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IETF RFC 5357
A Two-Way Active Measurement Protocol (TWAMP)
Last modified on Friday, October 3rd, 2008
 Permanent link to RFC 5357
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Network Working Group K. Hedayat
Request for Comments: 5357 Brix Networks
Category: Standards Track R. Krzanowski
Verizon
A. Morton
AT&T Labs
K. Yum
Juniper Networks
J. Babiarz
Nortel Networks
October 2008
A Two-Way Active Measurement Protocol (TWAMP)
 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.
Abstract
The One-way Active Measurement Protocol (OWAMP), specified in RFC
4656, provides a common protocol for measuring one-way metrics
between network devices. OWAMP can be used bi-directionally to
measure one-way metrics in both directions between two network
elements. However, it does not accommodate round-trip or two-way
measurements. This memo specifies a Two-Way Active Measurement
Protocol (TWAMP), based on the OWAMP, that adds two-way or round-trip
measurement capabilities. The TWAMP measurement architecture is
usually comprised of two hosts with specific roles, and this allows
for some protocol simplifications, making it an attractive
alternative in some circumstances.
Hedayat, et al. Standards Track PAGE 1 
RFC 5357 Two-Way Active Measurement Protocol October 2008
Table of Contents
1. Introduction ....................................................2
1.1. Relationship of Test and Control Protocols .................3
1.2. Logical Model ..............................................3
1.3. Pronunciation Guide ........................................4
2. Protocol Overview ...............................................5
3. TWAMP-Control ...................................................6
3.1. Connection Setup ...........................................6
3.2. Integrity Protection .......................................7
3.3. Values of the Accept Field .................................7
3.4. TWAMP-Control Commands .....................................7
3.5. Creating Test Sessions .....................................8
3.6. Send Schedules ............................................10
3.7. Starting Test Sessions ....................................10
3.8. Stop-Sessions .............................................10
3.9. Fetch-Session .............................................12
4. TWAMP-Test .....................................................12
4.1. Sender Behavior ...........................................12
4.1.1. Packet Timings .....................................12
4.1.2. Packet Format and Content ..........................12
4.2. Reflector Behavior ........................................13
4.2.1. TWAMP-Test Packet Format and Content ...............14
5. Implementers' Guide ............................................20
6. Security Considerations ........................................20
7. Acknowledgements ...............................................21
8. IANA Considerations ............................................21
8.1. Registry Specification ....................................22
8.2. Registry Management .......................................22
8.3. Experimental Numbers ......................................22
8.4. Initial Registry Contents .................................22
9. Internationalization Considerations ............................22
Appendix I - TWAMP Light (Informative) ............................23
Normative References ..............................................24
Informative References ............................................24
1. Introduction
The Internet Engineering Task Force (IETF) has completed a Proposed
Standard for the round-trip delay [RFC 2681] metric. The IETF has
also completed a protocol for the control and collection of one-way
measurements, the One-way Active Measurement Protocol (OWAMP)
[RFC 4656]. However, OWAMP does not accommodate round-trip or two-way
measurements.
Two-way measurements are common in IP networks, primarily because
synchronization between local and remote clocks is unnecessary for
round-trip delay, and measurement support at the remote end may be
Hedayat, et al. Standards Track PAGE 2
RFC 5357 Two-Way Active Measurement Protocol October 2008
limited to a simple echo function. However, the most common facility
for round-trip measurements is the ICMP Echo Request/Reply (used by
the ping tool), and issues with this method are documented in Section
2.6 of [RFC 2681]. This memo specifies the Two-Way Active Measurement
Protocol, or TWAMP. TWAMP uses the methodology and architecture of
OWAMP [RFC 4656] to define an open protocol for measurement of two-way
or round-trip metrics (henceforth in this document the term two-way
also signifies round-trip), in addition to the one-way metrics of
OWAMP. TWAMP employs time stamps applied at the echo destination
(reflector) to enable greater accuracy (processing delays can be
accounted for). The TWAMP measurement architecture is usually
comprised of only two hosts with specific roles, and this allows for
some protocol simplifications, making it an attractive alternative to
OWAMP in some circumstances.
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 [RFC 2119].
1.1. Relationship of Test and Control Protocols
Similar to OWAMP [RFC 4656], TWAMP consists of two inter-related
protocols: TWAMP-Control and TWAMP-Test. The relationship of these
protocols is as defined in Section 1.1 of OWAMP [RFC 4656]. TWAMP-
Control is used to initiate, start, and stop test sessions, whereas
TWAMP-Test is used to exchange test packets between two TWAMP
entities.
1.2. Logical Model
The role and definition of the logical entities are as defined in
Section 1.2 of OWAMP [RFC 4656] with the following exceptions:
- The Session-Receiver is called the Session-Reflector in the TWAMP
architecture. The Session-Reflector has the capability to create
and send a measurement packet when it receives a measurement
packet. Unlike the Session-Receiver, the Session-Reflector does
not collect any packet information.
- The Server is an end system that manages one or more TWAMP
sessions, and is capable of configuring per-session state in the
endpoints. However, a Server associated with a Session-Reflector
would not have the capability to return the results of a test
session, and this is a difference from OWAMP.
Hedayat, et al. Standards Track PAGE 3
RFC 5357 Two-Way Active Measurement Protocol October 2008
- The Fetch-Client entity does not exist in the TWAMP architecture,
as the Session-Reflector does not collect any packet information
to be fetched. Consequently, there is no need for the Fetch-
Client.
An example of possible relationship scenarios between these roles is
presented below. In this example, different logical roles are played
on different hosts. Unlabeled links in the figure are unspecified by
this document and may be proprietary protocols.
+----------------+ +-------------------+
| Session-Sender |<-TWAMP-Test-->| Session-Reflector |
+----------------+ +-------------------+
^ ^
| |
| |
| |
| +----------------+<----------------+
| | Server |
| +----------------+
| ^
| |
| TWAMP-Control
| |
v v
+----------------+
| Control-Client |
+----------------+
As in OWAMP [RFC 4656], different logical roles can be played by the
same host. For example, in the figure above, there could actually be
two hosts: one playing the roles of Control-Client and Session-
Sender, and the other playing the roles of Server and Session-
Reflector. This example is shown below.
+-----------------+ +-------------------+
| Control-Client |<--TWAMP-Control-->| Server |
| | | |
| Session-Sender |<--TWAMP-Test----->| Session-Reflector |
+-----------------+ +-------------------+
1.3. Pronunciation Guide
The acronym OWAMP is usually pronounced in two syllables, Oh-wamp.
The acronym TWAMP is also pronounced in two syllables, Tee-wamp.
Hedayat, et al. Standards Track PAGE 4
RFC 5357 Two-Way Active Measurement Protocol October 2008
2. Protocol Overview
The Two-Way Active Measurement Protocol is an open protocol for
measurement of two-way metrics. It is based on OWAMP [RFC 4656] and
adheres to OWAMP's overall architecture and design. The TWAMP-
Control and TWAMP-Test protocols accomplish their testing tasks as
outlined below:
- The Control-Client initiates a TCP connection on TWAMP's well-
known port, and the Server (its role now established) responds
with its Greeting message, indicating the security/integrity
mode(s) it is willing to support.
- The Control-Client responds with the chosen mode of communication
and information supporting integrity protection and encryption, if
the mode requires them. The Server responds to accept the mode
and give its start time. This completes the control-connection
setup.
- The Control-Client requests (and describes) a test session with a
unique TWAMP-Control message. The Server responds with its
acceptance and supporting information. More than one test session
may be requested with additional messages.
- The Control-Client initiates all requested testing with a Start-
Sessions message, and the Server acknowledges.
- The Session-Sender and the Session-Reflector exchange test packets
according to the TWAMP-Test protocol for each active session.
- When appropriate, the Control-Client sends a message to stop all
test sessions.
There are two recognized extension mechanisms in the TWAMP Protocol.
1) The Modes field is used to establish the communication options
during TWAMP-Control Connection Setup.
2) The TWAMP-Control Command Number is another intended extension
mechanism, allowing additional commands to be defined in the
future.
The TWAMP-Control protocol resolves different capability levels
between the Control-Client and Server.
All multi-octet quantities defined in this document are represented
as unsigned integers in network byte order, unless specified
otherwise.
Hedayat, et al. Standards Track PAGE 5
RFC 5357 Two-Way Active Measurement Protocol October 2008
Throughout this memo, the bits marked MBZ (Must Be Zero) MUST be set
to zero by senders and MUST be ignored by receivers.
3. TWAMP-Control
TWAMP-Control is a derivative of the OWAMP-Control for two-way
measurements. All TWAMP-Control messages are similar in format and
follow similar guidelines to those defined in Section 3 of OWAMP
[RFC 4656] with the exceptions outlined in the following sections.
One such exception is the Fetch-Session command, which is not used in
TWAMP.
3.1. Connection Setup
Connection establishment of TWAMP follows the same procedure defined
in Section 3.1 of OWAMP [RFC 4656]. The Modes field is a recognized
extension mechanism in TWAMP, and the current mode values are
identical to those used in OWAMP. The only exception is the well-
known port number for TWAMP-Control. A Client opens a TCP connection
to the Server on well-known port 862. The host that initiates the
TCP connection takes the roles of Control-Client and (in the two-host
implementation) the Session-Sender. The host that acknowledges the
TCP connection accepts the roles of Server and (in the two-host
implementation) the Session-Reflector.
The Control-Client MAY set a desired code point in the Diffserv Code
Point (DSCP) field in the IP header for ALL packets of a specific
control connection. The Server SHOULD use the DSCP of the Control-
Client's TCP SYN in ALL subsequent packets on that connection
(avoiding any ambiguity in case of re-marking).
The possibility exists for Control-Client failure after TWAMP-
Control connection establishment, or the path between the Control-
Client and Server may fail while a connection is in progress. The
Server MAY discontinue any established control connection when no
packet associated with that connection has been received within
SERVWAIT seconds. The Server SHALL suspend monitoring control
connection activity after receiving a Start-Sessions command, and
SHALL resume after receiving a Stop-Sessions command (IF the SERVWAIT
option is supported). Note that the REFWAIT timeout (described
below) covers failures during test sessions, and if REFWAIT expires
on ALL test sessions initiated by a TWAMP-Control connection, then
the SERVWAIT monitoring SHALL resume (as though a Stop-Sessions
command had been received). An implementation that supports the
SERVWAIT timeout SHOULD also implement the REFWAIT timeout. The
default value of SERVWAIT SHALL be 900 seconds, and this waiting time
MAY be configurable. This timeout allows the Server to free up
resources in case of failure.
Hedayat, et al. Standards Track PAGE 6
RFC 5357 Two-Way Active Measurement Protocol October 2008
Both the Server and the Client use the same mappings from KeyIDs to
shared secrets. The Server, being prepared to conduct sessions with
more than one Client, uses KeyIDs to choose the appropriate secret
key; a Client would typically have different secret keys for
different Servers. The shared secret is a passphrase. To maximize
passphrase interoperability, the passphrase character set MUST be
encoded using Appendix B of [RFC 5198] (the ASCII Network Virtual
Terminal Definition). It MUST not contain newlines (any combination
of Carriage-Return (CR) and/or Line-Feed (LF) characters), and
control characters SHOULD be avoided.
3.2. Integrity Protection
Integrity protection of TWAMP follows the same procedure defined in
Section 3.2 of OWAMP [RFC 4656]. As in OWAMP, each HMAC (Hashed
Message Authentication Code) sent covers everything sent in a given
direction between the previous HMAC (but not including it) and the
start of the new HMAC. This way, once encryption is set up, each bit
of the TWAMP-Control connection is authenticated by an HMAC exactly
once.
Note that the Server-Start message (sent by a Server during the
initial control-connection exchanges) does not terminate with an HMAC
field. Therefore, the HMAC in the first Accept-Session message also
covers the Server-Start message and includes the Start-Time field in
the HMAC calculation.
Also, in authenticated and encrypted modes, the HMAC in TWAMP-Control
packets is encrypted.
3.3. Values of the Accept Field
Accept values used in TWAMP are the same as the values defined in
Section 3.3 of OWAMP [RFC 4656].
3.4. TWAMP-Control Commands
TWAMP-Control commands conform to the rules defined in Section 3.4 of
OWAMP [RFC 4656].
The following commands are available for the Control-Client:
Request-TW-Session, Start-Sessions, and Stop-Sessions. The Server
can send specific messages in response to the commands it receives
(as described in the sections that follow).
Note that the OWAMP Request-Session command is replaced by the TWAMP
Request-TW-Session command, and the Fetch-Session command does not
appear in TWAMP.
Hedayat, et al. Standards Track PAGE 7
RFC 5357 Two-Way Active Measurement Protocol October 2008
3.5. Creating Test Sessions
Test session creation follows the same procedure as defined in
Section 3.5 of OWAMP [RFC 4656]. The Request-TW-Session command is
based on the OWAMP Request-Session command, and uses the message
format as described in Section 3.5 of OWAMP, but without the Schedule
Slot Descriptions field(s) and uses only one HMAC. The description
of the Request-TW-Session format follows.
In TWAMP, the first octet is referred to as the Command Number, and
the Command Number is a recognized extension mechanism. Readers are
encouraged to consult the TWAMP-Control Command Number registry to
determine if there have been additional values assigned.
The Command Number value of 5 indicates a Request-TW-Session command,
and the Server MUST interpret this command as a request for a two-way
test session using the TWAMP-Test protocol.
If a TWAMP Server receives an unexpected Command Number, it MUST
respond with the Accept field set to 3 (meaning "Some aspect of
request is not supported") in the Accept-Session message. Command
Numbers that are Forbidden (and possibly numbers that are Reserved)
are unexpected.
In OWAMP, the Conf-Sender field is set to 1 when the Request-Session
message describes a task where the Server will configure a one-way
test packet sender. Likewise, the Conf-Receiver field is set to 1
when the message describes the configuration for a Session-Receiver.
In TWAMP, both endpoints send and receive test packets, with the
Session-Sender first sending and then receiving test packets,
complimented by the Session-Reflector first receiving and then
sending.
Both the Conf-Sender field and Conf-Receiver field MUST be set to 0
since the Session-Reflector will both receive and send packets, and
the roles are established according to which host initiates the TCP
connection for control. The Server MUST interpret any non-zero value
as an improperly formatted command, and MUST respond with the Accept
field set to 3 (meaning "Some aspect of request is not supported") in
the Accept-Session message.
The Session-Reflector in TWAMP does not process incoming test packets
for performance metrics and consequently does not need to know the
number of incoming packets and their timing schedule. Consequently
the Number of Scheduled Slots and Number of Packets MUST be set to 0.
The Sender Port is the UDP port from which TWAMP-Test packets will be
sent and the port to which TWAMP-Test packets will be sent by the
Hedayat, et al. Standards Track PAGE 8
RFC 5357 Two-Way Active Measurement Protocol October 2008
Session-Reflector (the Session-Sender will use the same UDP port to
send and receive packets). The Receiver Port is the desired UDP port
to which TWAMP-Test packets will be sent by the Session-Sender (the
port where the Session-Reflector is asked to receive test packets).
The Receiver Port is also the UDP port from which TWAMP-Test packets
will be sent by the Session-Reflector (the Session-Reflector will use
the same UDP port to send and receive packets).
The Sender Address and Receiver Address fields contain, respectively,
the sender and receiver addresses of the endpoints of the Internet
path over which a TWAMP-Test session is requested. They MAY be set
to 0, in which case the IP addresses used for the Control-Client to
Server TWAMP-Control message exchange MUST be used in the test
packets.
The Session Identifier (SID) is as defined in OWAMP [RFC 4656]. Since
the SID is always generated by the receiving side, the Server
determines the SID, and the SID in the Request-TW-Session message
MUST be set to 0.
The Start Time is as defined in OWAMP [RFC 4656].
The Timeout is interpreted differently from the definition in OWAMP
[RFC 4656]. In TWAMP, Timeout is the interval that the Session-
Reflector MUST wait after receiving a Stop-Sessions message. In case
there are test packets still in transit, the Session-Reflector MUST
reflect them if they arrive within the Timeout interval following the
reception of the Stop-Sessions message. The Session-Reflector MUST
NOT reflect packets that are received beyond the timeout.
Type-P descriptor is as defined in OWAMP [RFC 4656]. The only
capability of this field is to set the Differentiated Services Code
Point (DSCP) as defined in [RFC 2474]. The same value of DSCP MUST be
used in test packets reflected by the Session-Reflector.
Since there are no Schedule Slot Descriptions, the Request-TW-Session
message is completed by MBZ (Must Be Zero) and HMAC fields. This
completes one logical message, referred to as the Request-TW-Session
command.
The Session-Reflector MUST respond to each Request-TW-Session command
with an Accept-Session message as defined in OWAMP [RFC 4656]. When
the Accept field = 0, the Port field confirms (repeats) the port to
which TWAMP-Test packets are sent by the Session-Sender toward the
Session-Reflector. In other words, the Port field indicates the port
number where the Session-Reflector expects to receive packets from
the Session-Sender.
Hedayat, et al. Standards Track PAGE 9
RFC 5357 Two-Way Active Measurement Protocol October 2008
When the requested Receiver Port is not available (e.g., port in
use), the Server at the Session-Reflector MAY suggest an alternate
and available port for this session in the Port field. The Session-
Sender either accepts the alternate port, or composes a new Session-
Request message with suitable parameters. Otherwise, the Server at
the Control-Client uses the Accept field to convey other forms of
session rejection or failure and MUST NOT suggest an alternate port;
in this case, the Port field MUST be set to zero.
3.6. Send Schedules
The send schedule for test packets defined in Section 3.6 of OWAMP
[RFC 4656] is not used in TWAMP. The Control-Client and Session-
Sender MAY autonomously decide the send schedule. The Session-
Reflector SHOULD return each test packet to the Session-Sender as
quickly as possible.
3.7. Starting Test Sessions
The procedure and guidelines for starting test sessions is the same
as defined in Section 3.7 of OWAMP [RFC 4656].
3.8. Stop-Sessions
The procedure and guidelines for stopping test sessions is similar to
that defined in Section 3.8 of OWAMP [RFC 4656]. The Stop-Sessions
command can only be issued by the Control-Client. The message MUST
NOT contain any session description records or skip ranges. The
message is terminated with a single block HMAC to complete the Stop-
Sessions command. Since the TWAMP Stop-Sessions command does not
convey SIDs, it applies to all sessions previously requested and
started with a Start-Sessions command.
Hedayat, et al. Standards Track PAGE 10
RFC 5357 Two-Way Active Measurement Protocol October 2008
Thus, the TWAMP Stop-Sessions command is constructed as follows:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 3 | Accept | MBZ |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Number of Sessions |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| MBZ (8 octets) |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| HMAC (16 octets) |
| |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Above, the Command Number in the first octet (3) indicates that this
is the Stop-Sessions command.
Non-zero Accept values indicate a failure of some sort. Zero values
indicate normal (but possibly premature) completion. The full list
of available Accept values is described in Section 3.3 of [RFC 4656],
"Values of the Accept Field".
If Accept has a non-zero value, results of all TWAMP-Test sessions
spawned by this TWAMP-Control session SHOULD be considered invalid.
If the Accept-Session message was not transmitted at all (for
whatever reason, including failure of the TCP connection used for
TWAMP-Control), the results of all TWAMP-Test sessions spawned by
this TWAMP-Control session MAY be considered invalid.
Number of Sessions indicates the number of sessions that the
Control-Client intends to stop.
Number of Sessions MUST contain the number of send sessions started
by the Control-Client that have not been previously terminated by a
Stop-Sessions command (i.e., the Control-Client MUST account for each
accepted Request-Session). If the Stop-Sessions message does not
account for exactly the number of sessions in progress, then it is to
be considered invalid, the TWAMP-Control connection SHOULD be closed,
and any results obtained considered invalid.
Upon receipt of a TWAMP-Control Stop-Sessions command, the Session-
Reflector MUST discard any TWAMP-Test packets that arrive at the
current time plus the Timeout (in the Request-TW-Session command).
Hedayat, et al. Standards Track PAGE 11
RFC 5357 Two-Way Active Measurement Protocol October 2008
3.9. Fetch-Session
One purpose of TWAMP is measurement of two-way metrics. Two-way
measurement methods do not require packet-level data to be collected
by the Session-Reflector (such as sequence number, timestamp, and
Time to Live (TTL)) because this data is communicated in the
"reflected" test packets. As such, the protocol does not require the
retrieval of packet-level data from the Server and the OWAMP Fetch-
Session command is not used in TWAMP.
4. TWAMP-Test
The TWAMP-Test protocol is similar to the OWAMP-test protocol
[RFC 4656] with the exception that the Session-Reflector transmits
test packets to the Session-Sender in response to each test packet it
receives. TWAMP defines two different test packet formats, one for
packets transmitted by the Session-Sender and one for packets
transmitted by the Session-Reflector. As with OWAMP-test protocol
[RFC 4656], there are three modes: unauthenticated, authenticated, and
encrypted.
4.1. Sender Behavior
The sender behavior is determined by the configuration of the
Session-Sender and is not defined in this standard. Further, the
Session-Reflector does not need to know the Session-Sender behavior
to the degree of detail as needed in OWAMP [RFC 4656]. Additionally,
the Session-Sender collects and records the necessary information
provided from the packets transmitted by the Session-Reflector for
measuring two-way metrics. The information recording based on the
packet(s) received by the Session-Sender is implementation dependent.
4.1.1. Packet Timings
Since the send schedule is not communicated to the Session-Reflector,
there is no need for a standardized computation of packet timing.
Regardless of any scheduling delays, each packet that is actually
sent MUST have the best possible approximation of its real time of
departure as its timestamp (in the packet).
4.1.2. Packet Format and Content
The Session-Sender packet format and content follow the same
procedure and guidelines as defined in Section 4.1.2 of OWAMP
[RFC 4656] (with the exception of the reference to the send schedule).
Hedayat, et al. Standards Track PAGE 12
RFC 5357 Two-Way Active Measurement Protocol October 2008
Note that the Reflector test packet formats are larger than the
Sender's formats. The Session-Sender MAY append sufficient Packet
Padding to allow the same IP packet payload lengths to be used in
each direction of transmission (this is usually desirable). To
compensate for the Reflector's larger test packet format, the Sender
appends at least 27 octets of padding in unauthenticated mode, and at
least 56 octets in authenticated and encrypted modes.
4.2. Reflector Behavior
TWAMP requires the Session-Reflector to transmit a packet to the
Session-Sender in response to each packet it receives.
As packets are received, the Session-Reflector will do the following:
- Timestamp the received packet. Each packet that is actually
received MUST have the best possible approximation of its real
time of arrival entered as its Received Timestamp (in the packet).
- In authenticated or encrypted mode, decrypt the appropriate
sections of the packet body (first block (16 octets) for
authenticated, 96 octets for encrypted), and then check integrity
of sections covered by the HMAC.
- Copy the packet sequence number into the corresponding reflected
packet to the Session-Sender.
- Extract the Sender TTL value from the TTL/Hop Limit value of
received packets. Session-Reflector implementations SHOULD fetch
the TTL/Hop Limit value from the IP header of the packet,
replacing the value of 255 set by the Session-Sender. If an
implementation does not fetch the actual TTL value (the only good
reason not to do so is an inability to access the TTL field of
arriving packets), it MUST set the Sender TTL value as 255.
- In authenticated and encrypted modes, the HMAC MUST be calculated
first, then the appropriate portion of the packet body is
encrypted.
- Transmit a test packet to the Session-Sender in response to every
received packet. The response MUST be generated as immediately as
possible. The format and content of the test packet is defined in
Section 4.2.1. Prior to the transmission of the test packet, the
Session-Reflector MUST enter the best possible approximation of
its actual sending time as its Timestamp (in the packet). This
permits the determination of the elapsed time between the
reception of the packet and its transmission.
Hedayat, et al. Standards Track PAGE 13
RFC 5357 Two-Way Active Measurement Protocol October 2008
- Packets not received within the Timeout (following the Stop-
Sessions command) MUST be ignored by the Reflector. The Session-
Reflector MUST NOT generate a test packet to the Session-Sender
for packets that are ignored.
The possibility exists for Session-Sender failure during a session,
or the path between the Session-Sender and Session-Reflector may fail
while a test session is in progress. The Session-Reflector MAY
discontinue any session that has been started when no packet
associated with that session has been received for REFWAIT seconds.
The default value of REFWAIT SHALL be 900 seconds, and this waiting
time MAY be configurable. This timeout allows a Session-Reflector to
free up resources in case of failure.
4.2.1. TWAMP-Test Packet Format and Content
The Session-Reflector MUST transmit a packet to the Session-Sender in
response to each packet received. The Session-Reflector SHOULD
transmit the packets as immediately as possible. The Session-
Reflector SHOULD set the TTL in IPv4 (or Hop Limit in IPv6) in the
UDP packet to 255.
The test packet will have the necessary information for calculating
two-way metrics by the Session-Sender. The format of the test packet
depends on the mode being used. The two formats are presented below.
Hedayat, et al. Standards Track PAGE 14
RFC 5357 Two-Way Active Measurement Protocol October 2008
For unauthenticated mode:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sequence Number |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Timestamp |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Error Estimate | MBZ |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Receive Timestamp |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender Sequence Number |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender Timestamp |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender Error Estimate | MBZ |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender TTL | |
+-+-+-+-+-+-+-+-+ +
| |
. .
. Packet Padding .
. .
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Hedayat, et al. Standards Track PAGE 15
RFC 5357 Two-Way Active Measurement Protocol October 2008
For authenticated and encrypted modes:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sequence Number |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| MBZ (12 octets) |
| |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Timestamp |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Error Estimate | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| MBZ (6 octets) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Receive Timestamp |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| MBZ (8 octets) |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender Sequence Number |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| MBZ (12 octets) |
| |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender Timestamp |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender Error Estimate | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| MBZ (6 octets) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sender TTL | |
+-+-+-+-+-+-+-+-+ +
| |
| |
| MBZ (15 octets) |
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| HMAC (16 octets) |
| |
| |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-|
Hedayat, et al. Standards Track PAGE 16
RFC 5357 Two-Way Active Measurement Protocol October 2008
| |
. .
. Packet Padding .
. .
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Note that all timestamps have the same format as OWAMP [RFC 4656] as
follows:
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Integer part of seconds |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Fractional part of seconds |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Sequence Number is the sequence number of the test packet according
to its transmit order. It starts with zero and is incremented by one
for each subsequent packet. The Sequence Number generated by the
Session-Reflector is independent from the sequence number of the
arriving packets.
Timestamp and Error Estimate are the Session-Reflector's transmit
timestamp and error estimate for the reflected test packet,
respectively. The format of all timestamp and error estimate fields
follow the definition and formats defined by OWAMP, Section 4.1.2 in
[RFC 4656].
Sender Timestamp and Sender Error Estimate are exact copies of the
timestamp and error estimate from the Session-Sender test packet that
corresponds to this test packet.
Sender TTL is 255 when transmitted by the Session-Sender. Sender TTL
is set to the Time To Live (or Hop Count) value of the received
packet from the IP packet header when transmitted by the Session-
Reflector.
Receive Timestamp is the time the test packet was received by the
reflector. The difference between Timestamp and Receive Timestamp is
the amount of time the packet was in transition in the Session-
Reflector. The Error Estimate associated with the Timestamp field
also applies to the Receive Timestamp.
Sender Sequence Number is a copy of the Sequence Number of the packet
transmitted by the Session-Sender that caused the Session-Reflector
to generate and send this test packet.
Hedayat, et al. Standards Track PAGE 17
RFC 5357 Two-Way Active Measurement Protocol October 2008
The HMAC field in TWAMP-Test packets covers the same fields as the
Advanced Encryption Standard (AES) encryption. Thus, in
authenticated mode, HMAC covers the first block (16 octets); in
encrypted mode, HMAC covers the first six blocks (96 octets). In
TWAMP-Test, the HMAC field MUST NOT be encrypted.
Packet Padding in TWAMP-Test SHOULD be pseudo-random (it MUST be
generated independently of any other pseudo-random numbers mentioned
in this document). However, implementations MUST provide a
configuration parameter, an option, or a different means of making
Packet Padding consist of all zeros. Packet Padding MUST NOT be
covered by the HMAC and MUST NOT be encrypted.
The minimum data segment length of TWAMP-Test packets in
unauthenticated mode is 41 octets, and 104 octets in both
authenticated mode and encrypted modes.
Note that the Session-Reflector Test packet formats are larger than
the Sender's formats. The Session-Reflector SHOULD reduce the length
of the Sender's Packet Padding to achieve equal IP packet payload
lengths in each direction of transmission, when sufficient padding is
present. The Session-Reflector MAY re-use the Sender's Packet
Padding (since the requirements for padding generation are the same
for each), and in this case the Session-Reflector SHOULD truncate the
padding such that the highest-number octets are discarded.
In unauthenticated mode, encryption or authentication MUST NOT be
applied.
The TWAMP-Test packet layout is identical in authenticated and
encrypted modes. The encryption operation for a Session-Sender
packet follows the same rules of Session-Sender packets as defined in
OWAMP section 4.1.2 of [RFC 4656].
The main difference between authenticated mode and encrypted mode is
the portion of the test packets that are covered by HMAC and
encrypted. Authenticated mode permits the timestamp to be fetched
after a portion of the packet is encrypted, but in encrypted mode all
the sequence numbers and timestamps are fetched before encryption to
provide maximum data-integrity protection.
In authenticated mode, only the sequence number in the first block is
encrypted, and the subsequent timestamps and sequence numbers are
sent in clear text. Sending the timestamp in clear text allows one
to reduce the time between when a timestamp is obtained by a
Session-Reflector and when that packet is sent out. This potentially
improves the timestamp accuracy, because the sequence number can be
encrypted before the timestamp is fetched.
Hedayat, et al. Standards Track PAGE 18
RFC 5357 Two-Way Active Measurement Protocol October 2008
In encrypted mode, the reflector MUST fetch the timestamps, generate
the HMAC, and encrypt the packet, then send it.
Obtaining the keys and encryption methods follows the same procedure
as OWAMP as described below. Each TWAMP-Test session has two keys,
an AES Session-key and an HMAC Session-key, and the keys are derived
from the TWAMP-Control keys and the SID.
The TWAMP-Test AES Session-key is obtained as follows: the TWAMP-
Control AES Session-key (the same AES Session-key as used for the
corresponding TWAMP-Control session) is encrypted with the 16-octet
session identifier (SID) as the key, using a single-block AES-ECB
encryption. The result is the TWAMP-Test AES Session-key to be used
in encrypting (and decrypting) the packets of the particular TWAMP-
Test session. Note that the TWAMP-Test AES Session-key, TWAMP-
Control AES Session-key, and the SID are all comprised of 16 octets.
The TWAMP-Test HMAC Session-key is obtained as follows: the TWAMP-
Control HMAC Session-key (the same HMAC Session-key as used for the
corresponding TWAMP-Control session) is encrypted using AES-CBC
(Cipher Block Chaining) with the 16-octet session identifier (SID) as
the key. This is a two-block CBC encryption that is always performed
with IV=0. Note that the TWAMP-Test HMAC Session-key and TWAMP-
Control HMAC Session-key are comprised of 32 octets, while the SID is
16 octets.
In authenticated mode, the first block (16 octets) of each TWAMP-Test
packet is encrypted using the AES Electronic Codebook (ECB) mode.
This mode does not involve any chaining, and lost, duplicated, or
reordered packets do not cause problems with deciphering any packet
in a TWAMP-Test session.
In encrypted mode, the first six blocks (96 octets) are encrypted
using AES-CBC mode. The AES Session-key to use is obtained in the
same way as the key for authenticated mode. Each TWAMP-Test packet
is encrypted as a separate stream, with just one chaining operation;
chaining does not span multiple packets so that lost, duplicated, or
reordered packets do not cause problems. The initialization vector
for the CBC encryption is a value with all bits equal to zero.
Implementation Note: Naturally, the key schedule for each TWAMP-Test
session MUST be set up at most once per session, not once per packet.
Hedayat, et al. Standards Track PAGE 19
RFC 5357 Two-Way Active Measurement Protocol October 2008
5. Implementers' Guide
This section serves as guidance to implementers of TWAMP. The
example architecture presented here is not a requirement. Similar to
OWAMP [RFC 4656], TWAMP is designed with enough flexibility to allow
different architectures that suit multiple system requirements.
In this example, the roles of Control-Client and Session-Sender are
implemented in one host referred to as the controller, and the roles
of Server and Session-Reflector are implemented in another host
referred to as the responder.
controller responder
+-----------------+ +-------------------+
| Control-Client |<--TWAMP-Control-->| Server |
| | | |
| Session-Sender |<--TWAMP-Test----->| Session-Reflector |
+-----------------+ +-------------------+
This example provides an architecture that supports the full TWAMP
standard. The controller establishes the test session with the
responder through the TWAMP-Control protocol. After the session is
established, the controller transmits test packets to the responder.
The responder follows the Session-Reflector behavior of TWAMP as
described in Section 4.2.
Appendix I provides an example for purely informational purposes. It
suggests an incremental path to adopting TWAMP, by implementing the
TWAMP-Test protocol first.
6. Security Considerations
Fundamentally, TWAMP and OWAMP use the same protocol for
establishment of Control and Test procedures. The main difference
between TWAMP and OWAMP is the Session-Reflector behavior in TWAMP
vs. the Session-Receiver behavior in OWAMP. This difference in
behavior does not introduce any known security vulnerabilities that
are not already addressed by the security features of OWAMP. The
entire security considerations of OWAMP [RFC 4656] applies to TWAMP.
The Server-Greeting message (defined in OWAMP, Section 3.1 of
[RFC 4656]) includes a Count field to specify the iteration counter
used in PKCS #5 to generate keys from shared secrets. OWAMP
recommends a lower limit of 1024 iterations, but no upper limit. The
Count field provides an opportunity for a denial-of-service (DOS)
attack because it is 32 bits long. If an attacking system set the
maximum value in Count (2**32), then the system under attack would
stall for a significant period of time while it attempts to generate
Hedayat, et al. Standards Track PAGE 20
RFC 5357 Two-Way Active Measurement Protocol October 2008
keys. Therefore, TWAMP-compliant systems SHOULD have a configuration
control to limit the maximum Count value. The default maximum Count
value SHOULD be 32768. As suggested in OWAMP, this value MAY be
increased when greater computing power becomes common. If a
Control-Client receives a Server-Greeting message with Count greater
that its maximum configured value, it SHOULD close the control
connection.
7. Acknowledgements
We would like to thank Nagarjuna Venna, Sharee McNab, Nick Kinraid,
Stanislav Shalunov, Matt Zekauskas, Walt Steverson, Jeff Boote,
Murtaza Chiba, and Kevin Earnst for their comments, suggestions,
reviews, helpful discussion, and proof-reading. Lars Eggert, Sam
Hartman, and Tim Polk contributed very useful AD-level reviews, and
the authors thank them for their contributions to the memo.
8. IANA Considerations
IANA has allocated a well-known TCP port number (861) for the OWAMP-
Control part of the OWAMP [RFC 4656] protocol.
...
owamp-control 861/tcp OWAMP-Control
owamp-control 861/udp OWAMP-Control
# [RFC 4656]
IANA has also allocated a well-known TCP/UDP port number for the
TWAMP-Control protocol.
...
twamp-control 862/tcp Two-way Active Measurement Protocol
(TWAMP) Control
twamp-control 862/udp Two-way Active Measurement Protocol
(TWAMP) Control
# [RFC 5357]
# 863-872 Unassigned
Since TWAMP adds an additional Control command beyond the OWAMP-
Control specification and describes behavior when this control
command is used, IANA has created a registry for the TWAMP Command
Number field. The field is not explicitly named in [RFC 4656] but is
called out for each command. This field is a recognized extension
mechanism for TWAMP.
Hedayat, et al. Standards Track PAGE 21
RFC 5357 Two-Way Active Measurement Protocol October 2008
8.1. Registry Specification
IANA has created a TWAMP-Control Command Number registry. TWAMP-
Control commands are specified by the first octet in OWAMP-Control
messages as shown in Section 3.5 of [RFC 4656], and modified by this
document. Thus, this registry may contain sixteen possible values.
8.2. Registry Management
Because the registry may only contain sixteen values, and because
OWAMP and TWAMP are IETF protocols, this registry must only be
updated by "IETF Consensus" as specified in [RFC 5226] -- an RFC
documenting the use that is approved by the IESG. We expect that new
values will be assigned as monotonically increasing integers in the
range [0-15], unless there is a good reason to do otherwise.
8.3. Experimental Numbers
[RFC 3692] recommends allocating an appropriate number of values for
experimentation and testing. It is not clear to the authors exactly
how many numbers might be useful in this space, or if it would be
useful that they were easily distinguishable or at the "high end" of
the number range. Two might be useful, say one for session control,
and one for session fetch. On the other hand, a single number would
allow for unlimited extension, because the format of the rest of the
message could be tailored, with allocation of other numbers done once
usefulness has been proven. Thus, this document allocates one number
(6) as designated for experimentation and testing.
8.4. Initial Registry Contents
TWAMP-Control Command Number Registry
Value Description Semantics Definition
0 Reserved
1 Forbidden
2 Start-Sessions RFC 4656, Section 3.7
3 Stop-Sessions RFC 4656, Section 3.8
4 Reserved
5 Request-TW-Session this document, Section 3.5
6 Experimentation undefined, see Section 8.3.
9. Internationalization Considerations
The protocol does not carry any information in a natural language,
with the possible exception of the KeyID in TWAMP-Control, which is
encoded in UTF-8 [RFC 3629, RFC 5198].
Hedayat, et al. Standards Track PAGE 22
RFC 5357 Two-Way Active Measurement Protocol October 2008
Appendix I - TWAMP Light (Informative)
In this example, the roles of Control-Client, Server, and Session-
Sender are implemented in one host referred to as the controller, and
the role of Session-Reflector is implemented in another host referred
to as the responder.
controller responder
+-----------------+ +-------------------+
| Server |<----------------->| |
| Control-Client | | Session-Reflector |
| Session-Sender |<--TWAMP-Test----->| |
+-----------------+ +-------------------+
This example provides a simple architecture for responders where
their role will be to simply act as light test points in the network.
The controller establishes the test session with the Server through
non-standard means. After the session is established, the controller
transmits test packets to the responder. The responder follows the
Session-Reflector behavior of TWAMP as described in section 4.2 with
the following exceptions.
In the case of TWAMP Light, the Session-Reflector does not
necessarily have knowledge of the session state. IF the Session-
Reflector does not have knowledge of the session state, THEN the
Session-Reflector MUST copy the Sequence Number of the received
packet to the Sequence Number field of the reflected packet. The
controller receives the reflected test packets and collects two-way
metrics. This architecture allows for collection of two-way metrics.
This example eliminates the need for the TWAMP-Control protocol, and
assumes that the Session-Reflector is configured and communicates its
configuration with the Server through non-standard means. The
Session-Reflector simply reflects the incoming packets back to the
controller while copying the necessary information and generating
sequence number and timestamp values per Section 4.2.1. TWAMP Light
introduces some additional security considerations. The non-standard
means to control the responder and establish test sessions SHOULD
offer the features listed below.
The non-standard responder control protocol SHOULD have an
authenticated mode of operation. The responder SHOULD be
configurable to accept only authenticated control sessions.
The non-standard responder control protocol SHOULD have a means to
activate the authenticated and encrypted modes of the TWAMP-Test
protocol.
Hedayat, et al. Standards Track PAGE 23
RFC 5357 Two-Way Active Measurement Protocol October 2008
When the TWAMP Light test sessions operate in authenticated or
encrypted mode, the Session-Reflector MUST have some mechanism for
generating keys (because the TWAMP-Control protocol normally plays a
role in this process, but is not present here). The specification of
the key generation mechanism is beyond the scope of this memo.
Normative References
[RFC 4656] Shalunov, S., Teitelbaum, B., Karp, A., Boote, J., and M.
Zekauskas, "A One-way Active Measurement Protocol (OWAMP)",
RFC 4656, September 2006.
[RFC 2681] Almes, G., Kalidindi, S., and M. Zekauskas, "A Round-trip
Delay Metric for IPPM", RFC 2681, September 1999.
[RFC 2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC 2474] Nichols, K., Blake, S., Baker, F., and D. Black,
"Definition of the Differentiated Services Field (DS Field)
in the IPv4 and IPv6 Headers", RFC 2474, December 1998.
[RFC 5226] Narten, T. and H. Alvestrand, "Guidelines for Writing an
IANA Considerations Section in RFCs", BCP 26, RFC 5226, May
2008.
[RFC 3629] Yergeau, F., "UTF-8, a transformation format of ISO 10646",
STD 63, RFC 3629, November 2003.
[RFC 5198] Klensin, J. and M. Padlipsky, "Unicode Format for Network
Interchange", RFC 5198, March 2008.
Informative References
[RFC 3692] Narten, T., "Assigning Experimental and Testing Numbers
Considered Useful", BCP 82, RFC 3692, January 2004.
Hedayat, et al. Standards Track PAGE 24
RFC 5357 Two-Way Active Measurement Protocol October 2008
Authors' Addresses
Kaynam Hedayat
Brix Networks
285 Mill Road
Chelmsford, MA 01824
USA
EMail: khedayat@brixnet.com
URI: http://www.brixnet.com/
Roman M. Krzanowski, Ph.D.
Verizon
500 Westchester Ave.
White Plains, NY
USA
EMail: roman.krzanowski@verizon.com
URI: http://www.verizon.com/
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
URI: http://home.comcast.net/~acmacm/
Kiho Yum
Juniper Networks
1194 Mathilda Ave.
Sunnyvale, CA
USA
EMail: kyum@juniper.net
URI: http://www.juniper.com/
Jozef Z. Babiarz
Nortel Networks
3500 Carling Avenue
Ottawa, Ont K2H 8E9
Canada
Email: babiarz@nortel.com
URI: http://www.nortel.com/
Hedayat, et al. Standards Track PAGE 25
RFC 5357 Two-Way Active Measurement Protocol October 2008
Full Copyright Statement
Copyright © The IETF Trust (2008).
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
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OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF
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Hedayat, et al. Standards Track PAGE 26
A Two-Way Active Measurement Protocol (TWAMP)
RFC TOTAL SIZE: 61960 bytes
PUBLICATION DATE: Friday, October 3rd, 2008
LEGAL RIGHTS: The IETF Trust (see BCP 78)
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