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IETF RFC 4737
Packet Reordering Metrics
Last modified on Thursday, November 23rd, 2006
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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 © 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.
Morton, et al. Standards Track PAGE 1 
RFC 4737 Packet Reordering Metrics November 2006
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
Morton, et al. Standards Track PAGE 2
RFC 4737 Packet Reordering Metrics November 2006
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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RFC 4737 Packet Reordering Metrics November 2006
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
[RFC 791] [RFC 2460] 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 [RFC 2330] 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 [RFC 793]. 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.
Morton, et al. Standards Track PAGE 4
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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" [RFC 2330] 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 [RFC 3432]), TCP-like
streams (as in [RFC 3148]), or Poisson streams (as in [RFC 2330]).
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 [RFC 2119]. 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 [RFC 2330] 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
Morton, et al. Standards Track PAGE 7
RFC 4737 Packet Reordering Metrics November 2006
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.
Morton, et al. Standards Track PAGE 8
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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;
Morton, et al. Standards Track PAGE 9
RFC 4737 Packet Reordering Metrics November 2006
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 [RFC 2679]. 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 [RFC 2330]), periodic
streams (as in [RFC 3432]), or TCP-like streams (as in [RFC 3148]);
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.
Morton, et al. Standards Track PAGE 11
RFC 4737 Packet Reordering Metrics November 2006
+ 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 [RFC 2680] 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.
Morton, et al. Standards Track PAGE 12
RFC 4737 Packet Reordering Metrics November 2006
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) [RFC 3393]
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 [RFC 3393] would not capture this either, because of
the lack of adjacent packet pairs. Assuming a periodic stream
[RFC 3432], 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
Morton, et al. Standards Track PAGE 18
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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. [RFC 3148] 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 [RFC 2581]). Three is the default
threshold for Stream Control Transport Protocol (SCTP) [RFC 2960],
and the Datagram Congestion Control Protocol (DCCP) [RFC 4340] when
used with Congestion Control ID 2: TCP-like Congestion Control
[RFC 4341].
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 [RFC 3148]
+ For real-time applications, it is RECOMMENDED to use periodic
streams as in [RFC 3432]
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It is acceptable to report the metrics of Sections 3 and 4 with other
IPPM metrics using Poisson streams [RFC 2330]. 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 [RFC 3432]). 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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RFC 4737 Packet Reordering Metrics November 2006
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 [RFC 1323] 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.
Morton, et al. Standards Track PAGE 27
RFC 4737 Packet Reordering Metrics November 2006
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.
Morton, et al. Standards Track PAGE 31
RFC 4737 Packet Reordering Metrics November 2006
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 [RFC 3763], and a protocol
specification for the One-Way Active Measurement Protocol (OWAMP) is
Morton, et al. Standards Track PAGE 32
RFC 4737 Packet Reordering Metrics November 2006
in [RFC 4656]. 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
[RFC 4148].
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
Morton, et al. Standards Track PAGE 33
RFC 4737 Packet Reordering Metrics November 2006
"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
Morton, et al. Standards Track PAGE 34
RFC 4737 Packet Reordering Metrics November 2006
"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
[RFC 791] Postel, J., "Internet Protocol", STD 5, RFC 791, September
1981.
[RFC 2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC 2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
"Framework for IP Performance Metrics", RFC 2330, May
1998.
[RFC 2460] Deering, S. and R. Hinden, "Internet Protocol, Version 6
(IPv6) Specification", RFC 2460, December 1998.
[RFC 3148] Mathis, M. and M. Allman, "A Framework for Defining
Empirical Bulk Transfer Capacity Metrics", RFC 3148, July
2001.
[RFC 3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network
performance measurement with periodic streams", RFC 3432,
November 2002.
[RFC 3763] Shalunov, S. and B. Teitelbaum, "One-way Active
Measurement Protocol (OWAMP) Requirements", RFC 3763,
April 2004.
[RFC 4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005.
[RFC 4656] Shalunov, S., Teitelbaum, B., Karp, A., Boote, J., and M.
Zeckauskas, "A One-way Active Measurement Protocol
(OWAMP)", RFC 4656, September 2006.
Morton, et al. Standards Track PAGE 35
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.
[RFC 793] Postel, J., "Transmission Control Protocol", STD 7, RFC
793, September 1981.
[RFC 1323] Jacobson, V., Braden, R., and D. Borman, "TCP Extensions
for High Performance", RFC 1323, May 1992.
Morton, et al. Standards Track PAGE 36
RFC 4737 Packet Reordering Metrics November 2006
[RFC 2581] Allman, M., Paxson, V., and W. Stevens, "TCP Congestion
Control ", RFC 2581, April 1999.
[RFC 2679] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
Delay Metric for IPPM", RFC 2679, September 1999.
[RFC 2680] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
Packet Loss Metric for IPPM", RFC 2680, September 1999.
[RFC 2960] 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.
[RFC 3393] Demichelis, C. and P. Chimento, "IP Packet Delay Variation
Metric for IP Performance Metrics (IPPM)", RFC 3393,
November 2002.
[RFC 4340] Kohler, E., Handley, M., and S. Floyd, "Datagram
Congestion Control Protocol (DCCP)", RFC 4340, March 2006.
[RFC 4341] 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 [RFC 2330].
Morton, et al. Standards Track PAGE 37
RFC 4737 Packet Reordering Metrics November 2006
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;
}
Morton, et al. Standards Track PAGE 38
RFC 4737 Packet Reordering Metrics November 2006
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 */
Morton, et al. Standards Track PAGE 39
RFC 4737 Packet Reordering Metrics November 2006
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.
Morton, et al. Standards Track PAGE 40
RFC 4737 Packet Reordering Metrics November 2006
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.
Morton, et al. Standards Track PAGE 41
RFC 4737 Packet Reordering Metrics November 2006
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 */
Morton, et al. Standards Track PAGE 42
RFC 4737 Packet Reordering Metrics November 2006
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.
Morton, et al. Standards Track PAGE 43
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
Copyright © The IETF Trust (2006).
This document is subject to the rights, licenses and restrictions
contained in BCP 78, and except as set forth therein, the authors
retain all their rights.
This document and the information contained herein are provided on an
"AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY, THE IETF TRUST,
AND THE INTERNET ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT
THE USE OF THE INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY
IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR
PURPOSE.
Intellectual Property
The IETF takes no position regarding the validity or scope of any
Intellectual Property Rights or other rights that might be claimed to
pertain to the implementation or use of the technology described in
this document or the extent to which any license under such rights
might or might not be available; nor does it represent that it has
made any independent effort to identify any such rights. Information
on the procedures with respect to rights in RFC documents can be
found in BCP 78 and BCP 79.
Copies of IPR disclosures made to the IETF Secretariat and any
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such proprietary rights by implementers or users of this
specification can be obtained from the IETF on-line IPR repository at
http://www.ietf.org/ipr.
The IETF invites any interested party to bring to its attention any
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Acknowledgement
Funding for the RFC Editor function is currently provided by the
Internet Society.
Morton, et al. Standards Track PAGE 45
Packet Reordering Metrics
RFC TOTAL SIZE: 94699 bytes
PUBLICATION DATE: Thursday, November 23rd, 2006
LEGAL RIGHTS: The IETF Trust (see BCP 78)
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