event and therefore consider this a loss
   event for the purposes of congestion control (the sender will half
   its congestion window). Detecting 3-reordering events is useful for
   determining the portion of reordered packets that are in fact as
   good as lost.

   We note that the definition of n-reordering events cannot predict
   the exact number of packets unnecessarily retransmitted by a TCP
   sender under some circumstances, such as closely-spaced reordering
   events. The definition is less complicated than a TCP implementation
   where both time and position influence the sender's behavior.

   A sample's reordering extents may be expressed as a histogram, to
   easily summarize the frequency of various extents.


4.3 Reordering Offset


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   Any packet whose sequence number causes the Next Expected value to
   increment by more than the usual increment indicates a discontinuity
   in the sequence. From this point on, any reordered packets can be
   assigned Offset values indicating the storage in bytes and lateness
   in terms of buffer time that a receiver must possess to accommodate
   them. The various Offset metrics are calculated only on reordered
   packets, as identified by the ordered arrival singleton in section
   3.

4.3.1 Metric Name: Type-P-packet-Late-Time-Poisson/Periodic-Stream

   Metric Parameters: In addition to the parameters defined for Type-P-
   Non-Reversing-Order, we specify:

   +  DstTime, the time that each packet in the stream arrives at Dst

   Definition: Lateness in time is calculated using Dst times. When
   packet i is reordered, and part of a reordering event with n extent
   (assuming j=i-n):

   LateTime(i) = DstTime(i)-DstTime(i-n)

   Alternatively, using similar notation to that of section 4.2, an
   equivalent definition is:
   LateTime(i) = DstTime[i]-DstTime[j], for min{j|1<=j<i} that
   satisfies s[j]>s[i], or SrcTime[j]>SrcTime[i].

4.3.2 Metric Name: Type-P-packet-Byte-Offset-Poisson/Periodic-Stream

   Metric Parameters: We use the same parameters defined above.

   Definition: Byte stream offset is the sum of the payload sizes of
   all intervening packets between the reordered packet and the
   discontinuity (including the packet at the discontinuity).

   For reordered packet i
   ByteOffset(i) = Sum[in-order packets to start of the reordering
   event]
                 = Sum[PayloadSize(packet at i-1),
                        PayloadSize(packet at i-2), ...
                        PayloadSize(packet at i-n)]

   Alternatively, if all payload sizes are equal:
   ByteOffset(i) = n * PayloadSize  where n is the reordering extent.
   >>>>Comment: Previous comments on the accuracy of extent n apply
   here as well.

4.3.3 Discussion

   The Offset metrics can predict whether reordered packets will be
   useful in a general receiver buffer system with finite limits.  The
   limit may be the number of bytes or packets the buffer can store, or

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   the time of storage prior to a cyclic play-out instant (as with de-
   jitter buffers).

   Note that the One-way IPDV [9] gives the delay variation for a
   packet w.r.t. the preceding packet in the source sequence. Lateness
   and IPDV give an indication of whether a buffer at Dst has
   sufficient storage to accommodate the network's behavior and restore
   order. When an earlier packet in the Src sequence is lost, IPDV will
   necessarily be undefined for adjacent packets, and Late Time may
   provide the only way to evaluate the usefulness of a packet.

   In the case of de-jitter buffers, there are circumstances where the
   receiver employs loss concealment at the intended play-out time of a
   late packet. However, if this packet arrives out of order, the Late
   Time determines whether the packet is still useful. IPDV no longer
   applies, because the receiver establishes a new play-out schedule
   with additional buffer delay to accommodate similar events in the
   future - this requires very minimal processing.

   When packets in the stream have variable sizes, it may be most
   useful to characterize Offset in terms of the payload size(s) of
   stored packets (using byte stream numbering).


4.4 Gaps between multiple Reordering Events


4.4.1 Metric Name:

   Type-P-packet-Reordering-Event-Gap-Poisson/Periodic-Stream

4.4.2 Parameters:

   No new parameters.

4.4.3 Definition:

   A reordering event with extent n is detected according to section
   4.2 with the arrival of packet s[i].  The next reordering event with
   extent n' is detected at packet i', and there are no reordering
   events between i and i'.

   The Reordering Event Gap is the difference between the arrival
   positions the packets, as shown below (assuming j=i-n):

   Gap(i) = (i'-n') - (i-n)

   Gaps may also be expressed in time:

   GapTime(i) = DstTime(i'-n') - DstTime(i-n)



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   The Gaps between a sample's reordering events may be expressed as a
   histogram, to easily summarize the frequency of various extents.

4.4.4 Discussion

   When separate reordering events can be distinguished, then an event
   count may also be reported (along with the event description, such
   as the number of reordered packets and their extents or offsets).
   The distribution of various metrics may also be reported and
   summarized by the mode, average, range, histogram, etc.

   The Gap metric may help to correlate the frequency of reordering
   events with their cause.

5. Measurement Issues

   The results of tests will be dependent on the time interval between
   measurement packets (both at the Src, and during transport where
   spacing may change).  Clearly, packets launched infrequently (e.g.,
   1 per 10 seconds) are unlikely to be reordered.

   Test streams may prefer to use a periodic sending interval so that a
   known temporal bias is maintained, also bringing simplified results
   analysis (as described in RFC 3432 [10]). In this case, the periodic
   sending interval should be chosen to reproduce the closest Src
   packet spacing expected.
   <<<<Ed.Note:  Need to expand this further, it is a very important
   consideration.

   The Non-reversing order criterion and all metrics described above
   remain valid and useful when a stream of packets experiences packet
   loss, or both loss and reordering. In other words, losses alone do
   not cause subsequent packets to be declared reordered.

   Assuming that the necessary sequence information (sequence number
   and/or source time stamp) is included in the packet payload
   (possibly in application headers such as RTP), packet sequence may
   be evaluated in a passive measurement arrangement.  Also, it is
   possible to evaluate sequence at a single point along a path, since
   the usual need for synchronized Src and Dst Clocks may be relaxed to
   some extent.

   When the Src sequence is based on byte stream, or payload numbering,
   care must be taken to avoid declaring retransmitted packets
   reordered. The additional reference of Src Time is one way to avoid
   this ambiguity.

   Since this metric definition may use sequence numbers with finite
   range, it is possible that the sequence numbers could reach end-of-
   range and roll over to zero during a measurement.  By definition,
   the Next Expected value cannot decrease, and all packets received
   after a roll-over would be declared reordered.  Sequence number

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   roll-over can be avoided by using combinations of counter size and
   test duration where roll-over is impossible (and sequence is reset
   to zero at the start). Also, message-based numbering results in
   slower sequence consumption.  There may still be cases where
   methodological mitigation of this problem is desirable (e.g., long-
   term testing).  The elements of mitigation are:

   1. There must be a test to detect if a roll-over has occurred.  It
   would be nearly impossible for the sequence numbers of successive
   packets to jump by more than half the total range, so these large
   discontinuities are designated as roll-over.

   2. All sequence numbers used in computations are represented in a
   sufficiently large precision.  The numbers have a correction applied
   (equivalent to adding a significant digit) whenever roll-over is
   detected.

   3. Reordered packets coincident with sequence numbers reaching end-
   of-range must also be detected for proper application of correction
   factor.

6. Examples of Arrival Order Evaluation

   This section provides some examples to illustrate how the non-
   reversing order criterion works, and the value of viewing reordering
   in both the dimensions of time and position.

   Table 1 gives a simple case of reordering, where one packet (the
   packet with s=4) arrives out-of-order. Packets are arranged
   according to their arrival, and message numbering is used.

   Table 1 Example with Packet 4 Reordered,
   Sending order(SrcNum@Src): 1,2,3,4,5,6,7,8,9,10
   s            Src     Dst                     Dst     Byte    Late
   @Dst NextExp Time    Time    Delay   IPDV    Order   Offset  Time
    1     1       0      68      68              1
    2     2      20      88      68       0      2
    3     3      40     108      68       0      3
    5     4      80     148      68     -82      4
    6     6     100     168      68       0      5
    7     7     120     188      68       0      6
    8     8     140     208      68       0      7
    4     9      60     210     150      82      8      400     62
    9     9     160     228      68       0      9
   10    10     180     248      68       0     10


   Each column gives the following information:

   S        Packet sequence number at the Source.
   NextExp  The value of NextExp when the packet arrived(before
   update).

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   SrcTime  Packet time stamp at the Source, ms.
   DstTime  Packet time stamp at the Destination, ms.
   Delay    1-way delay of the packet, ms.
   IPDV     IP Packet Delay Variation, ms
            IPDV = Delay(SrcNum)-Delay(SrcNum-1)
   DstOrder Order in which the packet arrived at the Destination.
   Byte Offset  The Byte Offset of a reordered packet, in bytes.
   LateTime The lateness of a reordered packet, in ms.

   We can see that when packet 4 arrives, NextExp=9, and it is declared
   reordered. We compute the extent of the reordering event as follows:

   Using the notation <s[1], ..., s[i], ..., s[l]>, the received
   packets are represented as:


                            \/
   s = 1, 2, 3, 5, 6, 7, 8, 4, 9, 10
   i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
                            /\
   when n=1, 7<=J<8, and 8 > 4, so the reordering extent is 1 or more.
   when n=2, 6<=J<8, and 7 > 4, so the reordering extent is 2 or more.
   when n=3, 5<=J<8, and 6 > 4, so the reordering extent is 3 or more.
   when n=4, 4<=J<8, and 5 > 4, so the reordering extent is 4 or more.
   when n=5, 3<=J<8, but 3 < 4, and 4 is the maximum extent.

   Further, we can compute the Late Time (210-148=62ms using DstTime)
   compared to packet 5's arrival.  If Dst has a de-jitter buffer that
   holds more than 4 packets, or at least 62 ms storage, packet 4 may
   be useful. Note that 1-way delay and IPDV also indicate unusual
   behavior for packet 4.

   If all packets contained 100 byte payloads, then Byte Offset is
   equal to 400 bytes.


   Table 2 Example with Packets 5 and 6 Reordered,
   Sending order(s @Src): 1,2,3,4,5,6,7,8,9,10
   s            Src     Dst                     Dst     Byte    Late
   @Dst NextExp Time    Time    Delay   IPDV    Order   Offset  Time
    1     1       0      68      68              1
    2     2      20      88      68       0      2
    3     3      40     108      68       0      3
    4     4      60     128      68       0      4
    7     5     120     188      68     -22      5
    5     8      80     189     109      41      6      100     1
    6     8     100     190      90     -19      7      100     2
    8     8     140     208      68       0      8
    9     9     160     228      68       0      9
   10    10     180     248      68       0     10



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   Table 2 shows a case where packets 5 and 6 arrive just behind packet
   7, so both 5 and 6 are reordered. The Late times (189-188=1, 190-
   188=2) are small.

   Using the notation <s[1], ..., s[i], ..., s[l]>, the received
   packets are represented as:

                      \/ \/
   s = 1, 2, 3, 4, 7, 5, 6, 8, 9, 10
   i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
                      /\ /\

   Considering packet 5[6] first:
   when n=1, 5<=J<6, and 7 > 5, so the reordering extent is 1 or more.
   when n=2, 4<=J<6, but 4 < 5, and 1 is the maximum extent.


   Considering packet 6[7] next:
   when n=1, 6<=J<7, and 5 < 6, so the packet at i=7 does not have its
   own reordering extent, and must be part of the same reordering event
   as packet 5[6].  Using the test of Section 4.2.4, Definition 2, we
   find that the condition is met for packet 6[7]:

                        s[i] <  s   < s[i-n]
                        5[6] < 6[7] < 7[5]

   A hypothetical sender/receiver pair may retransmit packet 5[8]
   unnecessarily, since it is reordered with extent n=1(in agreement
   with the singleton metric). However, the receiver cannot advance
   packet 7[5] to the higher layers until after packet 6[7] arrives.
   Therefore, the singleton metric correctly determined that 6[7] is
   reordered, and both packets are part of a 1-reordering event.

   Table 3 Example with Packets 4, 5, and 6 reordered
   Sending order(s @Src): 1,2,3,4,5,6,7,8,9,10,11
   s            Src     Dst                     Dst     Byte    Late
   @Dst NextExp Time    Time    Delay   IPDV    Order   Offset  Time
    1    1        0      68      68              1
    2    2       20      88      68       0      2
    3    3       40     108      68       0      3
    7    4      120     188      68     -68      4
    8    8      140     208      68       0      5
    9    9      160     228      68       0      6
   10   10      180     248      68       0      7
    4   11       60     250     190     122      8      400     62
    5   11       80     252     172     -18      9      400     64
    6   11      100     256     156     -16     10      400     68
   11   11      200     268      68       0     11

   The case in Table 3 is where three packets in sequence have long
   transit times (packets with s = 4,5,and 6). Delay, Late time, and
   Byte Offset capture this very well, and indicate variation in

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   reordering extent, while IPDV indicates that the spacing between
   packets 4,5,and 6 has changed.

   The histogram of Reordering extents (n) would be:

   Bin         1  2  3  4  5  6  7
   Frequency   0  0  0  3  0  0  0

   Using the notation <s[1], ..., s[i], ..., s[l]>, the received
   packets are represented as:

   s = 1, 2, 3, 7, 8, 9,10, 4, 5, 6, 11
   i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11


   Considering packet 4[8] first:
   when n=1, 7<=J<8, and 10> 4, so the reordering extent is 1 or more.
   when n=2, 6<=J<8, and 9 > 4, so the reordering extent is 2 or more.
   when n=3, 5<=J<8, and 8 > 4, so the reordering extent is 3 or more.
   when n=4, 4<=J<8, and 7 > 4, so the reordering extent is 4 or more.
   when n=5, 3<=J<8, but 3 < 4, and 4 is the maximum extent.

   Considering packet 5[9] next:
   when n=1, 8<=J<9, but 4 < 5, so the packet at i=9 does not have its
   own reordering extent, and must be part of the same reordering event
   as packet 4[8].  Using the test of Section 4.2.4, Definition 2, we
   find that the condition is met for both packets 5[9] and 6[10]:

                        s[i] <  s   < s[i-n]
                        4[8] < 5[9] < 7[4]
                        4[8] < 6[10]< 7[4]


   This example shows again that the n-reordering event definition
   identifies a single event (s=4) with a sufficient degree of
   reordering to result in one unnecessary packet retransmission by the
   New Reno TCP sender. Also, the reordered arrival of packets s=5 and
   s=6 will allow the receiver process to pass packets 7 through 10 up
   the protocol stack (the singleton metric indicates 5 and 6 are
   reordered, and they are all part of one reordering event).

7. Security Considerations

7.1 Denial of Service Attacks

   This metric requires a stream of packets sent from one host (Src) to
   another host (Dst) through intervening networks.  This method could
   be abused for denial of service attacks directed at Dst and/or the
   intervening network(s).

   Administrators of Src, Dst, and the intervening network(s) should
   establish bilateral or multi-lateral agreements regarding the

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   timing, size, and frequency of collection of sample metrics.  Use of
   this method in excess of the terms agreed between the participants
   may be cause for immediate rejection or discard of packets or other
   escalation procedures defined between the affected parties.

7.2 User data confidentiality

   Active use of this method generates packets for a sample, rather
   than taking samples based on user data, and does not threaten user
   data confidentiality. Passive measurement must restrict attention to
   the headers of interest. Since user payloads may be temporarily
   stored for length analysis, suitable precautions MUST be taken to
   keep this information safe and confidential.

7.3 Interference with the metric

   It may be possible to identify that a certain packet or stream of
   packets is part of a sample. With that knowledge at Dst and/or the
   intervening networks, it is possible to change the processing of the
   packets (e.g. increasing or decreasing delay) that may distort the
   measured performance.  It may also be possible to generate
   additional packets that appear to be part of the sample metric.
   These additional packets are likely to perturb the results of the
   sample measurement.

   To discourage the kind of interference mentioned above, packet
   interference checks, such as cryptographic hash, may be used.

8. IANA Considerations

   Since this metric does not define a protocol or well-known values,
   there are no IANA considerations in this memo.

9. References

   1  Bradner, S., "The Internet Standards Process -- Revision 3", BCP
      9, RFC 2026, October 1996.

   2  Bradner, S.,  "Key words for use in RFCs to Indicate Requirement
      Levels", RFC 2119, March 1997.

   3  Paxson, V., Almes, G., Mahdavi, J., and Mathis, M., "Framework
      for IP Performance Metrics", RFC 2330, May 1998.

   4  V.Paxson, "Measurements and Analysis of End-to-End Internet
      Dynamics," Ph.D. dissertation, U.C. Berkeley, 1997,
      ftp://ftp.ee.lbl.gov/papers/vp-thesis/dis.ps.gz.

   5  Postel, J., "Transmission Control Protocol", STD 7, RFC 793,
      September 1981.
      Obtain via: http://www.rfc-editor.org/rfc/rfc793.txt


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   6  L.Ciavattone and A.Morton, "Out-of-Sequence Packet Parameter
      Definition (for Y.1540)", Contribution number T1A1.3/2000-047,
      October 30, 2000. ftp://ftp.t1.org/pub/t1a1/2000-A13/0a130470.doc

   7  J.C.R.Bennett, C.Partridge, and N.Shectman, "Packet Reordering is
      Not Pathological Network Behavior," IEEE/ACM Transactions on
      Neteworking, vol.7, no.6, pp.789-798, December 1999.

   8  D.Loguinov and H.Radha, "Measurement Study of Low-bitrate
      Internet Video Streaming"' Proceedings of the ACM SIGCOMM
      Internet Measurement Workshop 2001 November 1-2, 2001, San
      Francisco, USA.

   9  Demichelis, C., and Chimento, P., "IP Packet Delay Variation
      Metric for IP Performance Metrics (IPPM)", RFC 3393, November
      2002.

   10 Raisanen, V., Grotefeld, G., and Morton, A., "Network performance
      measurement with periodic streams", RFC 3432, November 2002.

11. Acknowledgments

   The authors would like to acknowledge many helpful discussions with
   Matt Mathis and Jon Bennett.  We gratefully acknowledge the
   foundation laid by the authors of the IP performance Framework [3].

12. Appendix A (informative)

   Two example c-code implementations of reordering definitions follow:

   Example 1  n-reordering ============================================

   #include <stdio.h>

   #define MAX_N   100

   #define min(a, b) ((a) < (b)? (a): (b))
   #define loop(x) ((x) >= 0? x: x + MAX_N)

   /*
    * Read new sequence number and return it.  Return a sentinel value
   of EOF
    * (at least once) when there are no more sequence numbers.  In this
   example,
    * the sequence numbers come from stdin; in an actual test, they
   would come
    * from the network.
    */
   int
   read_sequence_number()

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   {
           int             res, rc;
           rc = scanf("%d\n", &res);
           if (rc == 1) return res;
           else return EOF;
   }


   int
   main()
   {
           int             m[MAX_N];       /* We have m[j-1] == number
   of
                                            * j-reordered packets. */
           int             ring[MAX_N];    /* Last sequence numbers
   seen. */
           int             r = 0;          /* Ring pointer for next
   write. */
           int             l = 0;          /* Number of sequence
   numbers read. */
           int             s;              /* Last sequence number
   read. */
           int             j;


           for (j = 0; j < MAX_N; j++) m[j] = 0;
           for (; (s = read_sequence_number()) != EOF; l++, r = (r+1) %
   MAX_N) {
                   for (j=0; j<min(l, MAX_N) && s<ring[loop(r-j-1)];
   j++) m[j]++;
                   ring[r] = s;
           }
           for (j = 0; j < MAX_N && m[j]; j++)
                   printf("%d-reordering = %f%%\n", j+1, 100.0*m[j]/(l-
   j-1));
           if (j == 0) printf("no reordering\n");
           else if (j < MAX_N) printf("no %d-reordering\n", j+1);
           else printf("only up to %d-reordering is handled\n", MAX_N);
           exit(0);
   }

   Example 2   singleton and n-reordering comparison =================

   #include <stdio.h>

   #define MAX_N   100
   #define min(a, b) ((a) < (b)? (a): (b))
   #define loop(x) ((x) >= 0? x: x + MAX_N)

   /* Global counters */
   int receive_packets=0;       /* number of recieved */
   int reorder_packets=0;       /* number of reordered packets */

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   /* function to test if current packet has been reordered
    * returns 0 = not reordered
    *         1 = reordered
    */
   int testorder1(int seqnum)   // Al
   {
        static int NextExp = 1;
        int iReturn = 0;

        if (seqnum >= NextExp) {
                NextExp = seqnum+1;
        } else {
                iReturn = 1;
        }
        return iReturn;
   }

   int testorder2(int seqnum)   // Stanislav
   {
           static int      ring[MAX_N];    /* Last sequence numbers
   seen. */
           static int   r = 0;          /* Ring pointer for next write.
   */
           int             l = 0;          /* Number of sequence
   numbers read. */
           int             j;
        int     iReturn = 0;

           l++;
        r = (r+1) % MAX_N;
           for (j=0; j<min(l, MAX_N) && seqnum<ring[loop(r-j-1)]; j++)
                    iReturn = 1;
           ring[r] = seqnum;
      return iReturn;
   }

   int main(int argc, char *argv[])
   {
           int i, packet;
        for (i=1; i< argc; i++) {
                receive_packets++;
                packet = atoi(argv[i]);
                reorder_packets += testorder2(packet);
        }
        printf("Received packets = %d, Reordered packets = %d\n",
   receive_packets, reorder_packets);
        exit(0);
   }

13. Author's Addresses


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Packet Reordering Metric for IPPM                             Mar 2003

   Al Morton
   AT&T Labs
   Room D3 - 3C06
   200 Laurel Ave. South
   Middletown, NJ 07748 USA
   Phone  +1 732 420 1571  Fax +1 732 368 1192
   <acmorton@att.com>

   Len Ciavattone
   AT&T Labs
   Room C4 - 2B29
   200 Laurel Ave. South
   Middletown, NJ 07748 USA
   Phone  +1 732 420 1239
   <lencia@att.com>

   Gomathi Ramachandran
   AT&T Labs
   Room C4 - 3D22
   200 Laurel Ave. South
   Middletown, NJ 07748 USA
   Phone  +1 732 420 2353
   <gomathi@att.com>

   Stanislav Shalunov
   Internet2
   200 Business Park Drive, Suite 307
   Armonk, NY 10504
   Phone: + 1 914 765 1182
   EMail: <shalunov@internet2.edu>

   Jerry Perser
   Spirent Communications
   26750 Agoura Road
   Calabasas, CA 91302  USA
   Phone: + 1 818 676 2300
   EMail: <jerry.perser@spirentcom.com>


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