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Versions: (draft-floyd-rfc3448bis) 00 01 02 03 04 05 06 RFC 5348

Internet Engineering Task Force                               M. Handley
INTERNET-DRAFT                                 University College London
draft-ietf-dccp-rfc3448bis-00.txt                               S. Floyd
Expires: April 2007                                                 ICIR
                                                               J. Padhye
                                                               Microsoft
                                                               J. Widmer
                                                  University of Mannheim
                                                         13 October 2006


                   TCP Friendly Rate Control (TFRC):
                         Protocol Specification


Status of this Memo

    By submitting this Internet-Draft, each author represents that any
    applicable patent or other IPR claims of which he or she is aware
    have been or will be disclosed, and any of which he or she becomes
    aware will be disclosed, in accordance with Section 6 of BCP 79.

    Internet-Drafts are working documents of the Internet Engineering
    Task Force (IETF), its areas, and its working groups.  Note that
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    Drafts.

    Internet-Drafts are draft documents valid for a maximum of six
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    reference material or to cite them other than as "work in progress."

    The list of current Internet-Drafts can be accessed at
    http://www.ietf.org/ietf/1id-abstracts.txt.

    The list of Internet-Draft Shadow Directories can be accessed at
    http://www.ietf.org/shadow.html.

    This Internet-Draft will expire on April 2007.

Abstract

    This document specifies TCP-Friendly Rate Control (TFRC).  TFRC is a
    congestion control mechanism for unicast flows operating in a best-
    effort Internet environment.  It is reasonably fair when competing



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    for bandwidth with TCP flows, but has a much lower variation of
    throughput over time compared with TCP, making it more suitable for
    applications such as telephony or streaming media where a relatively
    smooth sending rate is of importance.















































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Table of Contents

    1. Introduction ...................................................6
    2. Conventions ....................................................7
    3. Protocol Mechanism .............................................7
       3.1. TCP Throughput Equation ...................................8
       3.2. Packet Contents ...........................................9
            3.2.1. Data Packets .......................................9
            3.2.2. Feedback Packets ..................................10
    4. Data Sender Protocol ..........................................11
       4.1. Measuring the Segment Size ...............................11
       4.2. Sender Initialization ....................................12
       4.3. Sender behavior when a feedback packet is received .......13
       4.4. Expiration of nofeedback timer ...........................14
       4.5. Sending a packet after an idle period ....................15
       4.6. Preventing Oscillations ..................................15
       4.7. Scheduling of Packet Transmissions .......................16
    5. Calculation of the Loss Event Rate (p) ........................17
       5.1. Detection of Lost or Marked Packets ......................17
       5.2. Translation from Loss History to Loss Events .............18
       5.3. Inter-loss Event Interval ................................19
       5.4. Average Loss Interval ....................................19
       5.5. History Discounting ......................................20
    6. Data Receiver Protocol ........................................23
       6.1. Receiver behavior when a data packet is received .........23
       6.2. Expiration of feedback timer .............................23
       6.3. Receiver initialization ..................................24
            6.3.1. Initializing the Loss History after the First Loss
            Event ....................................................25
    7. Sender-based Variants .........................................26
    8. Implementation Issues .........................................26
    9. Changes from RFC 3448 .........................................27
    10. Security Considerations ......................................28
    11. IANA Considerations ..........................................29
    12. Acknowledgments ..............................................29
    13. Normative References .........................................29
    14. Informational References .....................................29
    15. Authors' Addresses ...........................................30
    Full Copyright Statement .........................................31
    Intellectual Property ............................................31











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    NOTE TO RFC EDITOR: PLEASE DELETE THIS NOTE UPON PUBLICATION.

     Changes from draft-floyd-rfc3448bis-00.txt:

     * Name change to draft-ietf-dccp-rfc3448bis-00.txt.

     Changes from RFC 3448:

     * Incorporated changes in the RFC 3448 errata:

       -  "If the sender does not receive a feedback report for
          four round trip times, it cuts its sending rate in half."
          ("Two" changed to "four", for consistency with the rest
          of the document.  Reported by Joerg Widmer).

       - "If the nofeedback timer expires when the sender does not
         yet have an RTT sample, and has not yet received any
         feedback from the receiver, or when p == 0,..."
         (Added "or when p == 0,", reported by Wim Heirman).

       - In Section 5.5, changed:
           for (i = 1 to n) { DF_i = 1; }
         to:
           for (i = 0 to n) { DF_i = 1; }
         Reported by Michele R.

     * Changed RFC 3448 to correspond to the larger initial windows
       specified in RFC 3390.  This includes the following:

       - Incorporated Section 5.1 from [RFC4342], saying that
         when reducing the sending rate after an idle period, don't
         reduce the sending rate below the initial sending rate.

       - Change for a datalimited sender:
         When the sender has been datalimited, the sender doesn't
         let the receive rate limit it to a sending rate less than
         the initial rate.

       - Small change to slow-start:
         Changed so that for the first feedback packet received,
         or for the first feedback packet received after an idle
         period, the receive rate is not used to limit the
         sending rate.  This is because the receiver might not yet
         have seen an entire window of data.

     * Clarified how the average loss interval is calculated when
       the receiver has not yet seen eight loss intervals.




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     * Discussed more about estimating the average segment size:

       - For initializing the loss history after the first loss event,
         either the receiver knows the sender's value for s, or
         the receiver uses the throughput equation for X_pps and does
         not need to know an estimate for s.

       - Added a discussion about estimating the average segment size
         s in Section 4.1 on "Measuring the Segment Size".

       - Changed "packet size" to "segment size".

     * Specified the receiver's initialization of the feedback timer
       when the first data packet doesn't have an estimate of the
       RTT.  From feedback from Dado Colussi.

     * Added, the procedure for sending receiver feedback packets when
       a coarse-grained timestamp is used.   From RFC 4243.

     * Specified the procedure for initializing the loss history then
       the first data packet sent is lost or ECN-marked.   *** TODO ***.

    END OF NOTE TO RFC EDITOR.




























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1.  Introduction

    This document specifies TCP-Friendly Rate Control (TFRC).  TFRC is a
    congestion control mechanism designed for unicast flows operating in
    an Internet environment and competing with TCP traffic [FHPW00].
    Instead of specifying a complete protocol, this document simply
    specifies a congestion control mechanism that could be used in a
    transport protocol such as DCCP (Datagram Congestion Control
    Protocol) [RFC4340], in an application incorporating end-to-end
    congestion control at the application level, or in the context of
    endpoint congestion management [BRS99]. This document does not
    discuss packet formats or reliability.  Implementation-related
    issues are discussed only briefly, in Section 8.

    TFRC is designed to be reasonably fair when competing for bandwidth
    with TCP flows, where a flow is "reasonably fair" if its sending
    rate is generally within a factor of two of the sending rate of a
    TCP flow under the same conditions.  However, TFRC has a much lower
    variation of throughput over time compared with TCP, which makes it
    more suitable for applications such as telephony or streaming media
    where a relatively smooth sending rate is of importance.

    The penalty of having smoother throughput than TCP while competing
    fairly for bandwidth is that TFRC responds slower than TCP to
    changes in available bandwidth.  Thus TFRC should only be used when
    the application has a requirement for smooth throughput, in
    particular, avoiding TCP's halving of the sending rate in response
    to a single packet drop.  For applications that simply need to
    transfer as much data as possible in as short a time as possible we
    recommend using TCP, or if reliability is not required, using an
    Additive-Increase, Multiplicative-Decrease (AIMD) congestion control
    scheme with similar parameters to those used by TCP.

    TFRC is designed for applications that use a fixed segment size, and
    vary their sending rate in packets per second in response to
    congestion.  TFRC can also be used by applications that don't have a
    fixed segment size, but where the segment size varies according to
    the needs of the application (e.g., video applications).

    Some applications (e.g., some audio applications) require a fixed
    interval of time between packets and vary their segment size instead
    of their packet rate in response to congestion.  The congestion
    control mechanism in this document is not designed for those
    applications; TFRC-SP (Small-Packet TFRC) is a variant of TFRC for
    applications that have a fixed sending rate in packets per second
    but either use small packets, or vary their packet size in response
    to congestion.  TFRC-SP will be specified in a later document.




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    This document specifies TFRC as a receiver-based mechanism, with the
    calculation of the congestion control information (i.e., the loss
    event rate) in the data receiver rather in the data sender.  This is
    well-suited to an application where the sender is a large server
    handling many concurrent connections, and the receiver has more
    memory and CPU cycles available for computation.  In addition, a
    receiver-based mechanism is more suitable as a building block for
    multicast congestion control.  However, it is also possible to
    implement TFRC in sender-based variants, as allowed in DCCP's
    Congestion Control ID 3 (CCID 3) [RFC4342].

2.  Conventions

    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.

3.  Protocol Mechanism

    For its congestion control mechanism, TFRC directly uses a
    throughput equation for the allowed sending rate as a function of
    the loss event rate and round-trip time.  In order to compete fairly
    with TCP, TFRC uses the TCP throughput equation, which roughly
    describes TCP's sending rate as a function of the loss event rate,
    round-trip time, and segment size.  We define a loss event as one or
    more lost or marked packets from a window of data, where a marked
    packet refers to a congestion indication from Explicit Congestion
    Notification (ECN) [RFC3168].

    Generally speaking, TFRC's congestion control mechanism works as
    follows:

    o   The receiver measures the loss event rate and feeds this
        information back to the sender.

    o   The sender also uses these feedback messages to measure the
        round-trip time (RTT).

    o   The loss event rate and RTT are then fed into TFRC's throughput
        equation, giving the acceptable transmit rate.

    o   The sender then adjusts its transmit rate to match the
        calculated rate.

    The dynamics of TFRC are sensitive to how the measurements are
    performed and applied.  We recommend specific mechanisms below to
    perform and apply these measurements.  Other mechanisms are
    possible, but it is important to understand how the interactions



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    between mechanisms affect the dynamics of TFRC.

3.1.  TCP Throughput Equation

    Any realistic equation giving TCP throughput as a function of loss
    event rate and RTT should be suitable for use in TFRC.  However, we
    note that the TCP throughput equation used must reflect TCP's
    retransmit timeout behavior, as this dominates TCP throughput at
    higher loss rates.  We also note that the assumptions implicit in
    the throughput equation about the loss event rate parameter have to
    be a reasonable match to how the loss rate or loss event rate is
    actually measured.  While this match is not perfect for the
    throughput equation and loss rate measurement mechanisms given
    below, in practice the assumptions turn out to be close enough.

    The throughput equation we currently recommend for TFRC is a
    slightly simplified version of the throughput equation for Reno TCP
    from [PFTK98]. Ideally we'd prefer a throughput equation based on
    SACK TCP, but no one has yet derived the throughput equation for
    SACK TCP, and from both simulations and experiments, the differences
    between the two equations are relatively minor.

    The throughput equation is:

                                       s
         X =  ----------------------------------------------------------
              R*sqrt(2*b*p/3) + (t_RTO * (3*sqrt(3*b*p/8) * p * (1+32*p^2)))


    Where:

        X is the transmit rate in bytes/second.

        s is the segment size in bytes.

        R is the round trip time in seconds.

        p is the loss event rate, between 0 and 1.0, of the number of
        loss events as a fraction of the number of packets transmitted.

        t_RTO is the TCP retransmission timeout value in seconds.

        b is the number of packets acknowledged by a single TCP
        acknowledgement.

    We further simplify this by setting t_RTO = 4*R.  A more accurate
    calculation of t_RTO is possible, but experiments with the current
    setting have resulted in reasonable fairness with existing TCP



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    implementations [W00]. Another possibility would be to set t_RTO =
    max(4R, one second), to match the recommended minimum of one second
    on the RTO [RFC2988].

    Many current TCP connections use delayed acknowledgements, sending
    an acknowledgement for every two data packets received, and thus
    have a sending rate modeled by b = 2.  However, TCP is also allowed
    to send an acknowledgement for every data packet, and this would be
    modeled by b = 1.  Because many TCP implementations do not use
    delayed acknowledgements, we recommend b = 1.

    In future, different TCP equations may be substituted for this
    equation.  The requirement is that the throughput equation be a
    reasonable approximation of the sending rate of TCP for conformant
    TCP congestion control.

    The throughput equation can also be expressed as

         X =  X_pps * s ,

    with X_pps, the sending rate in packets per second, given as

                                      1
    X_pps =  --------------------------------------------------------
             R*sqrt(2*b*p/3) + (t_RTO*(3*sqrt(3*b*p/8)*p*(1+32*p^2)))


    The parameters s (segment size), p (loss event rate) and R (RTT)
    need to be measured or calculated by a TFRC implementation.  The
    measurement of s is specified in Section 4.1, measurement of R is
    specified in Section 4.3, and measurement of p is specified in
    Section 5. In the rest of this document all data rates are measured
    in bytes/second.

3.2.  Packet Contents

    Before specifying the sender and receiver functionality, we describe
    the contents of the data packets sent by the sender and feedback
    packets sent by the receiver.  As TFRC will be used along with a
    transport protocol, we do not specify packet formats, as these
    depend on the details of the transport protocol used.


3.2.1.  Data Packets

    Each data packet sent by the data sender contains the following
    information:




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    o   A sequence number. This number is incremented by one for each
        data packet transmitted.  The field must be sufficiently large
        that it does not wrap causing two different packets with the
        same sequence number to be in the receiver's recent packet
        history at the same time.

    o   A timestamp indicating when the packet is sent. We denote by
        ts_i the timestamp of the packet with sequence number i.  The
        resolution of the timestamp should typically be measured in
        milliseconds.
        This timestamp is used by the receiver to determine which losses
        belong to the same loss event.  The timestamp is also echoed by
        the receiver to enable the sender to estimate the round-trip
        time, for senders that do not save timestamps of transmitted
        data packets.
        We note that as an alternative to a timestamp incremented in
        milliseconds, a "timestamp" that increments every quarter of a
        round-trip time would be sufficient for determining when losses
        belong to the same loss event, in the context of a protocol
        where this is understood by both sender and receiver, and where
        the sender saves the timestamps of transmitted data packets.

    o   The sender's current estimate of the round trip time. The
        estimate reported in packet i is denoted by R_i.  The round-trip
        time estimate is used by the receiver, along with the timestamp,
        to determine when multiple losses belong to the same loss event.
        The round-trip time estimate is also used by the receiver to
        determine the interval to use for calculating the receive rate,
        and to determine when to send feedback packets.
        If the sender sends a coarse-grained "timestamp" that increments
        every quarter of a round-trip time, as discussed above, then the
        sender does not need to send its current estimate of the round
        trip time.



3.2.2.  Feedback Packets

    Each feedback packet sent by the data receiver contains the
    following information:

    o   The timestamp of the last data packet received. We denote this
        by t_recvdata.  If the last packet received at the receiver has
        sequence number i, then t_recvdata = ts_i.
        This timestamp is used by the sender to estimate the round-trip
        time, and is only needed if the sender does not save timestamps
        of transmitted data packets.




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    o   The amount of time elapsed between the receipt of the last data
        packet at the receiver, and the generation of this feedback
        report. We denote this by t_delay.

    o   The rate at which the receiver estimates that data was received
        since the last feedback report was sent. We denote this by
        X_recv.

    o   The receiver's current estimate of the loss event rate, p.


4.  Data Sender Protocol

    The data sender sends a stream of data packets to the data receiver
    at a controlled rate. When a feedback packet is received from the
    data receiver, the data sender changes its sending rate, based on
    the information contained in the feedback report. If the sender does
    not receive a feedback report for four round trip times, it cuts its
    sending rate in half.  This is achieved by means of a timer called
    the nofeedback timer.

    We specify the sender-side protocol in the following steps:

    o   Measurement of the mean segment size being sent.

    o   The sender behavior when a feedback packet is received.

    o   The sender behavior when the nofeedback timer expires.

    o   Oscillation prevention (optional)

    o   Scheduling of transmission on non-realtime operating systems.


4.1.  Measuring the Segment Size

    The parameter s (segment size) is normally known to an application.
    This may not be so in two cases:

    o   (1) The segment size naturally varies depending on the data.  In
        this case, although the segment size varies, that variation is
        not coupled to the transmit rate.  The TFRC sender can either
        compute the average segment size or use the maximum segment size
        for the segment size s.

    o   (2) The application needs to change the segment size rather than
        the number of segments per second to perform congestion control.
        This would normally be the case with packet audio applications



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        where a fixed interval of time needs to be represented by each
        packet.  Such applications need to have a completely different
        way of measuring parameters.

    For the first class of applications where the segment size varies
    depending on the data, the sender MAY estimate the segment size s as
    the average segment size over the last four loss intervals.  The
    sender MAY also estimate the average segment size over longer time
    intervals, if so desired.  The TFRC sender uses the segment size s
    in the throughput equation, in the setting of the maximum receive
    rate and the minimum sending rate, and in the setting of the
    nofeedback timer.

    The TFRC receiver may use the average segment size s in initializing
    the loss history after the first loss event, but Section 6.3.1 also
    gives an alternate procedure that does not use the average segment
    size s.

    The second class of applications are discussed separately in a
    separate document on TFRC-SP.  For the remainder of this section we
    assume the sender can estimate the segment size, and that congestion
    control is performed by adjusting the number of packets sent per
    second.


4.2.  Sender Initialization

    The initial values for X and tld are undefined until they are set as
    described below.  If the sender is ready to send data when it does
    not yet have a round trip sample, the value of X is set to 1
    packet/second, the nofeedback timer is set to expire after 2
    seconds, and the tld, the Time Last Doubled during slow-start, is
    set to -1.  Upon receiving a round trip time measurement (e.g.,
    after the first feedback packet), tld is set to the current time,
    and the transmit rate X is set to W_init/R, for W_init below from
    [RFC3390]:

         W_init = min(4*MSS, max(2*MSS, 4380)),

    for MSS the Maximum Segment Size.  For responding to the initial
    feedback packet, this replaces step (4) of Section 4.3 below.

    If the sender does have a round trip sample when it is ready to
    first send data (e.g., from the SYN exchange or from a previous
    connection [RFC2140]), the initial transmit rate X is set to
    W_init/R, and tld is set to the current time.





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4.3.  Sender behavior when a feedback packet is received

    The sender knows its current sending rate, X, and maintains an
    estimate of the current round trip time, R, and an estimate of the
    timeout interval, t_RTO.

    When a feedback packet is received by the sender at time t_now, the
    following actions should be performed:


    1)  Calculate a new round trip sample.
        R_sample = (t_now - t_recvdata) - t_delay.

    2)  Update the round trip time estimate:

             If no feedback has been received before
                 R = R_sample;
             Else
                 R = q*R + (1-q)*R_sample;

        TFRC is not sensitive to the precise value for the filter
        constant q, but we recommend a default value of 0.9.

    3)  Update the timeout interval:

             t_RTO = 4*R.


    4)  Update the sending rate as follows:

             If (sender has been idle or data-limited)
                 min_rate = max(2*X_recv, W_init/R);
             Else
                 min_rate = 2*X_recv;
             If (p > 0)
                 Calculate X_calc using the TCP throughput equation.
                 X = max(min(X_calc, min_rate), s/t_mbi);
             Else if (not the first feedback packet, and
               not the first feedback packet after a nofeedback timer)
                 If (t_now - tld >= R)
                     X = max(min(2*X, min_rate), s/R);
                     tld = t_now;


    The condition ``if (sender has been idle or data-limited)'' prevents
    an idle or data-limited sender from having to reduce the sending
    rate to less than the initial sending rate as a result of
    limitations from a small receive rate.  The condition ``if (not the



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    first feedback packet, and not the first feedback packet after a
    nofeedback timer)'' prevents a sender from reducing the sending rate
    in response to a feedback packet that reports the receipt of only a
    few packets after start-up or after an idle period.

    Note that if p == 0, then the sender is in slow-start phase, where
    it approximately doubles the sending rate each round-trip time until
    a loss occurs. The s/R term gives a minimum sending rate during
    slow-start of one packet per RTT.  The parameter t_mbi is 64
    seconds, and represents the maximum inter-packet backoff interval in
    the persistent absence of feedback.  Thus, when p > 0 the sender
    sends at least one packet every 64 seconds.

    5)  Reset the nofeedback timer to expire after max(4*R, 2*s/X)
        seconds.

4.4.  Expiration of nofeedback timer

    If the nofeedback timer expires, the sender should perform the
    following actions:

    1)  Cut the sending rate in half.  If the sender has received
        feedback from the receiver, this is done by modifying the
        sender's cached copy of X_recv (the receive rate).  Because the
        sending rate is limited to at most twice X_recv, modifying
        X_recv limits the current sending rate, but allows the sender to
        slow-start, doubling its sending rate each RTT, if feedback
        messages resume reporting no losses.

            If (X_calc > 2*X_recv)
                X_recv = max(X_recv/2, s/(2*t_mbi));
            Else
                X_recv = X_calc/4;


        The term s/(2*t_mbi) limits the backoff to one packet every 64
        seconds in the case of persistent absence of feedback.


    2)  The value of X must then be recalculated as described under
        point (4) above.

        If the nofeedback timer expires when the sender does not yet
        have an RTT sample and has not yet received any feedback from
        the receiver, or when p == 0, then step (1) can be skipped, and
        the sending rate cut in half directly:





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               X = max(X/2, s/t_mbi)



    3)  Restart the nofeedback timer to expire after max(4*R, 2*s/X)
        seconds.

    Note that when the sender stops sending, the receiver will stop
    sending feedback.  When the sender's nofeedback timer expires, the
    sender will decrease X_recv.  If the sender subsequently starts to
    send again, X_recv will limit the transmit rate, and a normal
    slowstart phase will occur until the transmit rate reaches X_calc.

4.5.  Sending a packet after an idle period

    If the sender has been idle (unable to send because there is no data
    from the application), the allowed sending rate could have been
    reduced due to the nofeedback timer, as specified in the section
    above.  Because the sender is always restricted to sending at most
    twice the receive rate reported by the receiver, the sender will be
    limited to at most doubling its sending rate each round-trip time,
    until the sending rate reaches the allowed sending rate calculated
    by the throughput equation.

4.6.  Preventing Oscillations


    To prevent oscillatory behavior in environments with a low degree of
    statistical multiplexing it is useful to modify sender's transmit
    rate to provide congestion avoidance behavior by reducing the
    transmit rate as the queuing delay (and hence RTT) increases.  To do
    this the sender maintains an estimate of the long-term RTT and
    modifies its sending rate depending on how the most recent sample of
    the RTT differs from this value.  The long-term sample is R_sqmean,
    and is set as follows:

         If no feedback has been received before
             R_sqmean = sqrt(R_sample);
         Else
             R_sqmean = q2*R_sqmean + (1-q2)*sqrt(R_sample);

    Thus R_sqmean gives the exponentially weighted moving average of the
    square root of the RTT samples.  The constant q2 should be set
    similarly to q, and we recommend a value of 0.9 as the default.

    The sender obtains the base transmit rate, X, from the throughput
    function.  It then calculates a modified instantaneous transmit rate
    X_inst, as follows:



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         X_inst = X * R_sqmean / sqrt(R_sample);


    When sqrt(R_sample) is greater than R_sqmean then the queue is
    typically increasing and so the transmit rate needs to be decreased
    for stable operation.

    Note: This modification is not always strictly required, especially
    if the degree of statistical multiplexing in the network is high.
    However, we recommend that it is done because it does make TFRC
    behave better in environments with a low level of statistical
    multiplexing.  If it is not done, we recommend using a very low
    value of q, such that q is close to or exactly zero.

4.7.  Scheduling of Packet Transmissions

    As TFRC is rate-based, and as operating systems typically cannot
    schedule events precisely, it is necessary to be opportunistic about
    sending data packets so that the correct average rate is maintained
    despite the coarse-grain or irregular scheduling of the operating
    system.  Thus a typical sending loop will calculate the correct
    inter-packet interval, t_ipi, as follows:

         t_ipi = s/X_inst;

    When a sender first starts sending at time t_0, it calculates t_ipi,
    and calculates a nominal send time t_1 = t_0 + t_ipi for packet 1.
    When the application becomes idle, it checks the current time,
    t_now, and then requests re-scheduling after (t_ipi - (t_now - t_0))
    seconds.  When the application is re-scheduled, it checks the
    current time, t_now, again. If (t_now > t_1 - delta) then packet 1
    is sent.

    Now a new t_ipi may be calculated, and used to calculate a nominal
    send time t_2 for packet 2: t2 = t_1 + t_ipi.  The process then
    repeats, with each successive packet's send time being calculated
    from the nominal send time of the previous packet.

    In some cases, when the nominal send time, t_i, of the next packet
    is calculated, it may already be the case that t_now > t_i - delta.
    In such a case the packet should be sent immediately.  Thus if the
    operating system has coarse timer granularity and the transmit rate
    is high, then TFRC may send short bursts of several packets
    separated by intervals of the OS timer granularity.

    The parameter delta is to allow a degree of flexibility in the send
    time of a packet.  If the operating system has a scheduling timer
    granularity of t_gran seconds, then delta would typically be set to:



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         delta = min(t_ipi/2, t_gran/2);

    t_gran is 10ms on many Unix systems.  If t_gran is not known, a
    value of 10ms can be safely assumed.

5.  Calculation of the Loss Event Rate (p)

    Obtaining an accurate and stable measurement of the loss event rate
    is of primary importance for TFRC. Loss rate measurement is
    performed at the receiver, based on the detection of lost or marked
    packets from the sequence numbers of arriving packets. We describe
    this process before describing the rest of the receiver protocol.

5.1.  Detection of Lost or Marked Packets

    TFRC assumes that all packets contain a sequence number that is
    incremented by one for each packet that is sent.  For the purposes
    of this specification, we require that if a lost packet is
    retransmitted, the retransmission is given a new sequence number
    that is the latest in the transmission sequence, and not the same
    sequence number as the packet that was lost.  If a transport
    protocol has the requirement that it must retransmit with the
    original sequence number, then the transport protocol designer must
    figure out how to distinguish delayed from retransmitted packets and
    how to detect lost retransmissions.

    The receiver maintains a data structure that keeps track of which
    packets have arrived and which are missing.  For the purposes of
    specification, we assume that the data structure consists of a list
    of packets that have arrived along with the receiver timestamp when
    each packet was received.  In practice this data structure will
    normally be stored in a more compact representation, but this is
    implementation-specific.

    The loss of a packet is detected by the arrival of at least NDUPACK
    packets with a higher sequence number than the lost packet, for
    NDUPACK set to 3.  The requirement for NDUPACK subsequent packets is
    the same as with TCP, and is to make TFRC more robust in the
    presence of reordering.  In contrast to TCP, if a packet arrives
    late (after NDUPACK subsequent packets arrived) in TFRC, the late
    packet can fill the hole in TFRC's reception record, and the
    receiver can recalculate the loss event rate.  Future versions of
    TFRC might make the requirement for NDUPACK subsequent packets
    adaptive based on experienced packet reordering, but we do not
    specify such a mechanism here.

    For an ECN-capable connection, a marked packet is detected as a
    congestion event as soon as it arrives, without having to wait for



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    the arrival of subsequent packets.


5.2.  Translation from Loss History to Loss Events

    TFRC requires that the loss fraction be robust to several
    consecutive packets lost where those packets are part of the same
    loss event.  This is similar to TCP, which (typically) only performs
    one halving of the congestion window during any single RTT.  Thus
    the receiver needs to map the packet loss history into a loss event
    record, where a loss event is one or more packets lost in an RTT.
    To perform this mapping, the receiver needs to know the RTT to use,
    and this is supplied periodically by the sender, typically as
    control information piggy-backed onto a data packet.  TFRC is not
    sensitive to how the RTT measurement sent to the receiver is made,
    but we recommend using the sender's calculated RTT, R, (see Section
    4.3) for this purpose.

    To determine whether a lost or marked packet should start a new loss
    event, or be counted as part of an existing loss event, we need to
    compare the sequence numbers and timestamps of the packets that
    arrived at the receiver.  For a marked packet S_new, its reception
    time T_new can be noted directly.  For a lost packet, we can
    interpolate to infer the nominal "arrival time".  Assume:

        S_loss is the sequence number of a lost packet.

        S_before is the sequence number of the last packet to arrive
        with sequence number before S_loss.

        S_after is the sequence number of the first packet to arrive
        with sequence number after S_loss.

        T_before is the reception time of S_before.

        T_after is the reception time of S_after.

    Note that T_before can either be before or after T_after due to
    reordering.

    For a lost packet S_loss, we can interpolate its nominal "arrival
    time" at the receiver from the arrival times of S_before and
    S_after. Thus:

         T_loss = T_before + ( (T_after - T_before)
                     * (S_loss - S_before)/(S_after - S_before) );





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    Note that if the sequence space wrapped between S_before and
    S_after, then the sequence numbers must be modified to take this
    into account before performing this calculation.  If the largest
    possible sequence number is S_max, and S_before > S_after, then
    modifying each sequence number S by S' = (S + (S_max + 1)/2) mod
    (S_max + 1) would normally be sufficient.

    If the lost packet S_old was determined to have started the previous
    loss event, and we have just determined that S_new has been lost,
    then we interpolate the nominal arrival times of S_old and S_new,
    called T_old and T_new respectively.

    If T_old + R >= T_new, then S_new is part of the existing loss
    event. Otherwise S_new is the first packet in a new loss event.


5.3.  Inter-loss Event Interval

    If a loss interval, A, is determined to have started with packet
    sequence number S_A and the next loss interval, B, started with
    packet sequence number S_B, then the number of packets in loss
    interval A is given by (S_B - S_A).



5.4.  Average Loss Interval

    To calculate the loss event rate p, we first calculate the average
    loss interval.  This is done using a filter that weights the n most
    recent loss event intervals in such a way that the measured loss
    event rate changes smoothly.

    Weights w_0 to w_(n-1) are calculated as:

         If (i < n/2)
            w_i = 1;
         Else
            w_i = 1 - (i - (n/2 - 1))/(n/2 + 1);


    Thus if n=8, the values of w_0 to w_7 are:

        1.0, 1.0, 1.0, 1.0, 0.8, 0.6, 0.4, 0.2

    The value n for the number of loss intervals used in calculating the
    loss event rate determines TFRC's speed in responding to changes in
    the level of congestion.  As currently specified, TFRC should not be
    used for values of n significantly greater than 8, for traffic that



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    might compete in the global Internet with TCP.  At the very least,
    safe operation with values of n greater than 8 would require a
    slight change to TFRC's mechanisms to include a more severe response
    to two or more round-trip times with heavy packet loss.

    When calculating the average loss interval we need to decide whether
    to include the interval since the most recent packet loss event.  We
    only do this if it is sufficiently large to increase the average
    loss interval.

    Let the most recent loss intervals be I_0 to I_k, where I_0 is the
    interval since the most recent loss event.  If there have been at
    least n loss intervals, then k is set to n; otherwise k is the
    maximum number of loss intervals seen so far.  We calculate the
    average loss interval I_mean is:

         I_tot0 = 0;
         I_tot1 = 0;
         W_tot = 0;
         for (i = 0 to k-1) {
           I_tot0 = I_tot0 + (I_i * w_i);
           W_tot = W_tot + w_i;
         }
         for (i = 1 to k) {
           I_tot1 = I_tot1 + (I_i * w_(i-1));
         }
         I_tot = max(I_tot0, I_tot1);
         I_mean = I_tot/W_tot;

    The loss event rate, p is simply:

         p = 1 / I_mean;


5.5.  History Discounting

    As described in Section 5.4, the most recent loss interval is only
    assigned 1/(0.75*n) of the total weight in calculating the average
    loss interval, regardless of the size of the most recent loss
    interval.  This section describes an optional history discounting
    mechanism, discussed further in [FHPW00a] and [W00], that allows the
    TFRC receiver to adjust the weights, concentrating more of the
    relative weight on the most recent loss interval, when the most
    recent loss interval is more than twice as large as the computed
    average loss interval.

    To carry out history discounting, we associate a discount factor
    DF_i with each loss interval L_i, for i > 0, where each discount



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    factor is a floating point number.  The discount array maintains the
    cumulative history of discounting for each loss interval.  At the
    beginning, the values of DF_i in the discount array are initialized
    to 1:

         for (i = 0 to n) {
           DF_i = 1;
         }

    History discounting also uses a general discount factor DF, also a
    floating point number, that is also initialized to 1.  First we show
    how the discount factors are used in calculating the average loss
    interval, and then we describe later in this section how the
    discount factors are modified over time.

    As described in Section 5.4 the average loss interval is calculated
    using the n previous loss intervals I_1, ..., I_n, and the interval
    I_0 that represents the number of packets received since the last
    loss event.  The computation of the average loss interval using the
    discount factors is a simple modification of the procedure in
    Section 5.4, as follows:

         I_tot0 = I_0 * w_0
         I_tot1 = 0;
         W_tot0 = w_0
         W_tot1 = 0;
         for (i = 1 to n-1) {
           I_tot0 = I_tot0 + (I_i * w_i * DF_i * DF);
           W_tot0 = W_tot0 + w_i * DF_i * DF;
         }
         for (i = 1 to n) {
           I_tot1 = I_tot1 + (I_i * w_(i-1) * DF_i);
           W_tot1 = W_tot1 + w_(i-1) * DF_i;
         }
         p = min(W_tot0/I_tot0, W_tot1/I_tot1);

    The general discounting factor, DF is updated on every packet
    arrival as follows. First, the receiver computes the weighted
    average I_mean of the loss intervals I_1, ..., I_n:

         I_tot = 0;
         W_tot = 0;
         for (i = 1 to n) {
           W_tot = W_tot + w_(i-1) * DF_i;
           I_tot = I_tot + (I_i * w_(i-1) * DF_i);
         }
         I_mean = I_tot / W_tot;




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    This weighted average I_mean is compared to I_0, the number of
    packets received since the last loss event.  If I_0 is greater than
    twice I_mean, then the new loss interval is considerably larger than
    the old ones, and the general discount factor DF is updated to
    decrease the relative weight on the older intervals, as follows:


         if (I_0 > 2 * I_mean) {
           DF = 2 * I_mean/I_0;
           if (DF < THRESHOLD)
             DF = THRESHOLD;
         } else
           DF = 1;

    A nonzero value for THRESHOLD ensures that older loss intervals from
    an earlier time of high congestion are not discounted entirely.  We
    recommend a THRESHOLD of 0.5.  Note that with each new packet
    arrival, I_0 will increase further, and the discount factor DF will
    be updated.

    When a new loss event occurs, the current interval shifts from I_0
    to I_1, loss interval I_i shifts to interval I_(i+1), and the loss
    interval I_n is forgotten.  The previous discount factor DF has to
    be incorporated into the discount array.  Because DF_i carries the
    discount factor associated with loss interval I_i, the DF_i array
    has to be shifted as well. This is done as follows:

         for (i = 1 to n) {
           DF_i = DF * DF_i;
         }
         for (i = n-1 to 0 step -1) {
           DF_(i+1) = DF_i;
         }
         I_0 = 1;
         DF_0 = 1;
         DF = 1;


    This completes the description of the optional history discounting
    mechanism. We emphasize that this is an optional mechanism whose
    sole purpose is to allow TFRC to response somewhat more quickly to
    the sudden absence of congestion, as represented by a long current
    loss interval.








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6.  Data Receiver Protocol

    The receiver periodically sends feedback messages to the sender.
    Feedback packets should normally be sent at least once per RTT,
    unless the sender is sending at a rate of less than one packet per
    RTT, in which case a feedback packet should be send for every data
    packet received.  A feedback packet should also be sent whenever a
    new loss event is detected without waiting for the end of an RTT,
    and whenever an out-of-order data packet is received that removes a
    loss event from the history.

    If the sender is transmitting at a high rate (many packets per RTT)
    there may be some advantages to sending periodic feedback messages
    more than once per RTT as this allows faster response to changing
    RTT measurements, and more resilience to feedback packet loss.
    However, there is little gain from sending a large number of
    feedback messages per RTT.


6.1.  Receiver behavior when a data packet is received

    When a data packet is received, the receiver performs the following
    steps:

    1)  Add the packet to the packet history.

    2)  Let the previous value of p be p_prev.  Calculate the new value
        of p as described in Section 5.

    3)  If p > p_prev, cause the feedback timer to expire, and perform
        the actions described in Section 6.2

        If p <= p_prev no action need be performed.

        However an optimization might check to see if the arrival of the
        packet caused a hole in the packet history to be filled and
        consequently two loss intervals were merged into one.  If this
        is the case, the receiver might also send feedback immediately.
        The effects of such an optimization are normally expected to be
        small.


6.2.  Expiration of feedback timer

    When the feedback timer at the receiver expires, the action to be
    taken depends on whether data packets have been received since the
    last feedback was sent.




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    Let the maximum sequence number of a packet at the receiver so far
    be S_m, and the value of the RTT measurement included in packet S_m
    be R_m. If data packets have been received since the previous
    feedback was sent, the receiver performs the following steps:

    1)  Calculate the average loss event rate using the algorithm
        described above.

    2)  Calculate the measured receive rate, X_recv, based on the
        packets received within the previous R_m seconds.

    3)  Prepare and send a feedback packet containing the information
        described in Section 3.2.2

    4)  Restart the feedback timer to expire after R_m seconds.

    Note that rule 2) above gives a minimum value for the measured
    receive rate X_recv of one packet per round-trip time.  If the
    sender is limited to a sending rate of less than one packet per
    round-trip time, this will be due to the loss event rate, not from a
    limit imposed by the measured receive rate at the receiver.

    If no data packets have been received since the last feedback was
    sent, no feedback packet is sent, and the feedback timer is
    restarted to expire after R_m seconds.



6.3.  Receiver initialization

    The receiver is initialized by the first data packet that arrives at
    the receiver. Let the sequence number of this packet be i.

    When the first packet is received:

    o   Set p=0

    o   Set  X_recv = 0.

    o   Prepare and send a feedback packet.

    o   Set the feedback timer to expire after R_i seconds.

    If the first data packet doesn't contain an estimate R_i of the
    round-trip time, then the receiver sends a feedback packet for every
    arriving data packet, until a data packet arrives containing an
    estimate of the round-trip time.




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    If the sender is using a coarse-grained timestamp that increments
    every quarter of a round-trip time, then a feedback timer is not
    needed, and the following procedure from RFC 4342 is used to
    determine when to send feedback messages.

    o   Whenever the receiver sends a feedback message, the receiver
        sets a local variable last_counter to the greatest received
        value of the window counter since the last feedback message was
        sent, if any data packets have been received since the last
        feedback message was sent.

    o   If the receiver receives a data packet with a window counter
        value greater than or equal to last_counter + 4, then the
        receiver sends a new feedback packet.  ("Greater" and "greatest"
        are measured in circular window counter space.)


6.3.1.  Initializing the Loss History after the First Loss Event

    The number of packets until the first loss can not be used to
    compute the sending rate directly, as the sending rate changes
    rapidly during this time.  TFRC assumes that the correct data rate
    after the first loss is half of the sending rate when the loss
    occurred.  TFRC approximates this target rate by X_recv, the receive
    rate over the most recent round-trip time.  After the first loss,
    instead of initializing the first loss interval to the number of
    packets sent until the first loss, the TFRC receiver calculates the
    loss interval that would be required to produce the data rate
    X_recv, and uses this synthetic loss interval to seed the loss
    history mechanism.

    TFRC does this by finding some value p for which the throughput
    equation in Section 3.1 gives a sending rate within 5% of X_recv,
    given the round-trip time R, and the first loss interval is then set
    to 1/p.  If the receiver knows the segment size s used by the
    sender, then the receiver can use the throughput equation for X;
    otherwise, the receiver can meaure the receive rate in packets per
    second instead of bytes per second for this purpose, and use the
    throughput equation for X_pps.  (The 5% tolerance is introduced
    simply because the throughput equation is difficult to invert, and
    we want to reduce the costs of calculating p numerically.)

    If the first arriving data packet is lost or ECN-marked, then the
    loss event consists of the *** SALLY ***







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7.  Sender-based Variants

    It would be possible to implement a sender-based variant of TFRC,
    where the receiver uses reliable delivery to send information about
    packet losses to the sender, and the sender computes the packet loss
    rate and the acceptable transmit rate.  However, we do not specify
    the details of a sender-based variant in this document.

    The main advantages of a sender-based variant of TFRC would be that
    the sender would not have to trust the receiver's calculation of the
    packet loss rate.  However, with the requirement of reliable
    delivery of loss information from the receiver to the sender, a
    sender-based TFRC would have much tighter constraints on the
    transport protocol in which it is embedded.

    In contrast, the receiver-based variant of TFRC specified in this
    document is robust to the loss of feedback packets, and therefore
    does not require the reliable delivery of feedback packets.  It is
    also better suited for applications such as streaming media from web
    servers, where it is typically desirable to offload work from the
    server to the client as much as possible.

    The sender-based and receiver-based variants also have different
    properties in terms of upgrades.  For example, for changes in the
    procedure for calculating the packet loss rate, the sender would
    have to be upgraded in the sender-based variant, and the receiver
    would have to be upgraded in the receiver-based variant.


8.  Implementation Issues

    This document has specified the TFRC congestion control mechanism,
    for use by applications and transport protocols.  This section
    mentions briefly some of the few implementation issues.

    For t_RTO = 4*R and b = 1, the throughput equation in Section 3.1
    can be expressed as follows:

                 s
         X =  --------
              R * f(p)

    for

         f(p) =  sqrt(2*p/3) + (12*sqrt(3*p/8) * p * (1+32*p^2)).

    A table lookup could be used for the function f(p).




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    Many of the multiplications (e.g., q and 1-q for the round-trip time
    average, a factor of 4 for the timeout interval) are or could be by
    powers of two, and therefore could be implemented as simple shift
    operations.

    We note that the optional sender mechanism for preventing
    oscillations described in Section 4.6 uses a square-root
    computation.

    The calculation of the average loss interval in Section 5.4 involves
    multiplications by the weights w_0 to w_(n-1), which for n=8 are:

        1.0, 1.0, 1.0, 1.0, 0.8, 0.6, 0.4, 0.2.

    With a minor loss of smoothness, it would be possible to use weights
    that were powers of two or sums of powers of two, e.g.,

        1.0, 1.0, 1.0, 1.0, 0.75, 0.5, 0.25, 0.25.

    The optional history discounting mechanism described in Section 5.5
    is used in the calculation of the average loss rate.  The history
    discounting mechanism is invoked only when there has been an
    unusually long interval with no packet losses.  For a more efficient
    operation, the discount factor DF_i could be restricted to be a
    power of two.


9.  Changes from RFC 3448

    The changes from RFC 3448 are as follows:

    o   Changes to the initial sending rate: In RFC 3448, the initial
        sending rate was two packets per round trip time.  In this
        document, the initial sending rate can be as high as four
        packets per round trip time, following RFC 3390.

        Following Section 5.1 from [RFC4342], this document also
        specifies that when the sending rate is reduced after an idle
        period, it is not reduced below the initial sending rate.  In
        addition, when the sender has been data-limited and the sender
        is reducing the allowed transmit rate to twice the receive
        rate,, the sender doesn't reduce the allowed transmit rate to
        less than the initial sending rate.

        A larger initial sending rate is of little use if the receiver
        sends a feedback packet after the first packet is received, and
        the sender in response reduces the allowed sending rate to at
        most twice the receive rate.  In the current document, the



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        sender does not reduce the allowed sending rate to at most twice
        the receive rate in response to the first feedback packet.

    o   RFC 3448 had contradictory text about whether the sender halved
        its sending rate after *two* round-trip times without receiving
        a feedback report, or after *four* round-trip times.  This
        document clarifies that the sender halves its sending rate after
        four round-trip times without receiving a feedback report
        [RFC3448Err].

    o   Section 4.4 was clarified to specify that on the expiration of
        the nofeedback timer, if p = 0, step (2) applies instead of step
        (1) [RFC3448Err].

    o   A line in Section 5.5 was changed from ``for (i = 1 to n) { DF_i
        = 1; }'' to ``for (i = 0 to n) { DF_i = 1; }'' [RFC3448Err].

    o   Section 5.4 was modified to clarify the receiver's calculation
        of the average loss interval when the receiver has not yet seen
        eight loss intervals.

    o   Section 4.1 was modified to give a specific algorithm that could
        be used for estimating the average segment size.

10.  Security Considerations

    TFRC is not a transport protocol in its own right, but a congestion
    control mechanism that is intended to be used in conjunction with a
    transport protocol.  Therefore security primarily needs to be
    considered in the context of a specific transport protocol and its
    authentication mechanisms.

    Congestion control mechanisms can potentially be exploited to create
    denial of service.  This may occur through spoofed feedback.  Thus
    any transport protocol that uses TFRC should take care to ensure
    that feedback is only accepted from the receiver of the data.  The
    precise mechanism to achieve this will however depend on the
    transport protocol itself.

    In addition, congestion control mechanisms may potentially be
    manipulated by a greedy receiver that wishes to receive more than
    its fair share of network bandwidth.  A receiver might do this by
    claiming to have received packets that in fact were lost due to
    congestion.  Possible defenses against such a receiver would
    normally include some form of nonce that the receiver must feed back
    to the sender to prove receipt.  However, the details of such a
    nonce would depend on the transport protocol, and in particular on
    whether the transport protocol is reliable or unreliable.



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    We expect that protocols incorporating ECN with TFRC will also want
    to incorporate feedback from the receiver to the sender using the
    ECN nonce [RFC3540].   The ECN nonce is a modification to ECN that
    protects the sender from the accidental or malicious concealment of
    marked packets.  Again, the details of such a nonce would depend on
    the transport protocol, and are not addressed in this document.


11.  IANA Considerations

    There are no IANA actions required for this document.


12.  Acknowledgments

    We would like to acknowledge feedback and discussions on equation-
    based congestion control with a wide range of people, including
    members of the Reliable Multicast Research Group, the Reliable
    Multicast Transport Working Group, and the End-to-End Research
    Group.   We would like to thank Dado Colussi, Wim Heirman, Ken
    Lofgren, Mike Luby, Michele R., Vladica Stanisic, Randall Stewart,
    Eduardo Urzaiz, Shushan Wen, and Wendy Lee (lhh@zsu.edu.cn) for
    feedback on earlier versions of this document, and to thank Mark
    Allman for his extensive feedback from using the document to produce
    a working implementation.

13.  Normative References

14.  Informational References

     [BRS99]        Balakrishnan, H., Rahul, H., and Seshan, S., "An
                    Integrated Congestion Management Architecture for
                    Internet Hosts," Proc. ACM SIGCOMM, Cambridge, MA,
                    September 1999.

     [FHPW00]       S. Floyd, M. Handley, J. Padhye, and J. Widmer,
                    "Equation-Based Congestion Control for Unicast
                    Applications", August 2000, Proc SIGCOMM 2000.

     [FHPW00a]      S. Floyd, M. Handley, J. Padhye, and J. Widmer,
                    "Equation-Based Congestion Control for Unicast
                    Applications: the Extended Version", ICSI tech
                    report TR-00-03, March 2000.

     [PFTK98]       Padhye, J. and  Firoiu, V. and Towsley, D. and
                    Kurose, J., "Modeling TCP Throughput: A Simple Model
                    and its Empirical Validation", Proc ACM SIGCOMM
                    1998.



Handley/Floyd/Padhye/Widmer                       Section 14.  [Page 29]

INTERNET-DRAFT             Expires: April 2007              October 2006


     [RFC2119]      S. Bradner, Key Words For Use in RFCs to Indicate
                    Requirement Levels, RFC 2119.

     [RFC2140]      J. Touch, "TCP Control Block Interdependence", RFC
                    2140, April 1997.

     [RFC2988]      V. Paxson and M. Allman, "Computing TCP's
                    Retransmission Timer", RFC 2988, November 2000.

     [RFC3168]      K. Ramakrishnan and S. Floyd, "The Addition of
                    Explicit Congestion Notification (ECN) to IP", RFC
                    3168, September 2001.

     [RFC3390]      Allman, M., Floyd, S., and C. Partridge, "Increasing
                    TCP's Initial Window", RFC 3390, October 2002.

     [RFC3448Err]   RFC 3448 Errata, URL
                    ``http://www.icir.org/tfrc/rfc3448.errata''.

     [RFC3540]      Wetherall, D., Ely, D., and Spring, N., "Robust ECN
                    Signaling with Nonces", RFC 3540, Experimental, June
                    2003

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

     [RFC4342]      Floyd, S., Kohler, E., and J. Padhye, "Profile for
                    Datagram Congestion Control Protocol (DCCP)
                    Congestion Control ID 3: TCP-Friendly Rate Control
                    (TFRC)", RFC 4342, March 2006.

     [W00]          Widmer, J., "Equation-Based Congestion Control",
                    Diploma Thesis, University of Mannheim, February
                    2000.  URL "http://www.icir.org/tfrc/".


15.  Authors' Addresses













Handley/Floyd/Padhye/Widmer                       Section 15.  [Page 30]

INTERNET-DRAFT             Expires: April 2007              October 2006


         Mark Handley,
         Department of Computer Science
         University College London
         Gower Street
         London WC1E 6BT
         UK
         EMail: M.Handley@cs.ucl.ac.uk

         Sally Floyd
         ICIR/ICSI
         1947 Center St, Suite 600
         Berkeley, CA 94708
         floyd@icir.org

         Jitendra Padhye
         Microsoft Research
         padhye@microsoft.com


         Joerg Widmer
         Lehrstuhl Praktische Informatik IV
         Universitat Mannheim
         L 15, 16 - Room 415
         D-68131 Mannheim
         Germany
         widmer@informatik.uni-mannheim.de



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