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RFC 3448 - TCP Friendly Rate Control (TFRC): Protocol Specificat

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Network Working Group                                         M. Handley
Request for Comments: 3448                                      S. Floyd
Category: Standards Track                                           ICIR
                                                               J. Padhye
                                                               J. Widmer
                                                  University of Mannheim
                                                            January 2003

                   TCP Friendly Rate Control (TFRC):
                         Protocol Specification

Status of this Memo

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

Copyright Notice

   Copyright (C) The Internet Society (2003).  All Rights Reserved.


   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
   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.

Table of Contents

   1.  Introduction. . . . . . . . . . . . . . . . . . . . . .  2
   2.  Terminology . . . . . . . . . . . . . . . . . . . . . .  3
   3.  Protocol Mechanism. . . . . . . . . . . . . . . . . . .  3
       3.1. TCP Throughput Equation. . . . . . . . . . . . . .  4
       3.2. Packet Contents. . . . . . . . . . . . . . . . . .  6
            3.2.1. Data Packets. . . . . . . . . . . . . . . .  6
            3.2.2. Feedback Packets. . . . . . . . . . . . . .  7
   4.  Data Sender Protocol. . . . . . . . . . . . . . . . . .  7
       4.1. Measuring the Packet Size. . . . . . . . . . . . .  8
       4.2. Sender Initialization. . . . . . . . . . . . . . .  8

       4.3. Sender behavior when a feedback packet is
            received. . . . . . . . . . . . . .. . . . . . . .  8
       4.4. Expiration of nofeedback timer . . . . . . . . . .  9
       4.5. Preventing Oscillations. . . . . . . . . . . . . . 10
       4.6. Scheduling of Packet Transmissions . . . . . . . . 11
   5.  Calculation of the Loss Event Rate (p). . . . . . . . . 12
       5.1. Detection of Lost or Marked Packets. . . . . . . . 12
       5.2. Translation from Loss History to Loss Events . . . 13
       5.3. Inter-loss Event Interval. . . . . . . . . . . . . 14
       5.4. Average Loss Interval. . . . . . . . . . . . . . . 14
       5.5. History Discounting. . . . . . . . . . . . . . . . 15
   6.  Data Receiver Protocol. . . . . . . . . . . . . . . . . 17
       6.1. Receiver behavior when a data packet is
            received . . . . . . . . . . . . . . . . . . . . . 18
       6.2. Expiration of feedback timer . . . . . . . . . . . 18
       6.3. Receiver initialization. . . . . . . . . . . . . . 19
            6.3.1. Initializing the Loss History after the
                   First Loss Event . . . . . . . . . .  . . . 19
   7.  Sender-based Variants . . . . . . . . . . . . . . . . . 20
   8.  Implementation Issues . . . . . . . . . . . . . . . . . 20
   9.  Security Considerations . . . . . . . . . . . . . . . . 21
   10. IANA Considerations . . . . . . . . . . . . . . . . . . 22
   11. Acknowledgments . . . . . . . . . . . . . . . . . . . . 22
   12. Non-Normative References. . . . . . . . . . . . . . . . 22
   13. Authors' Addresses. . . . . . . . . . . . . . . . . . . 23
   14. Full Copyright Statement. . . . . . . . . . . . . . . . 24

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 [2].  Instead
   of specifying a complete protocol, this document simply specifies a
   congestion control mechanism that could be used in a transport
   protocol such as RTP [7], in an application incorporating end-to-end
   congestion control at the application level, or in the context of
   endpoint congestion management [1].  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 packet size, and
   vary their sending rate in packets per second in response to
   congestion.  Some audio applications require a fixed interval of time
   between packets and vary their packet size instead of their packet
   rate in response to congestion.  The congestion control mechanism in
   this document cannot be used by those applications; TFRC-PS (for
   TFRC-PacketSize) is a variant of TFRC for applications that have a
   fixed sending rate but vary their packet size in response to
   congestion.  TFRC-PS will be specified in a later document.

   TFRC is 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.

2.  Terminology

   In this document, the key words "MUST", "MUST NOT", "REQUIRED",
   and "OPTIONAL" are to be interpreted as described in BCP 14, RFC 2119
   and indicate requirement levels for compliant TFRC implementations.

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 packet 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)

   Generally speaking, TFRC's congestion control mechanism works as

   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

   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 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 [4].
   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:

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


      X is the transmit rate in bytes/second.

      s is the packet 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

   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
   implementations [9].  Another possibility would be to set t_RTO =
   max(4R, one second), to match the recommended minimum of one second
   on the RTO [5].

   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 parameters s (packet 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

   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.
      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

   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

   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

   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 two 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 packet 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 Packet Size

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

   o  The packet size naturally varies depending on the data.  In this
      case, although the packet size varies, that variation is not
      coupled to the transmit rate.  It should normally be safe to use
      an estimate of the mean packet size for s.

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

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

4.2.  Sender Initialization

   To initialize the sender, the value of X is set to 1 packet/second
   and the nofeedback timer is set to expire after 2 seconds.  The
   initial values for R (RTT) and t_RTO are undefined until they are set
   as described below.  The initial value of tld, for the Time Last
   Doubled during slow-start, is set to -1.

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;
                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 (p > 0)
             Calculate X_calc using the TCP throughput equation.
             X = max(min(X_calc, 2*X_recv), s/t_mbi);
             If (t_now - tld >= R)
                 X = max(min(2*X, 2*X_recv), s/R);
                 tld = t_now;

      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)

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));
             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, then step (1) can be skipped, and the sending rate cut
      in half directly:

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

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

   Note that when the sender stops sending, the receiver will stop
   sending feedback.  This will cause the nofeedback timer to start to
   expire and 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.

   If the sender has been idle since this nofeedback timer was set and
   X_recv is less than four packets per round-trip time, then X_recv
   should not be halved in response to the timer expiration.  This
   ensures that the allowed sending rate is never reduced to less than
   two packets per round-trip time as a result of an idle period.

4.5.  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);
            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:

        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.

4.6.  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 course-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:

        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

   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

   The loss of a packet is detected by the arrival of at least three
   packets with a higher sequence number than the lost packet.  The
   requirement for three 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 3 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 three
   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
   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

   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.

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

   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;
         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
   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

   Thus if the most recent loss intervals are I_0 to I_n, with I_0 being
   the interval since the most recent loss event, then we calculate the
   average loss interval I_mean as:

      I_tot0 = 0;
      I_tot1 = 0;
      W_tot = 0;
      for (i = 0 to n-1) {
        I_tot0 = I_tot0 + (I_i * w_i);
        W_tot = W_tot + w_i;
      for (i = 1 to n) {
        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 [3] and [9], 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

   To carry out history discounting, we associate a discount factor DF_i
   with each loss interval L_i, for i > 0, where each discount 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 = 1 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;

   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.

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

   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.

   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.

   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 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.

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 current packet size s and round-trip time R.  The first
   loss interval is then set to 1/p.  (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.)

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:

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


      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).

   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

   We note that the optional sender mechanism for preventing
   oscillations described in Section 4.5 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.  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.

   We expect that protocols incorporating ECN with TFRC will also want
   to incorporate feedback from the receiver to the sender using the ECN
   nonce [WES02].  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.

10.  IANA Considerations

   There are no IANA actions required for this document.

11.  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 Ken Lofgren, Mike Luby, Eduardo Urzaiz,
   Vladica Stanisic, Randall Stewart, 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.

12.  Informational References

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

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

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

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

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

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

   [7] Schulzrinne, H., Casner, S., Frederick, R. and V. Jacobson, "RTP:
       A Transport Protocol for Real-Time Applications", RFC 1889,
       January 1996.

   [8] Wetherall, D., Ely, D., N. Spring, S. Savage, and T. Anderson,
       "Robust Congestion Signaling", IEEE International Conference on
       Network Protocols, November 2001.

   [9] Widmer, J., "Equation-Based Congestion Control", Diploma Thesis,
       University of Mannheim, February 2000.  URL

13.  Authors' Addresses

   Mark Handley
   1947 Center St, Suite 600
   Berkeley, CA 94708

   EMail: mjh@icir.org

   Sally Floyd
   1947 Center St, Suite 600
   Berkeley, CA 94708

   EMail: floyd@icir.org

   Jitendra Padhye
   Microsoft Research

   EMail: padhye@microsoft.com

   Joerg Widmer
   Lehrstuhl Praktische Informatik IV
   Universitat Mannheim
   L 15, 16 - Room 415
   D-68131 Mannheim

   EMail: widmer@informatik.uni-mannheim.de

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