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Updated by: 6248 PROPOSED STANDARD

Network Working Group                                          A. Morton
Request for Comments: 4737                                 L. Ciavattone
Category: Standards Track                                G. Ramachandran
                                                               AT&T Labs
                                                             S. Shalunov
                                                               Internet2
                                                               J. Perser
                                                                Veriwave
                                                           November 2006


                       Packet Reordering Metrics

Status of This Memo

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

Copyright Notice

   Copyright (C) The IETF Trust (2006).

Abstract

   This memo defines metrics to evaluate whether a network has
   maintained packet order on a packet-by-packet basis.  It provides
   motivations for the new metrics and discusses the measurement issues,
   including the context information required for all metrics.  The memo
   first defines a reordered singleton, and then uses it as the basis
   for sample metrics to quantify the extent of reordering in several
   useful dimensions for network characterization or receiver design.
   Additional metrics quantify the frequency of reordering and the
   distance between separate occurrences.  We then define a metric
   oriented toward assessment of reordering effects on TCP.  Several
   examples of evaluation using the various sample metrics are included.
   An appendix gives extended definitions for evaluating order with
   packet fragmentation.











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Table of Contents

   1. Introduction ....................................................4
      1.1. Motivation .................................................4
      1.2. Goals and Objectives .......................................5
      1.3. Required Context for All Reordering Metrics ................6
   2. Conventions Used in this Document ...............................7
   3. A Reordered Packet Singleton Metric .............................7
      3.1. Metric Name ................................................8
      3.2. Metric Parameters ..........................................8
      3.3. Definition .................................................8
      3.4. Sequence Discontinuity Definition ..........................9
      3.5. Evaluation of Reordering in Dimensions of Time or Bytes ...10
      3.6. Discussion ................................................10
   4. Sample Metrics .................................................11
      4.1. Reordered Packet Ratio ....................................11
           4.1.1. Metric Name ........................................11
           4.1.2. Metric Parameters ..................................11
           4.1.3. Definition .........................................12
           4.1.4. Discussion .........................................12
      4.2. Reordering Extent .........................................12
           4.2.1. Metric Name ........................................12
           4.2.2. Notation and Metric Parameters .....................12
           4.2.3. Definition .........................................13
           4.2.4. Discussion .........................................13
      4.3. Reordering Late Time Offset ...............................14
           4.3.1. Metric Name ........................................14
           4.3.2. Metric Parameters ..................................14
           4.3.3. Definition .........................................15
           4.3.4. Discussion .........................................15
      4.4. Reordering Byte Offset ....................................16
           4.4.1. Metric Name ........................................16
           4.4.2. Metric Parameters ..................................16
           4.4.3. Definition .........................................16
           4.4.4. Discussion .........................................17
      4.5. Gaps between Multiple Reordering Discontinuities ..........17
           4.5.1. Metric Names .......................................17
           4.5.2. Parameters .........................................17
           4.5.3. Definition of Reordering Discontinuity .............17
           4.5.4. Definition of Reordering Gap .......................18
           4.5.5. Discussion .........................................18
      4.6. Reordering-Free Runs ......................................19
           4.6.1. Metric Names .......................................19
           4.6.2. Parameters .........................................19
           4.6.3. Definition .........................................19
           4.6.4. Discussion and Illustration ........................20





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   5. Metrics Focused on Receiver Assessment: A TCP-Relevant Metric ..21
      5.1. Metric Name ...............................................21
      5.2. Parameter Notation ........................................21
      5.3. Definitions ...............................................22
      5.4. Discussion ................................................22
   6. Measurement and Implementation Issues ..........................23
      6.1. Passive Measurement Considerations ........................26
   7. Examples of Arrival Order Evaluation ...........................26
      7.1. Example with a Single Packet Reordered ....................26
      7.2. Example with Two Packets Reordered ........................28
      7.3. Example with Three Packets Reordered ......................30
      7.4. Example with Multiple Packet Reordering Discontinuities ...31
   8. Security Considerations ........................................32
      8.1. Denial-of-Service Attacks .................................32
      8.2. User Data Confidentiality .................................32
      8.3. Interference with the Metric ..............................32
   9. IANA Considerations ............................................33
   10. Normative References ..........................................35
   11. Informative References ........................................36
   12. Acknowledgements ..............................................37
   Appendix A. Example Implementations in C (Informative) ............38
   Appendix B. Fragment Order Evaluation (Informative) ...............41
      B.1. Metric Name ...............................................41
      B.2. Additional Metric Parameters ..............................41
      B.3. Definition ................................................42
      B.4. Discussion: Notes on Sample Metrics When Evaluating
           Fragments .................................................43
   Appendix C. Disclaimer and License ................................43























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1.  Introduction

   Ordered arrival is a property found in packets that transit their
   path, where the packet sequence number increases with each new
   arrival and there are no backward steps.  The Internet Protocol
   [RFC791] [RFC2460] has no mechanisms to ensure either packet delivery
   or sequencing, and higher-layer protocols (above IP) should be
   prepared to deal with both loss and reordering.  This memo defines
   reordering metrics.

   A unique sequence identifier carried in each packet, such as an
   incrementing consecutive integer message number, establishes the
   source sequence.

   The detection of reordering at the destination is based on packet
   arrival order in comparison with a non-reversing reference value
   [Cia03].

   This metric is consistent with [RFC2330] and classifies arriving
   packets with sequence numbers smaller than their predecessors as
   out-of-order or reordered.  For example, if sequentially numbered
   packets arrive 1,2,4,5,3, then packet 3 is reordered.  This is
   equivalent to Paxon's reordering definition in [Pax98], 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].  Earlier work to define ordered delivery
   includes [Cia00], [Ben99], [Lou01], [Bel02], [Jai02], and [Cia03].

1.1.  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 may change during transfer, and several specific path
   characteristics can make reordering more likely.

   Examples are:

   * When two (or more) paths with slightly differing transfer times
     support a single packet stream or flow, packets traversing the
     longer path(s) may arrive out-of-order.  Multiple paths may be used
     to achieve load balancing or may arise from route instability.



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   * To increase capacity, a network device designed with multiple
     processors serving a single port (or parallel links) 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
     buffers have different occupation levels and/or service rates, then
     order will likely change.

   When one or more of the above path characteristics are present
   continuously, reordering may be present on a steady-state basis.  The
   steady-state reordering condition typically causes an appreciable
   fraction of packets to be reordered.  This form of reordering is most
   easily detected by minimizing the spacing between test packets.
   Transient reordering may occur in response to network instability;
   temporary routing loops can cause periods of extreme reordering.
   This condition is characterized by long, in-order streams with
   occasional instances of reordering, sometimes with extreme
   correlation.  However, we do not expect packet delivery in a
   completely random order, where, for example, the last packet or the
   first packet in a sample is equally likely to arrive first at the
   destination.  Thus, we expect at least a minimal degree of order in
   the packet arrivals, as exhibited in real networks.

   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.

1.2.  Goals and Objectives

   The definitions below intend to satisfy the goals of:

      1. Determining whether or not packet reordering has occurred.

      2. Quantifying the degree of reordering.  (We define a number of
         metrics to meet this goal, because receiving procedures differ
         by protocol or application.  Since the effects of packet
         reordering vary with these procedures, a metric that quantifies
         a key aspect of one receiver's behavior could be irrelevant to



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         a different receiver.  If all the metrics defined below are
         reported, they give a wide-ranging view of reordering
         conditions.)

   Reordering Metrics MUST:

   +  have one or more applications, such as receiver design or network
      characterization, and a compelling relevance in the view of the
      interested community.

   +  be computable "on the fly".

   +  work even if the stream has duplicate or lost packets.

   It is desirable for Reordering Metrics to have one or more of the
   following attributes:

   +  ability to concatenate results for segments measured separately to
      estimate the reordering of an entire path

   +  simplicity for easy consumption and understanding

   +  relevance to TCP design

   +  relevance to real-time application performance

   The current set of metrics meets all the requirements above and
   provides all but the concatenation attribute (except in the case
   where measurements of path segments exhibit no reordering, and one
   may estimate that the complete path composed of these segments would
   also exhibit no reordering).  However, satisfying these goals
   restricts the set of metrics to those that provide some clear insight
   into network characterization or receiver design.  They are not
   likely to be exhaustive in their coverage of reordering effects on
   applications, and additional measurements may be possible.

1.3.  Required Context for All Reordering Metrics

   A critical aspect of all reordering metrics is their inseparable bond
   with the measurement conditions.  Packet reordering is not well
   defined unless the full measurement context is reported.  Therefore,
   all reordering metric definitions include the following parameters:

   1. The "Packet of Type-P" [RFC2330] identifiers for the packet
      stream, including the transport addresses for source and
      destination, and any other information that may result in
      different packet treatments.




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   2. The stream parameter set for the sending discipline, such as the
      parameters unique to periodic streams (as in [RFC3432]), TCP-like
      streams (as in [RFC3148]), or Poisson streams (as in [RFC2330]).
      The stream parameters include the packet size, specified either as
      a fixed value or as a pattern of sizes (as applicable).

   Whenever a metric is reported, it MUST include a description of these
   parameters to provide a context for the results.

2.  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 [RFC2119].  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.

   In this memo, the characters "<=" should be read as "less than or
   equal to" and ">=" as "greater than or equal to".

3.  A Reordered Packet Singleton Metric

   The IPPM framework [RFC2330] describes the notions of singletons,
   samples, and statistics.  For easy reference:

         By a 'singleton' metric, we refer to metrics that are, in a
         sense, atomic.  For example, a single instance of "bulk
         throughput capacity" from one host to another might be defined
         as a singleton metric, even though the instance involves
         measuring the timing of a number of Internet packets.

   The evaluation of packet order requires several supporting concepts.
   The first is an algorithm (function) that produces a series of
   strictly monotonically increasing identifiers applied to packets at
   the source to uniquely establish the order of packet transmission
   (where a function, g(x), is strictly monotonically increasing if for
   any x>y, g(x)>g(y) ).  The unique sequence identifier may simply be
   an incrementing consecutive integer message number, or a sequence
   number as used below.  The prospect of sequence number rollover is
   discussed in Section 6.

   The second supporting concept is a stored value that 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 general, the receiver reproduces the



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   sender's algorithm and the sequence of identifiers so that the "next
   expected" can be determined.)

   Each packet within a packet stream can be evaluated with this order
   singleton metric.

3.1.  Metric Name

   Type-P-Reordered

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 source (or wire
      time).

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

   +  NextExp, the next expected sequence number at the destination, in
      units of messages.  The stored value in NextExp is determined from
      a previously arriving packet.

   And optionally:

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

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

3.3.  Definition

   If a packet s (sent at time, SrcTime) is found to be reordered by
   comparison with the NextExp value, its Type-P-Reordered = TRUE;
   otherwise, Type-P-Reordered = FALSE, as defined below:

   The value of Type-P-Reordered is defined as TRUE if s < NextExp (the
   packet is reordered).  In this case, the NextExp value does not
   change.

   The value of Type-P-Reordered is defined as FALSE if s >= NextExp
   (the packet is in-order).  In this case, NextExp is set to s+1 for
   comparison with the next packet to arrive.



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   Since the NextExp value cannot decrease, it provides a non-reversing
   order criterion to identify reordered packets.

   This definition can also be specified in pseudo-code.

   On successful arrival of a packet with sequence number s:

        if s >= NextExp then /* s is in-order */
                NextExp = s + 1;
                Type-P-Reordered = False;
        else     /* when s < NextExp */
                Type-P-Reordered = True

3.4.  Sequence Discontinuity Definition

   Packets with s > NextExp are a special case of in-order delivery.
   This condition indicates a sequence discontinuity, because of either
   packet loss or reordering.  Reordered packets must arrive for the
   sequence discontinuity to be defined as a reordering discontinuity
   (see Section 4).

   We define two different states for in-order packets.

   When s = NextExp, the original sequence has been maintained, and
   there is no discontinuity present.

   When s > NextExp, some packets in the original sequence have not yet
   arrived, and there is a sequence discontinuity associated with packet
   s.  The size of the discontinuity is s - NextExp, equal to the number
   of packets presently missing, either reordered or lost.

   In pseudo-code:

   On successful arrival of a packet with sequence number s:

        if s >= NextExp, then /* s is in-order */
                if s > NextExp then
                          SequenceDiscontinuty = True;
                          SeqDiscontinutySize = s - NextExp;
                else
                          SequenceDiscontinuty = False;
                NextExp = s + 1;
                Type-P-Reordered = False;

        else /* when s < NextExp */
                Type-P-Reordered = True;
                SequenceDiscontinuty = False;




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   Whether any sequence discontinuities occur (and their size) is
   determined by the conditions causing loss and/or reordering along the
   measurement path.  Note that a packet could be reordered at one point
   and subsequently lost elsewhere on the path, but this cannot be known
   from observations at the destination.

3.5.  Evaluation of Reordering in Dimensions of Time or Bytes

   It is possible to use alternate dimensions of time or payload bytes
   to test for reordering in the definition of Section 3.3, as long as
   the SrcTimes and SrcBytes are unique and reliable.  Sequence
   Discontinuities are easily defined and detected with message
   numbering; however, this is not so simple in the dimensions of time
   or bytes.  This is a detractor for the alternate dimensions because
   the sequence discontinuity definition plays a key role in the sample
   metrics that follow.

   It is possible to detect sequence discontinuities with payload byte
   numbering, but only when the test device knows exactly what value to
   assign as NextExp in response to any packet arrival.  This is
   possible when the complete pattern of payload sizes is stored at the
   destination, or if the size pattern can be generated using a pseudo-
   random number generator and a shared seed.  If payload size is
   constant, byte numbering adds needless complexity over message
   numbering.

   It may be possible to detect sequence discontinuities with periodic
   streams and source time numbering, but there are practical pitfalls
   with sending exactly on-schedule and with clock reliability.

   The dimensions of time and bytes remain an important basis for
   characterizing the extent of reordering, as described in Sections 4.3
   and 4.4.

3.6.  Discussion

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

   This metric assumes reassembly of packet fragments before evaluation.
   In principle, it is possible to use the Type-P-Reordered metric to
   evaluate reordering among packet fragments, but each fragment must
   contain source sequence information.  See Appendix B, "Fragment Order
   Evaluation", for more detail.



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   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 (copies would be declared reordered
   according to the definition above).  This requirement has the same
   storage implications as earlier IPPM metrics and follows the
   precedent of [RFC2679].  We provide a suggestion to minimize storage
   size needed in Section 6 on Measurement and Implementation Issues.

4.  Sample Metrics

   In this section, we define metrics applicable to a sample of packets
   from a single source sequence number system.  When reordering occurs,
   it is highly desirable to assert the degree to which a packet is
   out-of-order or reordered with respect other packets.  This section
   defines several metrics that quantify the extent of reordering in
   various units of measure.  Each metric highlights a relevant use.

   The metrics in the sub-sections below have a network characterization
   orientation, but also have relevance to receiver design where
   reordering compensation is of interest.  We begin with a simple ratio
   metric indicating the reordered portion of the sample.

4.1.  Reordered Packet Ratio

4.1.1.  Metric Name

   Type-P-Reordered-Ratio-Stream

4.1.2.  Metric Parameters

   The parameter set includes Type-P-Reordered singleton parameters; the
   parameters unique to Poisson streams (as in [RFC2330]), periodic
   streams (as in [RFC3432]), or TCP-like streams (as in [RFC3148]);
   packet size or size patterns; and the following:

   +  T0, a start time

   +  Tf, an end time

   +  dT, a waiting time for each packet to arrive, in seconds

   +  K, the total number of packets in the stream sent from source to
      destination

   +  L, the total number of packets received (arriving between T0 and
      Tf+dT) out of the K packets sent.  Recall that identical copies
      (duplicates) have been removed, so L <= K.




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   +  R, the ratio of reordered packets to received packets, defined
      below

   Note that parameter dT is effectively the threshold for declaring a
   packet as lost.  The IPPM Packet Loss Metric [RFC2680] declines to
   recommend a value for this threshold, saying instead that "good
   engineering, including an understanding of packet lifetimes, will be
   needed in practice."

4.1.3.  Definition

   Given a stream of packets sent from a source to a destination, the
   ratio of reordered packets in the sample is

   R = (Count of packets with Type-P-Reordered=TRUE) / ( L )

   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.

4.1.4.  Discussion

   When the Type-P-Reordered-Ratio-Stream is zero, no further reordering
   metrics need be examined for that sample.  Therefore, the value of
   this metric is its simple ability to summarize the results for a
   reordering-free sample.

4.2.  Reordering Extent

   This section defines the extent to which packets are reordered and
   associates a specific sequence discontinuity with each reordered
   packet.  This section inherits the Parameters defined above.

4.2.1.  Metric Name

   Type-P-Packet-Reordering-Extent-Stream

4.2.2.  Notation and Metric Parameters

   Recall that K is the number of packets in the stream at the source,
   and L is the number of packets received at the destination.

   Each packet has been assigned a sequence number, s, a consecutive
   integer from 1 to K in the order of packet transmission (at the
   source).

   Let s[1], s[2], ..., s[L] represent the original sequence numbers
   associated with the packets in order of arrival.



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   s[i] can be thought of as a vector, where the index i is the arrival
   position of the packet with sequence number s.  In theory, any source
   sequence number could appear in any arrival position, but this is
   unlikely in reality.

   Consider a reordered packet (Type-P-Reordered=TRUE) with arrival
   index i and source sequence number s[i].  There exists a set of
   indexes j (1 <= j < i) such that s[j] > s[i].

   The new parameters are:

   +  i, the index for arrival position, where i-1 represents an arrival
      earlier than i.

   +  j, a set of one or more arrival indexes, where 1 <= j < i.

   +  s[i], the original sequence numbers, s, in order of arrival.

   +  e, the Reordering Extent, in units of packets, defined below.

4.2.3.  Definition

   The reordering extent, e, of packet s[i] is defined to be i-j for the
   smallest value of j where s[j] > s[i].

   Informally, the reordering extent is the maximum distance, in
   packets, from a reordered packet to the earliest packet received that
   has a larger sequence number.  If a packet is in-order, its
   reordering extent is undefined.  The first packet to arrive is
   in-order by definition and has undefined reordering extent.

   Comment on the definition of extent:  For some arrival orders, the
   assignment of a simple position/distance as the reordering extent
   tends to overestimate the receiver storage needed to restore order.
   A more accurate and complex procedure to calculate packet storage
   would be to subtract any earlier reordered packets that the receiver
   could pass on to the upper layers (see the Byte Offset metric).  With
   the bias understood, this definition is deemed sufficient, especially
   for those who demand "on the fly" calculations.

4.2.4.  Discussion

   The packet with index j (s[j], identified in the Definition above) is
   the reordering discontinuity associated with packet s at index i
   (s[i]).  This definition is formalized below.






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   Note that the K packets in the stream could be some subset of a
   larger stream, but L is still the total number of packets received
   out of the K packets sent in that subset.

   If a receiver intends to restore order, then its buffer capacity
   determines its ability to handle packets that are reordered.  For
   cases with single reordered packets, the extent e gives the number of
   packets that must be held in the receiver's buffer while waiting for
   the reordered packet to complete the sequence.  For more complex
   scenarios, the extent may be an overestimate of required storage (see
   Section 4.4 on Reordering Byte Offset and the examples in Section 7).
   Also, if the receiver purges its buffer for any reason, the extent
   metric would not reflect this behavior, assuming instead that the
   receiver would exhaustively attempt to restore order.

   Although reordering extent primarily quantifies the offset in terms
   of arrival position, it may also be useful for determining the
   portion of reordered packets that can or cannot be restored to order
   in a typical receiver buffer based on their arrival order alone (and
   without the aid of retransmission).

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

4.3.  Reordering Late Time Offset

   Reordered packets can be assigned offset values indicating their
   lateness in terms of buffer time that a receiver must possess to
   accommodate them.  Offset metrics are calculated only on reordered
   packets, as identified by the reordered packet singleton metric in
   Section 3.

4.3.1.  Metric Name

   Type-P-Packet-Late-Time-Stream

4.3.2.  Metric Parameters

   In addition to the parameters defined for Type-P-Reordered-Ratio-
   Stream, we specify:

   +  DstTime, the time that each packet in the stream arrives at the
      destination, and may be associated with index i, or packet s[i]

   +  LateTime(s[i]), the offset of packet s[i] in units of seconds,
      defined below





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4.3.3.  Definition

   Lateness in time is calculated using destination times.  When
   received packet s[i] is reordered and has a reordering extent e,
   then:

   LateTime(s[i]) = DstTime(i)-DstTime(i-e)

   Alternatively, using similar notation to that of Section 4.2, an
   equivalent definition is:

   LateTime(s[i]) = DstTime(i)-DstTime(j), for min{j|1<=j<i} that
   satisfies s[j]>s[i].

4.3.4.  Discussion

   The offset metrics can help predict whether reordered packets will be
   useful in a general receiver buffer system with finite limits.  The
   limit may be the time of storage prior to a cyclic play-out instant
   (as with de-jitter buffers).

   Note that the one-way IP Packet Delay Variation (IPDV) [RFC3393]
   gives the delay variation for a packet with respect to the preceding
   packet in the source sequence.  Lateness and IPDV give an indication
   of whether a buffer at the destination has sufficient storage to
   accommodate the network's behavior and restore order.  When an
   earlier packet in the source sequence is lost, IPDV will necessarily
   be undefined for adjacent packets, and LateTime 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).

   The combination of loss and reordering influences the LateTime
   metric.  If presented with the arrival sequence 1, 10, 5 (where
   packets 2, 3, 4, and 6 through 9 are lost), LateTime would not
   indicate exactly how "late" packet 5 is from its intended arrival
   position.  IPDV [RFC3393] would not capture this either, because of
   the lack of adjacent packet pairs.  Assuming a periodic stream
   [RFC3432], an expected arrival time could be defined for all packets,
   but this is essentially a single-point delay variation metric (as
   defined in ITU-T Recommendations [I.356] and [Y.1540]), and not a
   reordering metric.



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   A sample's LateTime results may be expressed as a histogram to
   summarize the frequency of buffer times needed to accommodate
   reordered packets and permit buffer tuning on that basis.  A
   cumulative distribution function (CDF) with buffer time vs. percent
   of reordered packets accommodated may be informative.

4.4.  Reordering Byte Offset

   Reordered packets can be assigned offset values indicating the
   storage in bytes that a receiver must possess to accommodate them.
   Offset metrics are calculated only on reordered packets, as
   identified by the reordered packet singleton metric in Section 3.

4.4.1.  Metric Name

   Type-P-Packet-Byte-Offset-Stream

4.4.2.  Metric Parameters

   We use the same parameters defined earlier, including the optional
   parameters of SrcByte and PayloadSize, and define:

   +  ByteOffset(s[i]), the offset of packet s[i] in bytes

4.4.3.  Definition

   The Byte stream offset for reordered packet s[i] is the sum of the
   payload sizes of packets qualified by the following criteria:

   * The arrival is prior to the reordered packet, s[i], and

   * The send sequence number, s, is greater than s[i].

   Packets that meet both these criteria are normally buffered until the
   sequence beneath them is complete.  Note that these criteria apply to
   both in-order and reordered packets.

   For reordered packet s[i] with a reordering extent e:

   ByteOffset(s[i]) = Sum[qualified packets]
                    = Sum[PayloadSize(packet at i-1 if qualified),
                        PayloadSize(packet at i-2 if qualified), ...
                        PayloadSize(packet at i-e always qualified)]

   Using our earlier notation:

   ByteOffset(s[i]) =
               Sum[payloads of s[j] where s[j]>s[i] and i > j >= i-e]



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4.4.4.  Discussion

   We note that estimates of buffer size due to reordering depend
   greatly on the test stream, in terms of the spacing between test
   packets and their size, especially when packet size is variable.  In
   these and other circumstances, it may be most useful to characterize
   offset in terms of the payload size(s) of stored packets, using the
   Type-P-packet-Byte-Offset-Stream metric.

   The byte offset metric can help predict whether reordered packets
   will be useful in a general receiver buffer system with finite
   limits.  The limit is expressed as the number of bytes the buffer can
   store.

   A sample's ByteOffset results may be expressed as a histogram to
   summarize the frequency of buffer lengths needed to accommodate
   reordered packets and permit buffer tuning on that basis.  A CDF with
   buffer size vs. percent of reordered packets accommodated may be
   informative.

4.5.  Gaps between Multiple Reordering Discontinuities

4.5.1.  Metric Names

   Type-P-Packet-Reordering-Gap-Stream
   Type-P-Packet-Reordering-GapTime-Stream

4.5.2.  Parameters

   We use the same parameters defined earlier, but add the convention
   that index i' is greater than i, likewise j' > j, and define:

   +  Gap(s[j']), the Reordering Gap of packet s[j'] in units of integer
      messages

   and the OPTIONAL parameter:

   +  GapTime(s[j']), the Reordering Gap of packet s[j'] in units of
      seconds

4.5.3.  Definition of Reordering Discontinuity

   All reordered packets are associated with a packet at a reordering
   discontinuity, defined as the in-order packet s[j] that arrived at
   the minimum value of j (1<=j<i) for which s[j]> s[i].





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   Note that s[j] will have been found to cause a sequence
   discontinuity, where s > NextExp when evaluated with the reordered
   singleton metric as described in Section 3.4.

   Recall that i - e = min(j).  Subsequent reordered packets may be
   associated with the same s[j], or with a different discontinuity.
   This fact is used in the definition of the Reordering Gap, below.

4.5.4.  Definition of Reordering Gap

   A reordering gap is the distance between successive reordering
   discontinuities.  The Type-P-Packet-Reordering-Gap-Stream metric
   assigns a value for Gap(s[j']) to (all) packets in a stream (and a
   value for GapTime(s[j']), when reported).

   If:

      the packet s[j'] is found to be a reordering discontinuity, based
      on the arrival of reordered packet s[i'] with extent e', and

      an earlier reordering discontinuity s[j], based on the arrival of
      reordered packet s[i] with extent e was already detected, and

      i' > i, and

      there are no reordering discontinuities between j and j',

   then the Reordering Gap for packet s[j'] is the difference between
   the arrival positions the reordering discontinuities, as shown below:

   Gap(s[j'])    =   (j')  -  (j)

   Gaps MAY also be expressed in time:

   GapTime(s[j']) = DstTime(j') - DstTime(j)

   Otherwise:

   Gap(s[j']) (and GapTime(s[j']) ) for packet s[j'] is 0.

4.5.5.  Discussion

   When separate reordering discontinuities can be distinguished, a
   count may also be reported (along with the discontinuity description,
   such as the number of reordered packets associated with that
   discontinuity and their extents and offsets).  The Gaps between a





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   sample's reordering discontinuities may be expressed as a histogram
   to easily summarize the frequency of various gaps.  Reporting the
   mode, average, range, etc., may also summarize the distributions.

   The Gap metric may help to correlate the frequency of reordering
   discontinuities with their cause.  Gap lengths are also informative
   to receiver designers, revealing the period of reordering
   discontinuities.  The combination of reordering gaps and extent
   reveals whether receivers will be required to handle cases of
   overlapping reordered packets.

4.6.  Reordering-Free Runs

   This section defines a metric based on a count of consecutive
   in-order packets between reordered packets.

4.6.1.  Metric Names

   Type-P-Packet-Reordering-Free-Run-x-numruns-Stream
   Type-P-Packet-Reordering-Free-Run-q-squruns-Stream
   Type-P-Packet-Reordering-Free-Run-p-numpkts-Stream
   Type-P-Packet-Reordering-Free-Run-a-accpkts-Stream

4.6.2.  Parameters

   We use the same parameters defined earlier and define the following:

   +  r, the run counter

   +  x, the number of runs, also the number of reordered packets

   +  a, the accumulator of in-order packets

   +  p, the number of packets (when the stream is complete, p=(x+a)=L)

   +  q, the sum of the squares of the runs counted

4.6.3.  Definition

   As packets in a sample arrive at the destination, the count of in-
   order packets between reordered packets is a Reordering-Free run.
   Note that the minimum run-length is zero according to this
   definition.  A pseudo-code example follows:

   r = 0; /* r is the run counter */
   x = 0; /* x is the number of runs */
   a = 0; /* a is the accumulator of in-order packets */
   p = 0; /* p is the number of packets */



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   q = 0; /* q is the sum of the squares of the runs counted */

   while(packets arrive with sequence number s)
   {
        p++;
        if (s >= NextExp) /* s is in-order */
                then r++;
                a++;
        else    /* s is reordered */
                q+= r*r;
                r = 0;
                x++;
   }

   Each in-order arrival increments the run counter and the accumulator
   of in-order packets; each reordered packet resets the run counter
   after adding it to the sum of the squared lengths.

   Each arrival of a reordered packet yields a new run count.  Long runs
   accompany periods where order was maintained, while short runs
   indicate frequent or multi-packet reordering.

   The percent of packets in-order is 100*a/p

   The average Reordering-Free run length is a/x

   The q counter gives an indication of variation of the Reordering-Free
   runs from the average by comparing q/a to a/x ((q/a)/(a/x)).

4.6.4.  Discussion and Illustration

   Type-P-packet-Reordering-Free-Run-Stream parameters give a brief
   summary of the stream's reordering characteristics including the
   average reordering-free run length, and the variation of run lengths;
   therefore, a key application of this metric is network evaluation.

   For 36 packets with 3 runs of 11 in-order packets, we have:

      p = 36
      x = 3
      a = 33
      q = 3 * (11*11) = 363
      ave. reordering-free run = 11
      q/a = 11
      (q/a)/(a/x) = 1.0

   For 36 packets with 3 runs, 2 runs of length 1, and one of length 31,
   we have:



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      p = 36
      x = 3
      a = 33
      q = 1 + 1 + 961 = 963
      ave. reordering-free run = 11
      q/a = 29.18
      (q/a)/(a/x) = 2.65

   The variability in run length is prominent in the difference between
   the q values (sum of the squared run lengths) and in comparing
   average run length to the (q/a)/(a/x) ratios (equals 1 when all runs
   are the same length).

5.  Metrics Focused on Receiver Assessment: A TCP-Relevant Metric

   This section describes a metric that conveys information associated
   with the effect of reordering on TCP.  However, in order to infer
   anything about TCP performance, the test stream MUST bear a close
   resemblance to the TCP sender of interest.  [RFC3148] lists the
   specific aspects of congestion control algorithms that must be
   specified.  Further, RFC 3148 recommends that Bulk Transfer Capacity
   metrics SHOULD have instruments to distinguish three cases of packet
   reordering (in Section 3.3).  The sample metrics defined above
   satisfy the requirements to classify packets that are slightly or
   grossly out-of-order.  The metric in this section adds the capability
   to estimate whether reordering might cause the DUP-ACK threshold to
   be exceeded causing the Fast Retransmit algorithm to be invoked.
   Additional TCP Kernel Instruments are summarized in [Mat03].

5.1.  Metric Name

   Type-P-Packet-n-Reordering-Stream

5.2.  Parameter Notation

   Let n be a positive integer (a parameter).  Let k be a positive
   integer equal to the number of packets sent (sample size).  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, in order of packet
   emission.

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





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5.3.  Definitions

   Definition 1: Received packet number i (n < i <= l), with source
   sequence number s[i], is n-reordered if and only if for all j such
   that i-n <= j < i, s[j] > s[i].

   Claim: If, by this definition, a packet is n-reordered and 0 < n' <
   n, then the packet is also n'-reordered.

   Note: This definition is illustrated by C code in Appendix A.  The
   code determines and reports the n-reordering for n from 1 to a
   specified parameter (MAXN in the code, set to 100).  The value of n
   conjectured to be relevant for TCP is the TCP duplicate ACK threshold
   (set to the value of 3 by paragraph 2 of Section 3.2 of [RFC 2581]).

   This definition does not assign an n 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
   packet 4 is n-reordered, with n=3.)

   Definition 2: The degree of n-reordering of a sample is m/l, where m
   is the number of n-reordered packets in the sample.

   Definition 3: The degree of monotonic reordering of a sample is its
   degree of 1-reordering.

   Definition 4: A sample is said to have no reordering if its degree of
   monotonic reordering is 0.

   Note: As follows from the claim above, if monotonic reordering of a
   sample is 0, then the n-reordering of the sample is 0 for all n.

5.4.  Discussion

   The degree of n-reordering may be expressed as a percentage, in which
   case the number from Definition 2 is multiplied by 100.

   The n-reordering metric is helpful for matching the duplicate ACK
   threshold setting to a given path.  For example, if a path exhibits
   no more than 5-reordering, a DUP-ACK threshold of 6 may avoid
   unnecessary retransmissions.

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

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



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   - For n=3, a NewReno TCP sender would retransmit 1 packet in response
     to an instance of 3-reordering and therefore consider this packet
     lost for the purposes of congestion control (the sender will halve
     its congestion window, see [RFC2581]).  Three is the default
     threshold for Stream Control Transport Protocol (SCTP) [RFC2960],
     and the Datagram Congestion Control Protocol (DCCP) [RFC4340] when
     used with Congestion Control ID 2: TCP-like Congestion Control
     [RFC4341].

   A sample's n-reordering may be expressed as a histogram to summarize
   the frequency for each value of n.

   We note that the definition of n-reordering cannot predict the exact
   number of packets unnecessarily retransmitted by a TCP sender under
   some circumstances, such as cases with closely-spaced reordered
   singletons.  Both time and position influence the sender's behavior.

   A packet's n-reordering designation is sometimes equal to its
   reordering extent, e.  n-reordering is different in the following
   ways:

   1. n is a count of early packets with consecutive arrival positions
      at the receiver.

   2. Reordered packets (Type-P-Reordered=TRUE) may not be n-reordered,
      but will have an extent, e (see the examples).

6.  Measurement and Implementation Issues

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

   In order to gauge the reordering for an application according to the
   metrics defined in this memo, it is RECOMMENDED to use the same
   sending pattern as the application of interest.  In any case, the
   exact method of packet generation MUST be reported with the
   measurement results, including all stream parameters.

   +  To make inferences about applications that use TCP, it is REQUIRED
      to use TCP-like Streams as in [RFC3148]

   +  For real-time applications, it is RECOMMENDED to use periodic
      streams as in [RFC3432]






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   It is acceptable to report the metrics of Sections 3 and 4 with other
   IPPM metrics using Poisson streams [RFC2330].  Poisson streams
   represent an "unbiased sample" of network performance for packet loss
   and delay metrics.  However, it would be incorrect to make inferences
   about the application categories above using reordering metrics
   measured with Poisson streams.

   Test stream designers may prefer to use a periodic sending interval
   in order to maintain a known temporal bias and allow simplified
   results analysis (as described in [RFC3432]).  In this case, it is
   RECOMMENDED that the periodic sending interval be chosen to reproduce
   the closest source packet spacing expected.  Testers must recognize
   that streams sent at the link speed serialization limit MUST have
   limited duration and MUST consider packet loss an indication that the
   stream has caused congestion, and suspend further testing.

   When intending to compare independent measurements of reordering, it
   is RECOMMENDED to use the same test stream parameters in each
   measurement system.

   Packet lengths might also be varied to attempt to detect instances of
   parallel processing (they may cause steady state reordering).  For
   example, a line-speed burst of the longest (MTU-length) packets
   followed by a burst of the shortest possible packets may be an
   effective detecting pattern.  Other size patterns are possible.

   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.

   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
   NextExp value cannot decrease, and all packets received after a
   rollover would be declared reordered.  Sequence number rollover can
   be avoided by using combinations of counter size and test duration
   where rollover 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 rollover 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 rollover.




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   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
      rollover is detected.

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

   Ideally, the test instrument would have the ability to use all
   earlier packets at any point in the test stream.  In practice, there
   will be limited ability to determine the extent of reordering, due to
   the storage requirements for previous packets.  Saving only packets
   that indicate discontinuities (and their arrival positions) will
   reduce storage volume.

   Another solution is to use a sliding history window of packets, where
   the window size would be determined by an upper bound on the useful
   reordering extent.  This bound could be several packets or several
   seconds worth of packets, depending on the intended analysis.  When
   discarding all stream information beyond the window, the reordering
   extent or degree of n-reordering may need to be expressed as greater
   than the window length if the reordering discontinuity information
   has been discarded, and Gap calculations would not be possible.

   The requirement to ignore duplicate packets also mandates storage.
   Here, tracking the sequence numbers of missing packets may minimize
   storage size.  Missing packets may eventually be declared lost or be
   reordered if they arrive.  The missing packet list and the largest
   sequence number received thus far (NextExp - 1) are sufficient
   information to determine if a packet is a duplicate (assuming a
   manageable storage size for packets that are missing due to loss).

   It is important to note that practical IP networks also have limited
   ability to "store" packets, even when routing loops appear
   temporarily.  Therefore, the maximum storage for reordering metrics
   (and their complexity) would only approach the number packets in the
   sample, K, when the sending time for K packets is small with respect
   to the network's largest possible transfer time.  Another possible
   limitation on storage is the maximum length of the sequence number
   field, assuming that most test streams do not exhaust this length in
   practice.

   Last, we note that determining reordering extents and gaps is tricky
   when there are overlapped or nested events.  Test instrument
   complexity and reordering complexity are directly correlated.





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6.1.  Passive Measurement Considerations

   As with other IPPM metrics, the definitions have been constructed
   primarily for Active measurements.

   Assuming that the necessary sequence information (message number) is
   included in the packet payload (possibly in application headers such
   as RTP), reordering metrics may be evaluated in a passive measurement
   arrangement.  Also, it is possible to evaluate order at any point
   along a source-destination path, recognizing that intermediate
   measurements may differ from those made at the destination (where the
   reordering effect on applications can be inferred).

   It is possible to apply these metrics to evaluate reordering in a TCP
   sender's stream.  In this case, the source sequence numbers would be
   based on byte stream or segment numbering.  Since the stream may
   include retransmissions due to loss or reordering, care must be taken
   to avoid declaring retransmitted packets reordered.  The additional
   sequence reference of s or SrcTime helps avoid this ambiguity in
   active measurement, or the optional TCP timestamp field [RFC1323] in
   passive measurement.

7.  Examples of Arrival Order Evaluation

   This section provides some examples to illustrate how the non-
   reversing order criterion works, how n-reordering works in
   comparison, and the value of quantifying reordering in all the
   dimensions of time, bytes, and position.

   Throughout this section, we will refer to packets by their source
   sequence number, except where noted.  So "Packet 4" refers to the
   packet with source sequence number 4, and the reader should refer to
   the tables in each example to determine packet 4's arrival index
   number, if needed.

7.1.  Example with a Single Packet Reordered

   Table 1 gives a simple case of reordering, where one packet is
   reordered, Packet 4.  Packets are listed according to their arrival,
   and message numbering is used.  All packets contain PayloadSize=100
   bytes, with SrcByte=(s x 100)-99 for s=1,2,3,4,...










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   Table 1: Example with Packet 4 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
    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).
   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 reordering 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
                            /\

   Applying the definition of Type-P-Packet-Reordering-Extent-Stream:

   when j=7, 8 > 4, so the reordering extent is 1 or more.
   when j=6, 7 > 4, so the reordering extent is 2 or more.
   when j=5, 6 > 4, so the reordering extent is 3 or more.
   when j=4, 5 > 4, so the reordering extent is 4 or more.



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   when j=3, but 3 < 4, and 4 is the maximum extent, e=4 (assuming
   there are no earlier sequence discontinuities, as in this example).

   Further, we can compute the Late Time (210-148=62ms using DstTime)
   compared to Packet 5's arrival.  If the receiver 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 indicate
   unusual behavior for Packet 4.  Also, if Packet 4 had arrived at
   least 62ms earlier, it would have been in-order in this example.

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

   Following the definitions of Section 5.1, Packet 4 is designated
   4-reordered.

7.2.  Example with Two Packets Reordered

   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

   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
                      /\ /\





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   Considering Packet 5 first:

   when j=5, 7 > 5, so the reordering extent is 1 or more.
   when j=4, we have 4 < 5, so 1 is its maximum extent, and e=1.

   Considering Packet 6 next:

   when j=6, 5 < 6, the extent is not yet defined.
   when j=5, 7 > 6, so the reordering extent is i-j=2 or more.
   when j=4, 4 < 6, and we find 2 is its maximum extent, and e=2.

   We can also associate each of these reordered packets with a
   reordering discontinuity.  We find the minimum j=5 (for both packets)
   according to Section 4.2.3.  So Packet 6 is associated with the same
   reordering discontinuity as Packet 5, the Reordering Discontinuity at
   Packet 7.

   This is a case where reordering extent e would over-estimate the
   packet storage required to restore order.  Only one packet storage is
   required (to hold Packet 7), but e=2 for Packet 6.

   Following the definitions of Section 5, Packet 5 is designated
   1-reordered, but Packet 6 is not designated n-reordered.

   A hypothetical sender/receiver pair may retransmit Packet 5
   unnecessarily, since it is 1-reordered (in agreement with the
   singleton metric).  Though Packet 6 may not be unnecessarily
   retransmitted, the receiver cannot advance Packet 7 to the higher
   layers until after Packet 6 arrives.  Therefore, the singleton metric
   correctly determined that Packet 6 is reordered.





















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7.3.  Example with Three Packets Reordered

   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     -88      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
   reordering extent, while IPDV indicates that the spacing between
   packets 4,5,and 6 has changed.

   The histogram of Reordering extents (e) would be:

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


   We first calculate the n-reordering.  Considering Packet 4 first:

   when n=1, 7<=j<8, and 10> 4, so the packet is 1-reordered.
   when n=2, 6<=j<8, and 9 > 4, so the packet is 2-reordered.
   when n=3, 5<=j<8, and 8 > 4, so the packet is 3-reordered.
   when n=4, 4<=j<8, and 7 > 4, so the packet is 4-reordered.
   when n=5, 3<=j<8, but 3 < 4, and 4 is the maximum n-reordering.






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   Considering packet 5[9] next:
   when n=1, 8<=j<9, but 4 < 5, so the packet at i=9 is not designated
   as n-reordered.  We find the same result for Packet 6.

   We now consider whether reordered Packets 5 and 6 are associated with
   the same reordering discontinuity as Packet 4.  Using the test of
   Section 4.2.3, we find that the minimum j=4 for all three packets.
   They are all associated with the reordering discontinuity at Packet
   7.

   This example shows again that the n-reordering definition identifies
   a single Packet (4) with a sufficient degree of n-reordering that
   might cause one unnecessary packet retransmission by the New Reno TCP
   sender (with DUP-ACK threshold=3 or 4).  Also, the reordered arrival
   of Packets 5 and 6 will allow the receiver process to pass Packets 7
   through 10 up the protocol stack (the singleton Type-P-Reordered =
   TRUE for Packets 5 and 6, and they are all associated with a single
   reordering discontinuity).

7.4.  Example with Multiple Packet Reordering Discontinuities

   Table 4 Example with Multiple Packet Reordering Discontinuities
   Sending order(s @Src): 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16

          Discontinuity         Discontinuity
                |---------Gap---------|
   s = 1, 2, 3, 6, 7, 4, 5, 8, 9, 10, 12, 13, 11, 14, 15, 16
   i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

   r = 1, 2, 3, 4, 5, 0, 0, 1, 2,  3,  4,  5,  0,  1,  2,  3, ...
   number of runs,n = 1  2                     3
   end r counts =     5  0                     5
   (These values are computed after the packet arrives.)

   Packet 4 has extent e=2, Packet 5 has extent e=3, and Packet 11 has
   e=2.  There are two different reordering discontinuities, one at
   Packet 6 (where j=4) and one at Packet 12 (where j'=11).

   According to the definition of Reordering Gap
   Gap(s[j']) = (j') - (j)
   Gap(Packet 12) = (11) - (4) = 7

   We also have three reordering-free runs of lengths 5, 0, and 5.

   The differences between these two multiple-event metrics are evident
   here.  Gaps are the distance between sequence discontinuities that
   are subsequently defined as reordering discontinuities, while
   reordering-free runs capture the distance between reordered packets.



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8.  Security Considerations

8.1.  Denial-of-Service Attacks

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

   Administrators of the source, destination, and intervening network(s)
   should establish bilateral or multilateral agreements regarding the
   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.

8.2.  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.  In most cases, a hashing function
   will produce a value suitable for payload comparisons.

8.3.  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 the destination
   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.  The likely consequences of packet
   injection are that the additional packets would be declared
   duplicates, or that the original packets would be seen as duplicates
   (if they arrive after the corresponding injected packets), causing
   invalid measurements on the injected packets.

   The requirements for data collection resistance to interference by
   malicious parties and mechanisms to achieve such resistance are
   available in other IPPM memos.  A set of requirements for a data
   collection protocol can be found in [RFC3763], and a protocol
   specification for the One-Way Active Measurement Protocol (OWAMP) is





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   in [RFC4656].  The security considerations sections of the two OWAMP
   documents are extensive and should be consulted for additional
   details.

9.  IANA Considerations

   Metrics defined in this memo have been registered in the IANA IPPM
   METRICS REGISTRY as described in initial version of the registry
   [RFC4148].

   IANA has registered the following metrics in the IANA-IPPM-METRICS-
   REGISTRY-MIB:

   ietfReorderedSingleton OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Reordered"
       REFERENCE
          "Reference RFC 4737, Section 3"
       ::= { ianaIppmMetrics 34 }

   ietfReorderedPacketRatio OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Reordered-Ratio-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.1"
       ::= { ianaIppmMetrics 35 }

   ietfReorderingExtent OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-Reordering-Extent-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.2"
       ::= { ianaIppmMetrics 36 }

   ietfReorderingLateTimeOffset OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-Late-Time-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.3"
       ::= { ianaIppmMetrics 37 }

   ietfReorderingByteOffset OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION



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          "Type-P-Packet-Byte-Offset-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.4"
       ::= { ianaIppmMetrics 38 }

   ietfReorderingGap OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-Reordering-Gap-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.5"
       ::= { ianaIppmMetrics 39 }

   ietfReorderingGapTime OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-Reordering-GapTime-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.5"
       ::= { ianaIppmMetrics 40 }

   ietfReorderingFreeRunx OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-Reordering-Free-Run-x-numruns-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.6"
       ::= { ianaIppmMetrics 41 }

   ietfReorderingFreeRunq OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-Reordering-Free-Run-q-squruns-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.6"
       ::= { ianaIppmMetrics 42 }

   ietfReorderingFreeRunp OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-Reordering-Free-Run-p-numpkts-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.6"
       ::= { ianaIppmMetrics 43 }

   ietfReorderingFreeRuna OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION



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          "Type-P-Packet-Reordering-Free-Run-a-accpkts-Stream"
       REFERENCE
          "Reference RFC 4737, Section 4.6"
       ::= { ianaIppmMetrics 44 }

   ietfnReordering OBJECT-IDENTITY
       STATUS       current
       DESCRIPTION
          "Type-P-Packet-n-Reordering-Stream"
       REFERENCE
          "Reference RFC 4737, Section 5"
       ::= { ianaIppmMetrics 45 }

10.  Normative References

   [RFC791]   Postel, J., "Internet Protocol", STD 5, RFC 791, September
              1981.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC2330]  Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
              "Framework for IP Performance Metrics", RFC 2330, May
              1998.

   [RFC2460]  Deering, S. and R. Hinden, "Internet Protocol, Version 6
              (IPv6) Specification", RFC 2460, December 1998.

   [RFC3148]  Mathis, M. and M. Allman, "A Framework for Defining
              Empirical Bulk Transfer Capacity Metrics", RFC 3148, July
              2001.

   [RFC3432]  Raisanen, V., Grotefeld, G., and A. Morton, "Network
              performance measurement with periodic streams", RFC 3432,
              November 2002.

   [RFC3763]  Shalunov, S. and B. Teitelbaum, "One-way Active
              Measurement Protocol (OWAMP) Requirements", RFC 3763,
              April 2004.

   [RFC4148]  Stephan, E., "IP Performance Metrics (IPPM) Metrics
              Registry", BCP 108, RFC 4148, August 2005.

   [RFC4656]  Shalunov, S., Teitelbaum, B., Karp, A., Boote, J., and M.
              Zeckauskas,  "A One-way Active Measurement Protocol
              (OWAMP)", RFC 4656, September 2006.





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RFC 4737               Packet Reordering Metrics           November 2006


11.  Informative References

   [Bel02]    J. Bellardo and S. Savage, "Measuring Packet Reordering,"
              Proceedings of the ACM SIGCOMM Internet Measurement
              Workshop 2002, November 6-8, Marseille, France.

   [Ben99]    J.C.R. Bennett, C. Partridge, and N. Shectman, "Packet
              Reordering is Not Pathological Network Behavior," IEEE/ACM
              Transactions on Networking, vol. 7, no. 6, pp. 789-798,
              December 1999.

   [Cia00]    L. Ciavattone and A. Morton, "Out-of-Sequence Packet
              Parameter Definition (for Y.1540)", Contribution number
              T1A1.3/2000-047, October 30, 2000,
              http://home.comcast.net/~acmacm/IDcheck/0A130470.doc.

   [Cia03]    L. Ciavattone, A. Morton, and G. Ramachandran,
              "Standardized Active Measurements on a Tier 1 IP
              Backbone," IEEE Communications Mag., pp. 90-97, June 2003.

   [I.356]    ITU-T Recommendation I.356, "B-ISDN ATM layer cell
              transfer performance", March 2000.

   [Jai02]    S. Jaiswal et al., "Measurement and Classification of Out-
              of-Sequence Packets in a Tier-1 IP Backbone," Proceedings
              of the ACM SIGCOMM Internet Measurement Workshop 2002,
              November 6-8, Marseille, France.

   [Lou01]    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.

   [Mat03]    M. Mathis, J. Heffner, and R. Reddy, "Web100: Extended TCP
              Instrumentation for Research, Education and Diagnosis",
              ACM Computer Communications Review, Vol 33, Num 3, July
              2003, http://www.web100.org/docs/mathis03web100.pdf.

   [Pax98]    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.

   [RFC793]   Postel, J., "Transmission Control Protocol", STD 7, RFC
              793, September 1981.

   [RFC1323]  Jacobson, V., Braden, R., and D. Borman, "TCP Extensions
              for High Performance", RFC 1323, May 1992.




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RFC 4737               Packet Reordering Metrics           November 2006


   [RFC2581]  Allman, M., Paxson, V., and W. Stevens, "TCP Congestion
              Control ", RFC 2581, April 1999.

   [RFC2679]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Delay Metric for IPPM", RFC 2679, September 1999.

   [RFC2680]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Packet Loss Metric for IPPM", RFC 2680, September 1999.

   [RFC2960]  Stewart, R., Xie, Q., Morneault, K., Sharp, C.,
              Schwarzbauer, H., Taylor, T., Rytina, I., Kalla, M.,
              Zhang, L., and V. Paxson, "Stream Control Transmission
              Protocol", RFC 2960, October 2000.

   [RFC3393]  Demichelis, C. and P. Chimento, "IP Packet Delay Variation
              Metric for IP Performance Metrics (IPPM)", RFC 3393,
              November 2002.

   [RFC4340]  Kohler, E., Handley, M., and S. Floyd, "Datagram
              Congestion Control Protocol (DCCP)", RFC 4340, March 2006.

   [RFC4341]  Floyd, S. and E. Kohler, "Profile for Datagram Congestion
              Control Protocol (DCCP) Congestion Control ID 2: TCP-like
              Congestion Control", RFC 4341, March 2006.

   [TBABAJ02] T. Banka, A. Bare, A. P. Jayasumana, "Metrics for Degree
              of Reordering in Packet Sequences", Proc. 27th IEEE
              Conference on Local Computer Networks, Tampa, FL, Nov.
              2002.

   [Y.1540]   ITU-T Recommendation Y.1540, "Internet protocol data
              communication service - IP packet transfer and
              availability performance parameters", December 2002.

12.  Acknowledgements

   The authors would like to acknowledge many helpful discussions with
   Matt Zekauskas, Jon Bennett (who authored the sections on
   Reordering-Free Runs), and Matt Mathis.  We thank David Newman, Henk
   Uijterwaal, Mark Allman, Vern Paxson, and Phil Chimento for their
   reviews and suggestions, and Michal Przybylski for sharing
   implementation experiences with us on the ippm-list.  Anura
   Jayasumana and Nischal Piratla brought in recent work-in-progress
   [TBABAJ02].  We gratefully acknowledge the foundation laid by the
   authors of the IP performance framework [RFC2330].






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Appendix A.  Example Implementations in C (Informative)

   Two example c-code implementations of reordering definitions follow:

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

   #include <stdio.h>

   #define MAXN   100

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

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


   int
   main()
   {
           int     m[MAXN];       /* We have m[j-1] == number of
                                            * j-reordered packets.  */
           int     ring[MAXN];    /* 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 < MAXN; j++) m[j] = 0;
           for (;(s = read_sequence_number())!= EOF;l++,r=(r+1)%MAXN) {
             for (j=0; j<min(l, MAXN)&&s<ring[loop(r-j-1)];j++) m[j]++;
             ring[r] = s;
           }



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           for (j = 0; j < MAXN && 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 < MAXN) printf("no %d-reordering\n", j+1);
           else printf("only up to %d-reordering is handled\n", MAXN);
           exit(0);
   }


   /* Example 2   singleton and n-reordering comparison =======
      Author:  Jerry Perser 7-2002 (mod by acm 12-2004)
      Compile: $ gcc -o jpboth file.c
      Usage:   $ jpboth 1 2 3 7 8 4 5 6 (pkt sequence given on cmdline)
      Note to cut/pasters: line 59 may need repair
   */

      #include <stdio.h>

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

      /* Global counters */
      int receive_packets=0;       /* number of received */
      int reorder_packets_Al=0;    /* num reordered pkts (singleton) */
      int reorder_packets_Stas=0; /* num reordered pkts(n-reordering)*/

      /* 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[MAXN];    /* Last sequence numbers seen.  */
           static int  r = 0;         /* Ring pointer for next write */



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           int   l = 0;          /* Number of sequence numbers read.  */
           int   j;
           int  iReturn = 0;

           l++;
           r = (r+1) % MAXN;
           for (j=0; j<min(l, MAXN) && 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_Al += testorder1(packet); // singleton
                reorder_packets_Stas += testorder2(packet); //n-reord.
           }
           printf("Received packets = %d, Singleton Reordered = %d, n-
   reordered = %d\n",  receive_packets, reorder_packets_Al,
   reorder_packets_Stas );
           exit(0);
      }

   Reference

   ISO/IEC 9899:1999 (E), as amended by ISO/IEC 9899:1999/Cor.1:2001
   (E).  Also published as:

   The C Standard: Incorporating Technical Corrigendum 1, British
   Standards Institute, ISBN: 0-470-84573-2, Hardcover, 558 pages,
   September 2003.

















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Appendix B.  Fragment Order Evaluation (Informative)

   Section 3 stated that fragment reassembly is assumed prior to order
   evaluation, but that similar procedures could be applied prior to
   reassembly.  This appendix gives definitions and procedures to
   identify reordering in a packet stream that includes fragmentation.

B.1.  Metric Name

   The Metric retains the same name, Type-P-Reordered, but additional
   parameters are required.

   This appendix assumes that the device that divides a packet into
   fragments sends them according to ascending fragment offset.  Early
   Linux OS sent fragments in reverse order, so this possibility is
   worth checking.

B.2.  Additional Metric Parameters

   +  MoreFrag, the state of the More Fragments Flag in the IP header.

   +  FragOffset, the offset from the beginning of a fragmented packet,
      in 8 octet units (also from the IP header).

   +  FragSeq#, the sequence number from the IP header of a fragmented
      packet currently under evaluation for reordering.  When set to
      zero, fragment evaluation is not in progress.

   +  NextExpFrag, the next expected fragment offset at the destination,
      in 8 octet units.  Set to zero when fragment evaluation is not in
      progress.

   The packet sequence number, s, is assumed to be the same as the IP
   header sequence number.  Also, the value of NextExp does not change
   with the in-order arrival of fragments.  NextExp is only updated when
   a last fragment or a complete packet arrives.

   Note that packets with missing fragments MUST be declared lost, and
   the Reordering status of any fragments that do arrive MUST be
   excluded from sample metrics.











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B.3.  Definition

   The value of Type-P-Reordered is typically false (the packet is
   in-order) when

   * the sequence number s >= NextExp, AND

   * the fragment offset FragOffset >= NextExpFrag

   However, it is more efficient to define reordered conditions exactly
   and designate Type-P-Reordered as False otherwise.

   The value of Type-P-Reordered is defined as True (the packet is
   reordered) under the conditions below.  In these cases, the NextExp
   value does not change.

   Case 1: if s < NextExp

   Case 2: if s < FragSeq#

   Case 3: if s>= NextExp AND s = FragSeq# AND FragOffset < NextExpFrag

   This definition can also be illustrated in pseudo-code.  A version of
   the code follows, and some simplification may be possible.
   Housekeeping for the new parameters will be challenging.

   NextExp=0;
   NextExpFrag=0;
   FragSeq#=0;

   while(packets arrive with s, MoreFrag, FragOffset)
   {
   if (s>=NextExp AND MoreFrag==0 AND s>=FragSeq#){
        /* a normal packet or last frag of an in-order packet arrived */
        NextExp = s+1;
        FragSeq# = 0;
        NextExpFrag = 0;
        Reordering = False;
        }
   if (s>=NextExp AND MoreFrag==1 AND s>FragSeq#>=0){
        /* a fragment of a new packet arrived, possibly with a
        higher sequence number than the current fragmented packet */
        FragSeq# = s;
        NextExpFrag = FragOffset+1;
        Reordering = False;
        }
   if (s>=NextExp AND MoreFrag==1 AND s==FragSeq#){
        /* a fragment of the "current packet s" arrived */



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        if (FragOffset >= NextExpFrag){
                NextExpFrag = FragOffset+1;
                Reordering = False;
                }
        else{
                Reordering = True; /* fragment reordered  */
                }
        }
   if (s>=NextExp AND MoreFrag==1 AND s < FragSeq#){
        /* case where a late fragment arrived,
           for illustration only, redundant with else below */
        Reordering = True;
        }
   else { /* when s < NextExp, or MoreFrag==0 AND s < FragSeq# */
        Reordering = True;
        }
   }

   A working version of the code would include a check to ensure that
   all fragments of a packet arrive before using the Reordered status
   further, such as in sample metrics.

B.4.  Discussion: Notes on Sample Metrics When Evaluating Fragments

   All fragments with the same source sequence number are assigned the
   same source time.

   Evaluation with byte stream numbering may be simplified if the
   fragment offset is simply added to the SourceByte of the first packet
   (with fragment offset = 0), keeping the 8 octet units of the offset
   in mind.

Appendix C.  Disclaimer and License

   Regarding this entire document or any portion of it (including the
   pseudo-code and C code), the authors make no guarantees and are not
   responsible for any damage resulting from its use.  The authors grant
   irrevocable permission to anyone to use, modify, and distribute it in
   any way that does not diminish the rights of anyone else to use,
   modify, and distribute it, provided that redistributed derivative
   works do not contain misleading author or version information.
   Derivative works need not be licensed under similar terms.









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RFC 4737               Packet Reordering Metrics           November 2006


Authors' Addresses

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


   Len Ciavattone
   AT&T Labs
   Room A2 - 4G06
   200 Laurel Ave.  South
   Middletown, NJ 07748 USA
   Phone  +1 732 420 1239
   EMail: lencia@att.com


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


   Stanislav Shalunov
   Internet2
   1000 Oakbrook DR STE 300
   Ann Arbor, MI 48104
   Phone: +1 734 995 7060
   EMail: shalunov@internet2.edu


   Jerry Perser
   Veriwave
   8770 SW Nimbus Ave.
   Suite B
   Beaverton, OR 97008 USA
   Phone: +1 818 338 4112
   EMail: jperser@veriwave.com







Morton, et al.           Standards Track                       [Page 44]

RFC 4737               Packet Reordering Metrics           November 2006


Full Copyright Statement

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