





Network Working Group                                           S. Floyd
Request for Comments: 5348                                          ICIR
Obsoletes: 3448                                               M. Handley
Updates: 4342                                  University College London
                                                               J. Padhye
                                                               Microsoft
                                                               J. Widmer
                                                                  DoCoMo
                                                          September 2008


        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.

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
   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 streaming media where a relatively smooth
   sending rate is of importance.

   This document obsoletes RFC 3448 and updates RFC 4342.

Table of Contents

1. Introduction ....................................................3
2. Conventions .....................................................4
3. Protocol Mechanism ..............................................4
   3.1. TCP Throughput Equation ....................................5
   3.2. Packet Contents ............................................7
        3.2.1. Data Packets ........................................7
        3.2.2. Feedback Packets ....................................8
4. Data Sender Protocol ............................................8
   4.1. Measuring the Segment Size .................................9
   4.2. Sender Initialization .....................................10
   4.3. Sender Behavior When a Feedback Packet Is Received ........10
   4.4. Expiration of Nofeedback Timer ............................15
   4.5. Reducing Oscillations .....................................17



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   4.6. Scheduling of Packet Transmissions ........................18
5. Calculation of the Loss Event Rate (p) .........................19
   5.1. Detection of Lost or Marked Packets .......................19
   5.2. Translation from Loss History to Loss Events ..............20
   5.3. The Size of a Loss Interval ...............................22
   5.4. Average Loss Interval .....................................22
   5.5. History Discounting .......................................24
6. Data Receiver Protocol .........................................26
   6.1. Receiver Behavior When a Data Packet Is Received ..........27
   6.2. Expiration of Feedback Timer ..............................27
   6.3. Receiver Initialization ...................................28
        6.3.1. Initializing the Loss History after the
               First Loss Event ...................................29
7. Sender-Based Variants ..........................................30
8. Implementation Issues ..........................................31
   8.1. Computing the Throughput Equation .........................31
   8.2. Sender Behavior When a Feedback Packet Is Received ........32
        8.2.1. Determining If an Interval Was a
               Data-Limited Interval ..............................32
        8.2.2. Maintaining X_recv_set .............................34
   8.3. Sending Packets before Their Nominal Send Time ............34
   8.4. Calculation of the Average Loss Interval ..................36
   8.5. The Optional History Discounting Mechanism ................36
9. Changes from RFC 3448 ..........................................36
   9.1. Overview of Changes .......................................36
   9.2. Changes in Each Section ...................................37
10. Security Considerations .......................................39
   10.1. Security Considerations for TFRC in DCCP .................40
11. Acknowledgments ...............................................40
Appendix A. Terminology ...........................................41
Appendix B. The Initial Value of the Nofeedback Timer .............43
Appendix C. Response to Idle or Data-Limited Periods ..............44
   C.1.  Long Idle or Data-Limited Periods ........................45
   C.2.  Short Idle or Data-Limited Periods .......................48
   C.3.  Moderate Idle or Data-Limited Periods ....................49
   C.4.  Losses During Data-Limited Periods .......................50
   C.5.  Other Patterns ...........................................53
   C.6.  Evaluating TFRC's Response to Idle Periods ...............53
References ........................................................54
   Normative References ...........................................54
   Informative References .........................................54










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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 we call a flow "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 best performance with 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, perhaps with less
   optimal performance, with applications that do not 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 is specified in a separate document [RFC4828].



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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].

   This document obsoletes RFC 3448.  In the transport protocol DCCP
   (Datagram Congestion Control Protocol) [RFC4340], the Congestion
   Control ID Profiles CCID-3 [RFC4342] and CCID-4 [CCID-4] both specify
   the use of TFRC from RFC 3448.  CCID-3 and CCID-4 implementations
   SHOULD use this document instead of RFC 3448 for the specification of
   TFRC.

   The normative specification of TFRC is in Sections 3-6.  Section 7
   discusses sender-based variants, Section 8 discusses implementation
   issues, and Section 9 gives a non-normative overview of differences
   with RFC 3448.

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 [RFC2119].

   Appendix A gives a list of technical terms used in this document.

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.



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   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, and the resulting sending rate is limited to at most
       twice the receive rate to give the allowed transmit rate X.

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

   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 currently REQUIRED for TFRC is a slightly
   simplified version of the throughput equation for Reno TCP from
   [PFTK98].  Ideally, we would prefer a throughput equation based on
   selective acknowledgment (SACK) TCP, but no one has yet derived the
   throughput equation for SACK TCP, and simulations and experiments
   suggest that the differences between the two equations would be
   relatively minor [FF99] (Appendix B).

   The throughput equation for X_Bps, TCP's average sending rate in
   bytes per second, is:

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

   Where:

      X_Bps is TCP's average transmit rate in bytes per second.  (X_Bps
      is the same as X_calc in RFC 3448.)



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      s is the segment size in bytes (excluding IP and transport
      protocol headers).

      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 maximum number of packets acknowledged by a single TCP
      acknowledgement.

   Setting the TCP retransmission timeout value t_RTO:
   Implementations SHOULD set t_RTO = 4*R.  Implementations MAY choose
   to implement a more accurate calculation of t_RTO.  Implementations
   MAY also set t_RTO to max(4*R, one second), to match the recommended
   minimum of one second on the RTO [RFC2988].

   Setting the parameter b for delayed acknowledgements:
   Some current TCP connections use delayed acknowledgements, sending an
   acknowledgement for every two data packets received.  However, TCP is
   also allowed to send an acknowledgement for every data packet.  For
   the revised TCP congestion control mechanisms, [RFC2581bis] currently
   specifies that the delayed acknowledgement algorithm should be used
   with TCP.  However, [RFC2581bis] recommends increasing the congestion
   window during congestion avoidance by one segment per RTT even in the
   face of delayed acknowledgements, consistent with a TCP throughput
   equation with b = 1.  On an experimental basis, [RFC2581bis] allows
   for increases of the congestion window during slow-start that are
   also consistent with a TCP throughput equation with b = 1.  Thus, the
   use of b = 1 is consistent with [RFC2581bis].  The use of b = 1 is
   RECOMMENDED.

   With t_RTO=4*R and b=1, the throughput equation for X_Bps, the TCP
   sending rate in bytes per second, can be simplified as:

                                s
   X_Bps = -----------------------------------------------
           R * (sqrt(2*p/3) + 12*sqrt(3*p/8)*p*(1+32*p^2))

   In the future, updates to this document could specify different TCP
   equations to 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.






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   The throughput equation can also be expressed in terms of X_pps, the
   sending rate in packets per second, with

      X_pps =  X_Bps / s .

   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, the measurement of R is
   specified in Section 4.3, and the measurement of p is specified in
   Section 5.  In the rest of this document, data rates are measured in
   bytes per second unless otherwise specified.

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:

   o   A sequence number. This number MUST be 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 MAY be used 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.



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   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 is not required 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 the timestamps of transmitted
       data packets.

   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
       in the previous round-trip time.  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, then the sender
   cuts its sending rate in half.  This is achieved by means of a timer
   called the nofeedback timer.








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

   o   Measurement of the mean segment size being sent.

   o   Sender initialization.

   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 packet transmission and allowed burstiness.

4.1.  Measuring the Segment Size

   The TFRC sender uses the segment size, s, in the throughput equation,
   in the setting of the maximum receive rate, the setting of the
   minimum and initial sending rates, and 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.  As
   specified in Section 6.3.1, if the TFRC receiver does not know the
   segment size, s, used by the sender, the TFRC receiver MAY instead
   use the arrival rate in packets per second in initializing the loss
   history.

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

   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.

   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
       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 SHOULD estimate the segment size,
   s, as the average segment size over the last four loss intervals.
   The sender MAY estimate the average segment size over longer time
   intervals, if so desired.




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   The second class of applications are discussed separately in a
   separate document on TFRC-SP [RFC4828].  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 (the allowed sending rate in bytes per
   second) and tld (the Time Last Doubled during slow-start, in seconds)
   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 s bytes per second, for segment size s, the
   nofeedback timer is set to expire after two seconds, and tld is set
   to 0 (or to -1, either one is okay).  Upon receiving the first
   round-trip time measurement (e.g., after the first feedback packet or
   the SYN exchange from the connection setup, or from a previous
   connection [RFC2140]), tld is set to the current time, and the
   allowed transmit rate, X, is set to the initial_rate, specified as
   W_init/R, for W_init based on [RFC3390]:

      initial_rate = W_init/R; W_init = min(4*MSS, max(2*MSS, 4380)).

   In computing W_init, instead of using Maximum Segment Size (MSS), the
   TFRC sender SHOULD use the maximum segment size to be used for the
   initial round-trip time of data, if that is known by the TFRC sender
   when X is initialized.

   For responding to the initial feedback packet, this replaces step (4)
   of Section 4.3 below.

   Appendix B explains why the initial value of TFRC's nofeedback timer
   is set to two seconds, instead of the recommended initial value of
   three seconds for TCP's retransmit timer from [RFC2988].

4.3.  Sender Behavior When a Feedback Packet Is Received

   The sender knows its current allowed sending rate, X, and maintains
   an estimate of the current round-trip time R.  The sender also
   maintains X_recv_set as a small set of recent X_recv values
   (typically only two values).

   Initialization: X_recv_set is first initialized to contain a single
   item, with value Infinity.  (As an implementation-specific issue,
   X_recv_set MAY be initialized to a large number instead of to
   Infinity, e.g., to the largest integer that is easily representable.)





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   When a feedback packet is received by the sender at time t_now, the
   current time in seconds, the following actions MUST be performed.

   1)  Calculate a new round-trip sample:

      R_sample = (t_now - t_recvdata) - t_delay.

   As described in Section 3.2.2, t_delay gives the elapsed time at the
   receiver.

   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 a default value of 0.9 is RECOMMENDED.

   3)  Update the timeout interval:

      RTO = max(4*R, 2*s/X)

   4)  Update the allowed sending rate as follows.  This procedure uses
       the variables t_mbi and recv_limit:

      t_mbi: the maximum backoff interval of 64 seconds.
      recv_limit: the limit on the sending rate computed from
                       X_recv_set.

   This procedure also uses the procedures Maximize X_recv_set() and
   Update X_recv_set(), which are defined below.

















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   The procedure for updating the allowed sending rate:

      If (the entire interval covered by the feedback packet
            was a data-limited interval) {
          If (the feedback packet reports a new loss event or an
                       increase in the loss event rate p) {
              Halve entries in X_recv_set;
              X_recv = 0.85 * X_recv;
              Maximize X_recv_set();
              recv_limit = max (X_recv_set);
          } Else {
              Maximize X_recv_set();
              recv_limit = 2 * max (X_recv_set);
          }
      } Else {                      // typical behavior
          Update X_recv_set();
          recv_limit = 2 * max (X_recv_set);
      }
      If (p > 0) {          // congestion avoidance phase
          Calculate X_Bps using the TCP throughput equation.
          X = max(min(X_Bps, recv_limit), s/t_mbi);
      } Else if (t_now - tld >= R) {
          // initial slow-start
          X = max(min(2*X, recv_limit), initial_rate);
          tld = t_now;
      }

   5)  If oscillation reduction is used, calculate the instantaneous
       transmit rate, X_inst, following Section 4.5.

   6)  Reset the nofeedback timer to expire after RTO seconds.

   The procedure for maximizing X_recv_set keeps a single value, the
   largest value from X_recv_set and the new X_recv.

      Maximize X_recv_set():
          Add X_recv to X_recv_set;
          Delete initial value Infinity from X_recv_set,
             if it is still a member.
          Set the timestamp of the largest item to the current time;
          Delete all other items.










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   The procedure for updating X_recv_set keeps a set of X_recv values
   with timestamps from the two most recent round-trip times.

      Update X_recv_set():
          Add X_recv to X_recv_set;
          Delete from X_recv_set values older than
              two round-trip times.

   Definition of a data-limited interval:
   We define a sender as data-limited any time it is not sending as much
   as it is allowed to send.  We define an interval as a 'data-limited
   interval' if the sender was data-limited over the *entire* interval;
   Section 8.2.1 discusses implementation issues for a sender in
   determining if an interval was a data-limited interval.  The term
   'data-limited interval' is used in the first "if" condition in step
   (4), which prevents a sender from having to reduce its sending rate
   as a result of a feedback packet reporting the receive rate from a
   data-limited period.

   As an example, consider a sender that is sending at its full allowed
   rate, except that it is sending packets in pairs, rather than sending
   each packet as soon as it can.  Such a sender is considered data-
   limited part of the time, because it is not always sending packets as
   soon as it can.  However, consider an interval that covers this
   sender's transmission of at least two data packets; such an interval
   does not meet the definition of a data-limited interval because the
   sender was not data-limited *over the entire interval*.

   If the feedback packet reports a receive rate X_recv of zero (i.e.,
   the first feedback packet), the sender does not consider that the
   entire interval covered by the feedback packet was a data-limited
   interval.

   X_recv_set and the first feedback packet:
   Because X_recv_set is initialized with a single item, with value
   Infinity, recv_limit is set to Infinity for the first two round-trip
   times of the connection.  As a result, the sending rate is not
   limited by the receive rate during that period.  This avoids the
   problem of the sending rate being limited by the value of X_recv from
   the first feedback packet.

   The interval covered by a feedback packet:
   How does the sender determine the period covered by a feedback
   packet?  This is discussed in more detail in Section 8.2.  In
   general, the receiver will be sending a feedback packet once per
   round-trip time; so typically, the sender will be able to determine
   exactly the period covered by the current feedback packet from the
   previous feedback packet.  However, in cases when the previous



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   feedback packet was lost, or when the receiver sends a feedback
   packet early because it detected a lost or ECN-marked packet, the
   sender will have to estimate the interval covered by the feedback
   packet.  As specified in Section 6.2, each feedback packet sent by
   the receiver covers a round-trip time, for the round-trip time
   estimate R_m maintained by the receiver R_m seconds before the
   feedback packet was sent.

   The response to a loss during a data-limited interval:
   In TFRC, after the initial slow-start, the sender always updates the
   calculated transmit rate, X_Bps, after a feedback packet is received,
   and the allowed sending rate, X, is always limited by X_Bps.
   However, during a data-limited interval, when the actual sending rate
   is usually below X_Bps, the sending rate is still limited by
   recv_limit, derived from X_recv_set.  If the sender is data-limited,
   possibly with a varying sending rate from one round-trip time to the
   next, and is experiencing losses, then we decrease the entry in
   X_recv_set in order to reduce the allowed sending rate.

   The sender can detect a loss event during a data-limited period
   either from explicit feedback from the receiver, or from a reported
   increase in the loss event rate.  When the sender receives a feedback
   packet reporting such a loss event in a data-limited interval, the
   sender limits the allowed increases in the sending rate during the
   data-limited interval.

   The initial slow-start phase:
   Note that when p=0, the sender has not yet learned of any loss
   events, and the sender is in the initial slow-start phase.  In this
   initial slow-start phase, the sender can approximately double the
   sending rate each round-trip time until a loss occurs.  The
   initial_rate term in step (4) gives a minimum allowed sending rate
   during slow-start of the initial allowed sending rate.

   We note that if the sender is data-limited during slow-start, or if
   the connection is limited by the path bandwidth, then the sender is
   not necessarily able to double its sending rate each round-trip time;
   the sender's sending rate is limited to at most twice the past
   receive rate, or at most initial_rate, whichever is larger.  This is
   similar to TCP's behavior, where the sending rate is limited by the
   rate of incoming acknowledgement packets as well as by the congestion
   window.  Thus, in TCP's slow-start, for the most aggressive case of
   the TCP receiver acknowledging every data packet, the TCP sender's
   sending rate is limited to at most twice the rate of these incoming
   acknowledgment packets.






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   The minimum allowed sending rate:
   The term s/t_mbi ensures that when p > 0, the sender is allowed to
   send at least one packet every 64 seconds.

4.4.  Expiration of Nofeedback Timer

   This section specifies the sender's response to a nofeedback timer.
   The nofeedback timer could expire because of an idle period or
   because of data or feedback packets dropped in the network.

   This section uses the variable recover_rate.  If the TFRC sender has
   been idle ever since the nofeedback timer was set, the allowed
   sending rate is not reduced below the recover_rate.  For this
   document, the recover_rate is set to the initial_rate (specified in
   Section 4.2).  Future updates to this specification may explore other
   possible values for the recover_rate.

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

   1)  Cut the allowed sending rate in half.

      If the nofeedback timer expires when the sender has had at least
      one RTT measurement, the allowed sending rate is reduced by
      modifying X_recv_set as described in the pseudocode below
      (including item (2)).  In the general case, the sending rate is
      limited to at most twice X_recv.  Modifying X_recv_set limits the
      sending rate, but still allows the sender to slow-start, doubling
      its sending rate each RTT, if feedback messages resume reporting
      no losses.

      If the sender has been idle since this nofeedback timer was set
      and X_recv is less than the recover_rate, then the allowed sending
      rate is not halved, and X_recv_set is not changed.  This ensures
      that the allowed sending rate is not reduced to less than half the
      recover_rate as a result of an idle period.

      In the general case, the allowed sending rate is halved in
      response to the expiration of the nofeedback timer.  The details,
      in the pseudocode below, depend on whether the sender is in slow-
      start, is in congestion avoidance limited by X_recv, or is in
      congestion avoidance limited by the throughput equation.









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      X_recv = max (X_recv_set);
      If (sender does not have an RTT sample,
          has not received any feedback from receiver,
          and has not been idle ever since the nofeedback timer
          was set) {
          // We do not have X_Bps or recover_rate yet.
          // Halve the allowed sending rate.
          X = max(X/2, s/t_mbi);
      } Else if (((p>0 && X_recv < recover_rate) or
            (p==0 && X < 2 * recover_rate)), and
             sender has been idle ever
             since nofeedback timer was set) {
          // Don't halve the allowed sending rate.
          Do nothing;
      } Else if (p==0) {
          // We do not have X_Bps yet.
          // Halve the allowed sending rate.
          X = max(X/2, s/t_mbi);
      } Else if (X_Bps > 2*X_recv)) {
          // 2*X_recv was already limiting the sending rate.
          // Halve the allowed sending rate.
          Update_Limits(X_recv;)
      } Else {
          // The sending rate was limited by X_Bps, not by X_recv.
          // Halve the allowed sending rate.
          Update_Limits(X_Bps/2);
      }

      The term s/t_mbi limits the backoff to one packet every 64
      seconds.

      The procedure Update_Limits() uses the variable timer_limit for
      the limit on the sending rate computed from the expiration of the
      nofeedback timer, as follows:

      Update_Limits(timer_limit):
          If (timer_limit < s/t_mbi)
              timer_limit = s/t_mbi;
          Replace X_recv_set contents with the single item
               timer_limit/2;
          Recalculate X as in step (4) of Section 4.3;

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

   If the sender has been data-limited but not idle since the nofeedback
   timer was set, it is possible that the nofeedback timer expired
   because data or feedback packets were dropped in the network.  In



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   this case, the nofeedback timer is the backup mechanism for the
   sender to detect these losses, similar to the retransmit timer in
   TCP.

   Note that when the sender stops sending data for a period of time,
   the receiver will stop sending feedback.  When the sender's
   nofeedback timer expires, the sender could use the procedure above to
   limit the sending rate.  If the sender subsequently starts to send
   again, X_recv_set will be used to limit the transmit rate, and slow-
   start behavior will occur until the transmit rate reaches X_Bps.

   The TFRC sender's reduction of the allowed sending rate after the
   nofeedback timer expires is similar to TCP's reduction of the
   congestion window, cwnd, after each RTO seconds of an idle period,
   for TCP with Congestion Window Validation [RFC2861].

4.5.  Reducing Oscillations

   To reduce oscillations in queueing delay and sending rate in
   environments with a low degree of statistical multiplexing at the
   congested link, it is RECOMMENDED that the sender reduce the transmit
   rate as the queueing delay (and hence RTT) increases.  To do this,
   the sender maintains R_sqmean, a long-term estimate of the square
   root of the RTT, and modifies its sending rate depending on how the
   square root of R_sample, the most recent sample of the RTT, differs
   from the long-term estimate.  The long-term estimate R_sqmean 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, the constant used in the round-trip time estimate R.
   A value of 0.9 as the default for q2 is RECOMMENDED.

   When sqrt(R_sample) is greater than R_sqmean, then the current
   round-trip time is greater than the long-term average, implying that
   queueing delay is probably increasing.  In this case, the transmit
   rate is decreased to minimize oscillations in queueing delay.

   The sender obtains the base allowed transmit rate, X, as described in
   step (4) of Section 4.3 above.  It then calculates a modified
   instantaneous transmit rate X_inst, as follows:




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      X_inst = X * R_sqmean / sqrt(R_sample);
      If (X_inst < s/t_mbi)
          X_inst = s/t_mbi;

   Because we are using square roots, there is generally only a moderate
   difference between the instantaneous transmit rate X_inst and the
   allowed transmit rate X.  For example, in a somewhat extreme case
   when the current RTT sample R_sample is twice as large as the long-
   term average, then sqrt(R_sample) will be roughly 1.44 times
   R_sqmean, and the allowed transmit rate will be reduced by a factor
   of roughly 0.7.

   We note that this modification for reducing oscillatory behavior is
   not always needed, especially if the degree of statistical
   multiplexing in the network is high.  We also note that the
   modification for reducing oscillatory behavior could cause problems
   for connections where the round-trip time is not strongly correlated
   with the queueing delay (e.g., in some wireless links, over paths
   with frequent routing changes, etc.).  However, this modification
   SHOULD be implemented because it makes TFRC behave better in some
   environments with a low level of statistical multiplexing.  The
   performance of this modification is illustrated in Section 3.1.3 of
   [FHPW00].  If it is not implemented, implementations SHOULD use a
   very low value of the weight q for the average round-trip time.

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 coarse-grain or irregular scheduling of the operating
   system.  To help maintain the correct average sending rate, the TFRC
   sender MAY send some packets before their nominal send time.

   In addition, the scheduling of packet transmissions controls the
   allowed burstiness of senders after an idle or data-limited period.
   The TFRC sender MAY accumulate sending 'credits' for past unused send
   times; this allows the TFRC sender to send a burst of data after an
   idle or data-limited period.  To compare with TCP, TCP may send up to
   a round-trip time's worth of packets in a single burst, but never
   more.  As examples, packet bursts can be sent by TCP when an ACK
   arrives acknowledging a window of data, or when a data-limited sender
   suddenly has a window of data to send after a delay of nearly a
   round-trip time.







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   To limit burstiness, a TFRC implementation MUST prevent bursts of
   arbitrary size.  This limit MUST be less than or equal to one round-
   trip time's worth of packets.  A TFRC implementation MAY limit bursts
   to less than a round-trip time's worth of packets.  In addition, a
   TFRC implementation MAY use rate-based pacing to smooth bursts.

   As an implementation-specific example, a sending loop could calculate
   the correct inter-packet interval, t_ipi, as follows:

      t_ipi = s/X_inst;

   Let t_now be the current time and i be a natural number, i = 0, 1,
   ..., with t_i the nominal send time for the i-th packet.  Then, the
   nominal send time t_(i+1) would derive recursively as:

      t_0 = t_now,
      t_(i+1) = t_i + t_ipi.

   For TFRC senders allowed to accumulate sending credits for unused
   send time over the last T seconds, the sender would be allowed to use
   unused nominal send times t_j for t_j < now - T, for T set to the
   round-trip time.

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.  If
   the receiver has not yet detected a lost or marked packet, then the
   receiver does not calculate the loss event rate, but reports a loss
   event rate of zero.

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, it is REQUIRED 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.





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   The receiver maintains a data structure that keeps track of which
   packets have arrived and which are missing.  For the purposes of this
   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 such a mechanism is not part of
   the current specification.

   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.

   If an ECN-marked packet is preceded by a possibly-lost packet, then
   the first detected congestion event begins with the lost packet.  For
   example, if the receiver receives a data packet with sequence number
   n-1, followed by an unmarked data packet with sequence number n+1,
   and a marked data packet with sequence number n+2, then the receiver
   detects a congestion event when it receives the marked packet n+2.
   The first congestion event detected begins with the lost packet n.
   The guidelines in Section 5.2 below are used to determine whether the
   lost and marked packets belong to the same loss event or to separate
   loss events.

5.2.  Translation from Loss History to Loss Events

   TFRC requires that the loss fraction be robust to several consecutive
   packets lost or marked in 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 or marked 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






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   piggy-backed onto a data packet.  TFRC is not sensitive to how the
   RTT measurement sent to the receiver is made, but it is RECOMMENDED
   to use 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,
      before any packet arrivals with a sequence number above S_loss,
      with a sequence number below S_loss.

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

      S_max is the largest sequence number.

   Therefore, S_before < S_loss < S_after <= S_max.

      T_loss is the nominal estimated arrival time for the lost packet.

      T_before is the reception time of S_before.

      T_after is the reception time of S_after.

   Note that T_before < T_after.

   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) );

   To address sequence number wrapping, let S_MAX = 2^b, where b is the
   bit-length of sequence numbers in a given implementation.  In this
   case, we can interpolate the arrival time T_loss as follows:








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

   where

      Dist(S_A, S_B) = (S_A + S_MAX - S_B) % S_MAX

   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.  The Size of a Loss Interval

   After the detection of the first loss event, the receiver divides the
   sequence space into loss intervals.  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).
   Thus, loss interval A contains all of the packets transmitted by the
   sender starting with the first packet transmitted in loss interval A
   and ending with but not including the first packet transmitted in
   loss interval B.

   The current loss interval I_0 is defined as the loss interval
   containing the most recent loss event.  If that loss event started
   with packet sequence number S_A, and S_C is the highest received
   sequence number so far, then the size of I_0 is S_C - S_A + 1.  As an
   example, if the current loss interval consists of a single ECN-
   marked packet, then S_A == S_C, and the size of the loss interval is
   one.

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.  If the receiver has not yet seen a lost
   or marked packet, then the receiver does not calculate the average
   loss interval.








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

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

   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.  It is RECOMMENDED to set the value n to 8.
   TFRC SHOULD NOT use values of n 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 current loss interval.  We only include the current
   loss interval 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
   current loss interval.  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
   as follows:

      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;



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5.5.  History Discounting

   As described in Section 5.4, when there have been at least n loss
   intervals, 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
   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 current
   loss interval I_0.  The computation of the average loss interval
   using the discount factors is a simple modification of the procedure
   in Section 5.4, as follows:
















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      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 size of current
   loss interval.  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 0.25.  Note that with each new packet
   arrival, I_0 will increase further, and the discount factor DF will
   be updated.





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   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 respond 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 sent 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.

   If the receiver was sending k feedback packets per RTT, for k>1, step
   (4) of Section 6.2 would be modified to set the feedback timer to
   expire after R_m/k seconds.  However, each feedback packet would
   still report the receiver rate over the last RTT, not over a fraction
   of an RTT.  In this document, we do not specify the modifications
   that might be required for a receiver sending more than one feedback
   packet per RTT.  We note that there is little gain from sending a
   large number of feedback messages per RTT.




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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)  Check if done: If the new packet results in the detection of a
       new loss event, or if no feedback packet was sent when the
       feedback timer last expired, go to step 3.  Otherwise, no action
       need be performed (unless the optimization in the next paragraph
       is used), so exit the procedure.

       An OPTIONAL 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.

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

   4)  Expire feedback timer: If p > p_prev, cause the feedback timer to
       expire and perform the actions described in Section 6.2.

       If p <= p_prev and no feedback packet was sent when the feedback
       timer last expired, cause the feedback timer to expire and
       perform the actions described in Section 6.2.  If p <= p_prev and
       a feedback packet was sent when the feedback timer last expired,
       no action need be performed.

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.

   For the m-th expiration of the feedback timer, 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.  As
   described in Section 3.2.1, R_m is the sender's most recent estimate
   of the round-trip time, as reported in data packets.  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 in Section 5.



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   2)  Calculate the measured receive rate, X_recv, based on the packets
       received within the previous R_(m-1) seconds.  This is performed
       whether the feedback timer expired at its normal time or expired
       early due to a new lost or marked packet (i.e., step (3) in
       Section 6.1).

       In the typical case, when the receiver is sending only one
       feedback packet per round-trip time and the feedback timer did
       not expire early due to a new lost packet, then the time interval
       since the feedback timer last expired would be R_(m-1) seconds.

       We note that when the feedback timer expires early due to a new
       lost or marked packet, the time interval since the feedback timer
       last expired is likely to be smaller than R_(m-1) seconds.

       For ease of implementation, if the time interval since the
       feedback timer last expired is not R_(m-1) seconds, the receive
       rate MAY be calculated over a longer time interval, the time
       interval going back to the most recent feedback timer expiration
       that was at least R_(m-1) seconds ago.

   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, then 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.



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   o   Set the feedback timer to expire after R_i seconds.

   If the first data packet does not 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.

   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

   This section describes the procedure that MUST be used for
   initializing the loss history after the first loss event.

   The number of packets until the first loss cannot be used to compute
   the allowed 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 maximum sending rate before the
   loss occurred.  TFRC approximates this target rate, X_target, by the
   maximum value of X_recv so far.  (For slow-start, for a particular
   round-trip time, the sender's sending rate is generally twice the
   receiver's receive rate for data sent over the previous 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_target, 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_target,
   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



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   sender, then the receiver MAY use the throughput equation for X;
   otherwise, the receiver MAY measure 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.)

   Special care is needed for initializing the first loss interval when
   the first data packet is lost or marked.  When the first data packet
   is lost in TCP, the TCP sender retransmits the packet after the
   retransmit timer expires.  If TCP's first data packet is ECN-marked,
   the TCP sender resets the retransmit timer, and sends a new data
   packet only when the retransmit timer expires [RFC3168] (Section
   6.1.2).  For TFRC, if the first data packet is lost or ECN-marked,
   then the first loss interval consists of the null interval with no
   data packets.  In this case, the loss interval length for this (null)
   loss interval SHOULD be set to give a similar sending rate to that of
   TCP, as specified in the paragraph below.

   When the first TFRC loss interval is null, meaning that the first
   data packet is lost or ECN-marked, in order to follow the behavior of
   TCP, TFRC wants the allowed sending rate to be 1 packet every two
   round-trip times, or equivalently, 0.5 packets per RTT.  Thus, the
   TFRC receiver calculates the loss interval that would be required to
   produce the target rate X_target of 0.5/R packets per second, for the
   round-trip time R, and uses this synthetic loss interval for the
   first loss interval.  The TFRC receiver uses 0.5/R packets per second
   as the minimum value for X_target when initializing the first loss
   interval.

   We note that even though the TFRC receiver reports a synthetic loss
   interval after the first loss event, the TFRC receiver still reports
   the measured receive rate X_recv, as specified in Section 6.2 above.

7.  Sender-Based Variants

   In a sender-based variant of TFRC, 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.

   The main advantage of a sender-based variant of TFRC is that the
   sender does 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.




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   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 where it is desirable to offload
   work from the server to the client as much as possible.

   RFC 4340 and RFC 4342 together specify DCCP's CCID 3, which can be
   used as a sender-based variant of TFRC.  In CCID 3, each feedback
   packet from the receiver contains a Loss Intervals option, reporting
   the lengths of the most recent loss intervals.  Feedback packets may
   also include the Ack Vector option, allowing the sender to determine
   exactly which packets were dropped or marked and to check the
   information reported in the Loss Intervals options.  The Ack Vector
   option can also include ECN Nonce Echoes, allowing the sender to
   verify the receiver's report of having received an unmarked data
   packet.  The Ack Vector option allows the sender to see for itself
   which data packets were lost or ECN-marked, to determine loss
   intervals, and to calculate the loss event rate.  Section 9 of RFC
   4342 discusses issues in the sender verifying information reported by
   the receiver.

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 implementation issues.

8.1.  Computing the Throughput Equation

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

                  s
      X_Bps =  --------
               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).

   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.





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8.2.  Sender Behavior When a Feedback Packet Is Received

   This section discusses implementation issues for sender behavior when
   a feedback packet is received, from Section 4.3.

8.2.1.  Determining If an Interval Was a Data-Limited Interval

   When a feedback packet is received, the sender has to determine if
   the entire interval covered by that feedback packet was a data-
   limited period.  This section discusses one possible implementation
   for the sender to determine if the interval covered by a feedback
   packet was a data-limited period.

   If the feedback packets all report the timestamp of the last data
   packet received, then let t_new be the timestamp reported by this
   feedback packet.  Because all feedback packets cover an interval of
   at least a round-trip time, it is sufficient for the sender to
   determine if there was any time in the period (t_old, t_new] when the
   sender was not data-limited, for R the sender's estimate of the
   round-trip time, and for t_old set to t_new - R.  (This procedure
   estimates the interval covered by the feedback packet, rather than
   computing it exactly.  This seems fine to us.)

   The pseudocode for determining if the sender was data-limited over
   the entire interval covered in a feedback packet is given below.  The
   variables NotLimited1 and NotLimited2 both represent times when the
   sender was *not* data-limited.

   Initialization:
       NotLimited1 = NotLimited2 = t_new = t_next = 0;
       t_now = current time;

   After sending a segment:
       If (sender has sent all it is allowed to send) {
           // Sender is not data-limited at this instant.
           If NotLimited1 <= t_new
               // Goal: NotLimited1 > t_new.
               NotLimited1 = t_now;
           Else if (NotLimited2 <= t_next)
               // Goal: NotLimited2 > t_next.
               NotLimited2 = t_now;
       }









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   When a feedback packet is received, is this interval data-limited:
       t_new = timestamp reported in feedback packet.
       t_old = t_new - R.                         // local variable
       t_next = t_now;
       If ((t_old < NotLimited1 <= t_new) or
           (t_old < NotLimited2 <= t_new))
           This was not a data-limited interval;
       Else
           This was a data-limited interval.
       If (NotLimited1 <= t_new && NotLimited2 > t_new)
           NotLimited1 = NotLimited2;

   Transmission times refer to transmission of a segment or segments to
   the layer below.

   Between feedback packets, (t_old, t_new] gives the transmission time
   interval estimated to be covered by the most recent feedback packet,
   and t_next gives a time at least a round-trip time greater than
   t_new.  The next feedback packet can be expected to cover roughly the
   interval (t_new, t_next] (unless the receiver sends the feedback
   packet early because it is reporting a new loss event).  The goal is
   for NotLimited1 to save a non-data-limited time in (t_new, t_next],
   if there was one, and for NotLimited2 to save a non-data-limited time
   after t_next.

   When a feedback packet was received, if either NotLimited1 or
   NotLimited2 is in the time interval covered by the feedback packet,
   then the interval is not a data-limited interval; the sender was not
   data-limited at least once during that time interval.  If neither
   NotLimited1 nor NotLimited2 is in the time interval covered by a
   feedback packet, then the sender is assumed to have been data-limited
   over that time interval.

   We note that this procedure is a heuristic, and in some cases the
   sender might not determine correctly if the sender was data-limited
   over the entire interval covered by the feedback packet.  This
   heuristic does not address the possible complications of reordering.

   That seems acceptable to us.  In order to improve its accuracy in
   identifying if the entire interval covered by a feedback packet was a
   data-limited interval, the sender could save more NotLimited times.

   In some implementations of TFRC, the sender sends coarse-grained
   timestamps that increment every quarter of a round-trip time, and the
   feedback packet reports the greatest valid sequence number received
   so far instead of reporting the timestamp of the last packet
   received.  In this case, the sender can maintain per-packet state to




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   determine t_new (the time that the acknowledged packet was sent), or
   the sender can estimate t_new from its estimate of the round-trip
   time and the elapsed time t_delay reported by the feedback packet.

8.2.2.  Maintaining X_recv_set

   To reduce the complexity of maintaining X_recv_set, it is sufficient
   to limit X_recv_set to at most N=3 elements.  In this case, the
   procedure Update X_recv_set() would be modified as follows:

      Update X_recv_set():
          Add X_recv to X_recv_set;
          Delete from X_recv_set values older than
              two round-trip times.
          Keep only the most recent N values.

   Maintaining at most *two* elements in X_recv_set would be sufficient
   for the sender to save an old value of X_recv from before a data-
   limited period, and to allow the sender not to be limited by the
   first feedback packet after an idle period (reporting a receive rate
   of one packet per round-trip time).  However, it is *possible* that
   maintaining at most two elements in X_recv_set would not give quite
   as good performance as maintaining at most three elements.
   Maintaining three elements in X_recv_set would allow X_recv_set to
   contain X_recv values from two successive feedback packets, plus a
   more recent X_recv value from a loss event.

8.3.  Sending Packets before Their Nominal Send Time

   This section discusses one possible scheduling mechanism for a sender
   in an operating system with a coarse-grained timing granularity (from
   Section 4.6).

   Let t_gran be the scheduling timer granularity of the operating
   system.  Let t_ipi be the inter-packet interval, as specified in
   Section 4.6.  If the operating system has a coarse timer granularity
   or otherwise cannot support short t_ipi intervals, then either the
   TFRC sender will be restricted to a sending rate of at most 1 packet
   every t_gran seconds, or the TFRC sender must be allowed to send
   short bursts of packets.  In addition to allowing the sender to
   accumulate sending credits for past unused send times, it can be
   useful to allow the sender to send a packet before its scheduled send
   time, as described in the section below.

   A parameter, t_delta, may be used to allow a packet to be sent before
   its nominal send time.  Consider an application that becomes idle and
   requests re-scheduling for time t_i = t_(i-1) + t_ipi, for t_(i-1)
   the send time for the previous packet.  When the application is



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   rescheduled, it checks the current time, t_now.  If
   (t_now > t_i - t_delta), then packet i is sent.  When the nominal
   send time, t_i, of the next packet is calculated, it may already be
   the case that t_now > t_i - t_delta.  In such a case, the packet
   would be sent immediately.

   In order to send at most one packet before its nominal send time, and
   never to send a packet more than a round-trip time before its nominal
   send time, the parameter t_delta would be set as follows:

      t_delta = min(t_ipi, t_gran, rtt)/2;

   (The scheduling granularity t_gran is 10 ms on some older Unix
   systems.)

   As an example, consider a TFRC flow with an allowed sending rate X of
   10 packets per round-trip time (PPR), a round-trip time of 100 ms, a
   system with a scheduling granularity t_gran of 10 ms, and the ability
   to accumulate unused sending credits for a round-trip time.  In this
   case, t_ipi is 1 ms.  The TFRC sender would be allowed to send
   packets 0.5 ms before their nominal sending time, and would be
   allowed to save unused sending credits for 100 ms.  The scheduling
   granularity of 10 ms would not significantly affect the performance
   of the connection.

   As a different example, consider a TFRC flow with a scheduling
   granularity greater than the round-trip time, for example, with a
   round-trip time of 0.1 ms and a system with a scheduling granularity
   of 1 ms, and with the ability to accumulate unused sending credits
   for a round-trip time.  The TFRC sender would be allowed to save
   unused sending credits for 0.1 ms.  If the scheduling granularity
   *did not* affect the sender's response to an incoming feedback
   packet, then the TFRC sender would be able to send an RTT of data (as
   determined by the allowed sending rate) each RTT, in response to
   incoming feedback packets.  In this case, the coarse scheduling
   granularity would not significantly reduce the sending rate, but the
   sending rate would be bursty, with a round-trip time of data sent in
   response to each feedback packet.

   However, performance would be different, in this case, if the
   operating system scheduling granularity affected the sender's
   response to feedback packets as well as the general scheduling of the
   sender.  In this case, the sender's performance would be severely
   limited by the scheduling granularity being greater than the round-
   trip time, with the sender able to send an RTT of data, at the
   allowed sending rate, at most once every 1 ms.  This restriction of
   the sending rate is an unavoidable consequence of allowing burstiness
   of at most a round-trip time of data.



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8.4.  Calculation of the Average Loss Interval

   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.

8.5.  The Optional History Discounting Mechanism

   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

9.1.  Overview of Changes

   This section summarizes the changes from RFC 3448.  At a high level,
   the main change is to add mechanisms to address the case of a data-
   limited sender.  This document also explicitly allows the TFRC sender
   to accumulate up to a round-trip time of unused send credits, and as
   a result to send a burst of packets if data arrives from the
   application in a burst after a data-limited period.  This issue was
   not explicitly addressed in RFC 3448.

   This document changes RFC 3448 to incorporate TCP's higher initial
   sending rates from RFC 3390.  This document also changes RFC 3448 to
   allow RFC 4342's use of a coarse-grained timestamp on data packets
   instead of a more fine-grained timestamp.

   Other changes address corner cases involving slow-start, the response
   when the first data packet is dropped, and the like.  This document
   also incorporates the items in the RFC 3448 Errata.

   This section is non-normative;  the normative text is in the cited
   sections.







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9.2.  Changes in Each Section

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

   Section 4.2, update 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.  The initial sending rate was
   changed to be in terms of the segment size s, not in terms of the
   MSS.

   Section 4.2 now says that tld, the Time Last Doubled during slow-
   start, can be initialized to either 0 or to -1.  Section 4.2 was also
   clarified to say that RTT measurements do not only come from feedback
   packets; they could also come from other places, such as the SYN
   exchange.

   Section 4.3, response to feedback packets: Section 4.3 was modified
   to change the way that the receive rate is used in limiting the
   sender's allowed sending rate, by using the set of receive rate
   values of the last two round-trip times, and initializing the set of
   receive rate values by a large value.

   The larger initial sending rate in Section 4.2 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 two packets per RTT, which would be twice the receive
   rate.  Because of the change in the sender's processing of the
   receive rate, the sender now does not reduce the allowed sending rate
   to twice the reported receive rate in response to the first feedback
   packet.

   During a data-limited period, the sender saves the receive rate
   reported from just before the data-limited period, if it is larger
   than the receive rate during the data-limited period.  The sender
   also reduces the saved values in X_recv_set in response to a loss
   during a data-limited period.  Appendix C discusses this response
   further.

   Section 4.4, response to an idle period: Following Section 5.1 from
   [RFC4342], this document specifies that when the sending rate is
   reduced after an idle period that covers the period since the
   nofeedback timer was set, the allowed sending rate is not reduced
   below the initial sending rate.  (In Section 4.4, the variable
   recover_rate is set to the initial sending rate.)




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   Section 4.4, correction from [RFC3448Err].  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].

   Section 4.4, clarification for slow-start: Section 4.4 was clarified
   to specify that on the expiration of the nofeedback timer, if p = 0,
   X_Bps cannot be used, because the sender does not yet have a value
   for X_Bps.  Section 4.4 was also clarified to check the case when the
   sender does not yet have an RTT sample, but has sent a packet since
   the nofeedback timer was set.

   Section 4.6: credits for unused send time:

   Section 4.6 has been clarified to say that the TFRC sender gets to
   accumulate up to an RTT of credits for unused send time.  Section 4.6
   was also rewritten to clarify what is specification and what is
   implementation.

   Section 5.4, clarification: Section 5.4 was modified to clarify the
   receiver's calculation of the average loss interval when the receiver
   has not yet seen n loss intervals.

   Section 5.5, correction: Section 5.5 was corrected to say that the
   loss interval I_0 includes all transmitted packets, including lost
   and marked packets (as defined in Section 5.3 in the general
   definition of loss intervals).

   Section 5.5, correction from [RFC3448Err]: 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].

   Section 5.5, history discounting: THRESHOLD, the lower bound on the
   history discounting parameter DF, has been changed from 0.5 to 0.25,
   to allow more history discounting when the current interval is long.

   Section 6, multiple feedback packets: Section 6 now contains more
   discussion of procedures if the receiver sends multiple feedback
   packets each round-trip time.



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   Section 6.3, initialization of the feedback timer: Section 6.3 now
   specifies the receiver's initialization of the feedback timer if the
   first data packet received does not have an estimate of the round-
   trip time.

   Section 6.3, a coarse-grained timestamp: Section 6.3 was modified to
   incorporate, as an option, a coarse-grained timestamp from the sender
   that increments every quarter of a round-trip time, instead of a more
   fine-grained timestamp.  This follows RFC 4342.

   Section 6.3.1, after the first loss event: Section 6.3.1 now says
   that for initializing the loss history after the first loss event,
   the receiver uses the maximum receive rate so far, instead of the
   receive rate in the last round-trip time.

   Section 6.3.1, if the first data packet is dropped: Section 6.3.1 now
   contains a specification for initializing the loss history if the
   first data packet sent is lost or ECN-marked.

   Section 7, sender-based variants: Section 7's discussion of sender-
   based variants has been expanded, with reference to RFC 4342.

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.

10.1.  Security Considerations for TFRC in DCCP

   TFRC is currently used in Congestion Control ID 3 (CCID 3) [RFC4342]
   of the Datagram Congestion Control Protocol (DCCP) [RFC4340].  The
   Security Considerations section of RFC 4340 [RFC4340] (Section 18)
   discusses some of the security issues of DCCP, including sequence
   number validity checks to protect against hijacked connections.
   Section 18 of RFC 4340 also discusses mechanisms in DCCP to limit the
   potential impact of denial-of-service attacks.

   RFC 4342 specifies the use of TFRC in CCID 3.  RFC 4342 includes
   extensive discussions of the mechanisms the sender can use to verify
   the information sent by the receiver.  When ECN is used with CCID 3,
   the receiver returns ECN Nonce information to the sender, to allow
   the sender to verify information sent by the receiver.  When ECN is
   not used, Section 9 of RFC 4342 discusses how the sender could still
   use various techniques that might catch the receiver in an error in
   reporting congestion.  However, as stated in RFC 4342, this is not as
   robust or non-intrusive as the verification provided by the ECN
   Nonce.

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 Dado Colussi, Gorry Fairhurst, Ladan Gharai,
   Wim Heirman, Eddie Kohler, Ken Lofgren, Mike Luby, Ian McDonald,
   Vladimir Moltchanov, Colin Perkins, Michele R., Gerrit Renker, Arjuna
   Sathiaseelan, 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 [RFC3448] to produce a working implementation.










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Appendix A.  Terminology

   This document uses the following terms.  Timer variables (e.g.,
   t_now, tld) are assumed to be in seconds, with a timer resolution of
   at least a millisecond.

   data-limited interval:
      An interval where the sender is data-limited (not sending as much
      as it is allowed to send) over the entire interval (Section 4.3).

   DF: Discount factor for a loss interval (Section 5.5).

   initial_rate:
      Allowed initial sending rate.

   last_counter:
      Greatest received value of the window counter (Section 6.3).

   n:  Number of loss intervals.

   NDUPACK:
      Number of dupacks for inferring loss (constant) (Section 5.1).

   nofeedback timer:
      Sender-side timer (Section 4).

   p:  Estimated Loss Event Rate.

   p_prev:
      Previous value of p (Section 6.1).

   q:  Filter constant for RTT (constant) (Section 4.3).

   q2: Filter constant for long-term RTT (constant) (Section 4.6).

   R:  Estimated path round-trip time.

   R_m:
      A specific estimate of the path round-trip time (Sections 4.3, 6).

   R_sample:
      Measured path RTT (Section 4.3).

   R_sqmean:
      Long-term estimate of the square root of the RTT (Section 4.6).

   recover_rate:
      Allowed rate for resuming after an idle period (Section 4.4).



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   recv_limit;
      Limit on sending rate computed from X_recv_set (Section 4.3).

   s:  Nominal packet size in bytes.

   S:  Sequence number.

   t_delay:
      Reported time delay between receipt of the last packet at the
      receiver and the generation of the feedback packet (Section
      3.2.2).

   t_delta:
      Parameter for flexibility in send time (Section 8.3).

   t_gran:
      Scheduling timer granularity of the operating system (constant)
      (Section 8.3).

   t_ipi:
      Inter-packet interval for sending packets (Section 4.6).

   t_mbi:
      Maximum RTO value of TCP (constant) (Section 4.3).

   t_recvdata:
      Timestamp of the last data packet received (Section 3.2.2).

   timer_limit:
      Limit on the sending rate from the expiration of the nofeedback
      timer (Section 4.4).

   tld:
      Time Last Doubled (Section 4.2).

   t_now:
      Current time (Section 4.3).

   t_RTO:
      Estimated RTO of TCP (Section 4.3).

   X:  Allowed transmit rate, as limited by the receive rate.

   X_Bps:
      Calculated sending rate in bytes per second (Section 3.1).

   X_pps:
      Calculated sending rate in packets per second (Section 3.1).



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   X_inst:
      Instantaneous allowed transmit rate (Section 4.6).

   X_recv:
      Estimated receive rate at the receiver (Section 3.2.2).

   X_recv_set:
      A small set of recent X_recv values (Section 4.3).

   X_target:
      The target sending rate after the first loss event (Section
      6.3.1).

   W_init:
      TCP initial window (constant) (Section 4.2).

Appendix B.  The Initial Value of the Nofeedback Timer

   Why is the initial value of TFRC's nofeedback timer set to two
   seconds, instead of the recommended initial value of three seconds
   for TCP's retransmit timer, from [RFC2988]?  There is not any
   particular reason why TFRC's nofeedback timer should have the same
   initial value as TCP's retransmit timer.  TCP's retransmit timer is
   used not only to reduce the sending rate in response to congestion,
   but also to retransmit a packet that is assumed to have been dropped
   in the network.  In contrast, TFRC's nofeedback timer is only used to
   reduce the allowed sending rate, not to trigger the sending of a new
   packet.  As a result, there is no danger to the network for the
   initial value of TFRC's nofeedback timer to be smaller than the
   recommended initial value for TCP's retransmit timer.

   Further, when the nofeedback timer has not yet expired, TFRC has a
   more slowly responding congestion control mechanism than TCP, and
   TFRC's use of the receive rate for limiting the sending rate is
   somewhat less precise than TCP's use of windows and ack-clocking, so
   the nofeedback timer is a particularly important safety mechanism for
   TFRC.  For all of these reasons, it is perfectly reasonable for
   TFRC's nofeedback timer to have a smaller initial value than that of
   TCP's retransmit timer.












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Appendix C.  Response to Idle or Data-Limited Periods

   Future work could explore alternate responses to using the receive
   rate during a data-limited period, and to responding to a loss event
   during a data-limited period.

   In particular, an Experimental RFC [RFC2861] specifies Congestion
   Window Validation (CWV) for TCP.  For this discussion, we use the
   term "Standard TCP" to refer to the TCP congestion control mechanisms
   in [RFC2581] and [RFC2581bis].  [RFC2861] specifies a different
   response to idle or data-limited periods than those of Standard TCP.
   With CWV, the TCP sender halves the congestion window after each RTO
   during an idle period, down to the initial window.  Similarly, with
   CWV the TCP sender halves the congestion window half-way down to the
   flight size after each RTO during a data-limited period.

   This document already specifies a TFRC response to idle periods that
   is similar to that of TCP with Congestion Window Validation.
   However, this document does not specify a TFRC response to data-
   limited periods similar to that of CWV.  Adding such a mechanism to
   TFRC would require a one-line change to step (4) of Section 4.3.  In
   particular, the sender's response to a feedback packet could be
   changed from:

      If (the entire interval covered by the feedback packet
            was a data-limited interval) {
          If (the feedback packet reports a new loss event or an
                       increase in the loss event rate p) {
              Halve entries in X_recv_set;
              X_recv = 0.85 * X_recv;
              Maximize X_recv_set();
              recv_limit = max (X_recv_set);
          } Else {
              Maximize X_recv_set();
              recv_limit = 2 * max (X_recv_set);
          }
      }














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   to:

      If (the entire interval covered by the feedback packet
            was a data-limited interval) {
          Multiply old entries in X_recv_set by 0.85;
          If (the feedback packet reports a new loss event or an
                       increase in the loss event rate p) {
              Multiply new value X_recv by 0.85.
          }
          Maximize X_recv_set();
          recv_limit = 2 * max (X_recv_set);
      }

   In particular, if the receive rate from before a data-limited period
   is saved in X_recv_set, then the change in step (4) above would
   multiply that receive rate by 0.85 each time that a feedback packet
   is received and the above code is executed.  As a result, after four
   successive round-trip times of data-limited intervals, the receive
   rate from before the data-limited period would be reduced by 0.85^4 =
   0.52.  Thus, this one-line change to step (4) of Section 4.3 would
   result in the allowed sending rate being halved for each four
   roundtrip times in which the sender was data-limited.  Because of the
   nature of X_recv_set, this mechanism would never reduce the allowed
   sending rate below twice the most recent receive rate.

   We note that in the suggested code above, with CWV-style behavior in
   response to data-limited intervals, we keep

      recv_limit = 2 * max (X_recv_set);

   instead of using

      recv_limit = max (X_recv_set);

   following loss events in data-limited intervals.  This relaxed
   response to a loss event is allowed because the CWV-style behavior
   itself limits rapid fluctuations in the sending rate during data-
   limited periods.

C.1.  Long Idle or Data-Limited Periods

   Table 1 summarizes the response of Standard TCP [RFC2581], TCP with
   Congestion Window Validation [RFC2861], Standard TFRC [RFC3448], and
   Revised TFRC (this document) in response to long idle or data-limited
   periods.  For the purposes of this section, we define a long period
   as a period of at least an RTO.





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     Protocol         Long idle periods      Long data-limited periods
   --------------   --------------------     ----------------------
   Standard TCP:       Window -> initial.     Window increases for
                                              each cwnd of data.

   TCP with CWV:         Halve window         Reduce window half way
                   (not below initial cwnd).    to used window.

   Standard TFRC:        Halve rate            Rate limited to
                    (not below 2 pkts/rtt).      twice receive rate.
                    One RTT after sending pkt,
                    rate is limited by X_recv.

   Revised TFRC:         Halve rate             Rate limited to twice
                    (not below initial rate).     max (current X_recv,
                                                  receive rate before
                                                  data-limited period).

     Table 1: Response to Long Idle or Data-Limited Periods

   Standard TCP after long idle periods: For Standard TCP, [RFC2581]
   specifies that TCP SHOULD set the congestion window to no more than
   the initial window after an idle period of at least an RTO.  (To be
   precise, RFC 2581 specifies that the TCP sender should set cwnd to
   the initial window if the sender has not sent data in an interval
   exceeding the retransmission timeout.)

   Standard TCP after long data-limited periods: Standard TCP [RFC2581]
   does not reduce TCP's congestion window after a data-limited period,
   when the congestion window is not fully used.  Standard TCP in
   [RFC2581] uses the FlightSize, the amount of outstanding data in the
   network, only in setting the slow-start threshold after a retransmit
   timeout.  Standard TCP is not limited by TCP's ack-clocking mechanism
   during a data-limited period.

   Standard TCP's lax response to a data-limited period is quite
   different from its stringent response to an idle period.

   TCP with Congestion Window Validation (CWV) after long idle periods:
   As an experimental alternative, [RFC2861] specifies a more moderate
   response to an idle period than that of Standard TCP, where during an
   idle period the TCP sender halves cwnd after each RTO, down to the
   initial cwnd.

   TCP with Congestion Window Validation after long data-limited
   periods: As an experimental alternative, [RFC2861] specifies a more
   stringent response to a data-limited period than that of Standard
   TCP, where after each RTO seconds of a data-limited period, the



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   congestion window is reduced half way down to the window that is
   actually used.

   The response of TCP with CWV to an idle period is similar to its
   response to a data-limited period.  TCP with CWV is less restrictive
   than Standard TCP in response to an idle period, and more restrictive
   than Standard TCP in response to a data-limited period.

   Standard TFRC after long idle periods: For Standard TFRC, [RFC3448]
   specifies that the allowed sending rate is halved after each RTO
   seconds of an idle period.  The allowed sending rate is not reduced
   below two packets per RTT after idle periods.  After an idle period,
   the first feedback packet received reports a receive rate of one
   packet per round-trip time, and this receive rate is used to limit
   the sending rate.  Standard TFRC effectively slow-starts up from this
   allowed sending rate.

   Standard TFRC after long data-limited periods: [RFC3448] does not
   distinguish between data-limited and non-data-limited periods.  As a
   consequence, the allowed sending rate is limited to at most twice the
   receive rate during and after a data-limited period.  This is a very
   restrictive response, more restrictive than that of either Standard
   TCP or of TCP with CWV.

   Revised TFRC after long idle periods: For Revised TFRC, this document
   specifies that the allowed sending rate is halved after each RTO
   seconds of an idle period.  The allowed sending rate is not reduced
   below the initial sending rate as the result of an idle period.  The
   first feedback packet received after the idle period reports a
   receive rate of one packet per round-trip time.  However, the Revised
   TFRC sender does not use this receive rate for limiting the sending
   rate.  Thus, Revised TFRC differs from Standard TFRC in the lower
   limit used in the reduction of the sending rate, and in the better
   response to the first feedback packet received after the idle period.

   Revised TFRC after long data-limited periods: For Revised TFRC, this
   document distinguishes between data-limited and non-data-limited
   periods.  As specified in Section 4.3, during a data-limited period
   Revised TFRC remembers the receive rate before the data-limited
   period began, and does not reduce the allowed sending rate below
   twice that receive rate.  This is somewhat similar to the response of
   Standard TCP, and is quite different from the very restrictive
   response of Standard TFRC to a data-limited period.  However, the
   response of Revised TFRC is not as conservative as the response of
   TCP with Congestion Window Validation, where the congestion window is
   gradually reduced down to the window actually used during a data-
   limited period.




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   We note that for current TCP implementations, the congestion window
   is generally not increased during a data-limited period (when the
   current congestion window is not being fully used) [MAF05] (Section
   5.7).  We note that there is no mechanism comparable to this in
   Revised TFRC.

   Recovery after idle or data-limited periods: When TCP reduces the
   congestion window after an idle or data-utilized period, TCP can set
   the slow-start threshold, ssthresh, to allow the TCP sender to slow-
   start back up towards its old sending rate when the idle or data-
   limited period is over.  However, in TFRC, even when the TFRC
   sender's sending rate is restricted by twice the previous receive
   rate, this results in the sender being able to double the sending
   rate from one round-trip time to the next, if permitted by the
   throughput equation.  Thus, TFRC does not need a mechanism such as
   TCP's setting of ssthresh to allow a slow-start after an idle or
   data-limited period.

   For future work, one avenue to explore would be the addition of
   Congestion Window Validation mechanisms for TFRC's response to data-
   limited periods.  Currently, following Standard TCP, during data-
   limited periods Revised TFRC does not limit its allowed sending rate
   as a function of the receive rate.

C.2.  Short Idle or Data-Limited Periods

   Table 2 summarizes the response of Standard TCP [RFC2581], TCP with
   Congestion Window Validation [RFC2861], Standard TFRC [RFC3448], and
   Revised TFRC (this document) in response to short idle or data-
   limited periods.  For the purposes of this section, we define a short
   period as a period of less than an RTT.

     Protocol         Short idle periods   Short data-limited periods
   --------------   --------------------     ----------------------
   Standard TCP:    Send a burst up to cwnd.  Send a burst up to cwnd.

   TCP with CWV:    Send a burst up to cwnd.  Send a burst up to cwnd.

   Standard TFRC:             ?                         ?

   Revised TFRC:         Send a burst               Send a burst
                        (up to an RTT of           (up to an RTT of
                      unused send credits).      unused send credits).

     Table 2: Response to Short Idle or Data-Limited Periods

   Table 2 shows that Revised TFRC has a similar response to that of
   Standard TCP and of TCP with CWV to a short idle or data-limited



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   period.  For a short idle or data-limited period, TCP is limited only
   by the size of the unused congestion window, and Revised TFRC is
   limited only by the number of unused send credits (up to an RTT's
   worth).  For Standard TFRC, [RFC3448] did not explicitly specify the
   behavior with respect to unused send credits.

C.3.  Moderate Idle or Data-Limited Periods

   Table 3 summarizes the response of Standard TCP [RFC2581], TCP with
   Congestion Window Validation [RFC2861], Standard TFRC [RFC3448], and
   Revised TFRC (this document) in response to moderate idle or data-
   limited periods.  For the purposes of this section, we define a
   moderate period as a period greater than an RTT, but less than an
   RTO.

     Protocol      Moderate idle periods  Moderate data-limited periods
   -------------   ---------------------      -------------------------
   Standard TCP:    Send a burst up to cwnd.  Send a burst up to cwnd.

   TCP with CWV:    Send a burst up to cwnd.  Send a burst up to cwnd.

   Standard TFRC:             ?                   Limited by X_recv.

   Revised TFRC:         Send a burst               Send a burst
                        (up to an RTT of           (up to an RTT of
                      unused send credits).      unused send credits).

     Table 3: Response to Moderate Idle or Data-Limited Periods

   Table 3 shows that Revised TFRC has a similar response to that of
   Standard TCP and of TCP with CWV to a moderate idle or data-limited
   period.  For a moderate idle or data-limited period, TCP is limited
   only by the size of the unused congestion window.  For a moderate
   idle period, Revised TFRC is limited only by the number of unused
   send credits (up to an RTT's worth).  For a moderate data-limited
   period, Standard TFRC would be limited by X_recv from the most recent
   feedback packet.  In contrast, Revised TFRC is not limited by the
   receive rate from data-limited periods that cover an entire feedback
   period of a round-trip time.  For Standard TFRC, [RFC3448] did not
   explicitly specify the behavior with respect to unused send credits.











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C.4.  Losses During Data-Limited Periods

   This section discusses the response to a loss during a data-limited
   period.

     Protocol      Response to a loss during a data-limited period
   -------------   -----------------------------------------------
   Standard TCP:   Set ssthresh, cwnd to FlightSize/2.

   TCP with CWV:   Same as Standard TCP.

   Standard TFRC:  Calculate X_Bps, send at most 2*X_recv.

   Revised TFRC:   Calculate X_Bps, send at most recv_limit.
                   In addition, modify X_recv_set.

     Table 4: Response to a Loss during a Data-Limited Period

   In TCP [RFC2581], the response to a loss during a data-limited period
   is the same as the response to a loss at any other time in TCP.  This
   response is to set the congestion window to half of the FlightSize,
   where the FlightSize is the actual amount of unacknowledged data.
   Thus, after a loss during a data-limited period, the TCP sender must
   halve its allowed sending rate, as it normally does in response to a
   loss.

   In Standard TFRC, the response to a loss during a data-limited period
   is also the same as the response to a loss at any other time in
   Standard TFRC.  The sending rate is limited by X_Bps, from the
   throughput equation, and the sending rate is also limited by twice
   X_recv, the most recent receive rate.  As a result, after a loss in a
   data-limited period, the sender can at most double its sending rate
   to twice X_recv, even if the throughput equation X_Bps would allow a
   sending rate much higher than that.

   In Revised TFRC, there have been changes to the use of the receive
   rate X_recv during data-limited intervals; the sender is limited to
   sending at most recv_limit, where the sender can remember the receive
   rate X_recv from just before the data-limited period.  This allows
   the sender to more than double its sending rate during data-limited
   periods, up to the receive rate from before the data-limited period
   (if allowed by the throughput equation as given in X_Bps).  This is
   similar to Standard TCP's practice of not reducing the window during
   data-limited periods (in the absence of loss).

   As with Standard TFRC, during a data-limited period the Revised TFRC
   sender is sending less than is allowed by the throughput equation
   X_Bps.  After the loss event, the sender still might not want to be



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   sending as much as allowed by the recalculated value of X_Bps that
   takes into account the new loss event.  Revised TFRC adds an
   additional mechanism to gradually limit the sender's sending rate
   after losses during data-limited periods.  Unlike TCP's response of
   setting cwnd to half the FlightSize, this additional mechanism in
   Revised TFRC uses TFRC's practice of using slowly-responding changes
   for both increases and decreases in the allowed sending rate.

   This is done in Revised TFRC (in step (4) of Section 4.3) by
   decreasing the entry in X_recv_set after a loss in a data-limited
   interval, and by allowing the sender to send at most max
   (X_recv_set), instead of at most twice max (X_recv_set), in the
   immediate round-trip time following the reported loss.  Thus, the
   'price' for allowing the sender to send more than twice the most
   immediately reported value of X_recv during a data-limited interval
   is the introduction of an additional mechanism to reduce this allowed
   sending rate following losses in data-limited periods.

   In TFRC's response to a loss in a data-limited interval, we have
   considered the following examples.

   Example 1, Losses *after* a Data-Limited Period: This example shows
   that losses after a data-limited period has ended are addressed by
   the throughput equation X_Bps.

   -------------------------------------------------------------------
   Stage 1: Not data-limited.
            Sending 100 packets per round-trip time (PPR).
   Stage 2: Data-limited, sending 10 PPR.
   Stage 3: Not data-limited.
            Sending 100 PPR again, as allowed by X_Bps.
            A packet loss in the first RTT of Stage 3.
            X_Bps is updated,
   Response of Revised TFRC: a slight reduction in the allowed sending
     rate, depending on the number of packets since the last loss event.
   -------------------------------------------------------------------

      Table 5:  Example 1, Losses after a Data-Limited Period

   For example 1, when there is a packet loss in the first RTT of Stage
   3, this will be reflected in a modified value of X_Bps, and future
   loss events would result in future reductions of the throughput
   equation X_Bps.  In particular, following TFRC's standard use of the
   throughput equation [FHPW00] (Section A.2), the allowed TFRC sending
   rate would be halved after something like five successive round-trip
   times with loss.





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   Example 2, a Mildly Data-Limited Sender: This example considers
   losses in a data-limited period when, during the data-limited period,
   the sender is sending *almost* as much as it is allowed to send.

   -------------------------------------------------------------------
   Stage 1: Not data-limited.  Sending 100 PPR.
   Stage 2: Data-limited, sending 99 PPR.
            A packet loss in Stage 2.
   Response of Revised TFRC: a slight reduction in the allowed sending
     rate, down to 85 PPR or less, depending on the number of packets
     since the last loss event.
   -------------------------------------------------------------------

      Table 6:  Example 2, a Mildly Data-Limited Sender

   Consider a Revised TFRC connection where the sender has been sending
   a hundred PPR and then enters a data-limited period of sending only
   99 PPR because of data limitations from the application.  (That is,
   at every instance of time during the data-limited period, the sender
   could have sent one more packet.)  If there are losses in the data-
   limited period, the allowed sending rate is reduced to min(X_Bps,
   recv_limit), where both the throughput equation X_Bps and the limit
   recv_limit force a slight reduction in the allowed sending rate.

   Example 3, a Single Packet Loss during a Data-Limited Period.  This
   example considers the loss of a single packet during a data-limited
   period, after the sender has not sent a packet for two RTTs.

   -------------------------------------------------------------------
   Stage 1: Not data-limited.  Sending 100 PPR.
   Stage 2: Data-limited, sending 10 PPR.
   Stage 3: Data-limited, sending no data for two RTTs.
   Stage 4: Data-limited, sending one packet, which is ECN-marked.
   Response of Revised TFRC: a reduction in the allowed sending
     rate, down to 50 PPR or less.  For each loss event during
     the data-limited period, the 'remembered' X_recv from before
     the data-limited period is effectively halved.
   -------------------------------------------------------------------

      Table 7:  Example 3, a Single Packet Loss

   Consider a Revised TFRC connection where the sender has been sending
   a hundred PPR, and then enters a data-limited period of sending only
   ten PPR, and then does not send any packets for two RTTs, and then
   sends a single packet, which is ECN-marked.  In this case, with
   Revised TFRC, for each loss event during the data-limited period, the
   sender halves its 'remembered' X_recv from before the data-limited
   period



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   Example 4, Losses after Increasing the Sending Rate during a Data-
   Limited Period.  This example considers losses when the sender
   significantly increases its sending rate during a data-limited
   period.

   -------------------------------------------------------------------
   Stage 1: Not data-limited.  Sending 100 PPR.
   Stage 2: Data-limited, sending 1 PPR.
   Stage 3: Data-limited, sending 20 PPR.
            Several packets are lost in each RTT of Stage 3.
            During Stage 3, the sender would *like* to send 20 PPR.
   Response of Revised TFRC:  For each loss event during
     the data-limited period, the 'remembered' X_recv from before
     the data-limited period is effectively halved, and the most
     recent X_recv is reduced by 0.85.
   -------------------------------------------------------------------

      Table 8:  Example 4, Losses after Increasing the Sending Rate

   Consider a Revised TFRC connection where the sender has been sending
   a hundred PPR, and then enters a data-limited period of sending only
   one PPR, and then, while still data-limited, increases its sending
   rate to twenty PPR, where it experiences a number of successive loss
   events.

   In this case, with Revised TFRC, for each loss event during the
   data-limited period, the sender halves its 'remembered' X_recv from
   before the data-limited period, and the most recent X_recv is reduced
   by 0.85.

C.5.  Other Patterns

   Other possible patterns to consider in evaluating Revised TFRC would
   be to compare the behavior of TCP, Standard TFRC, and Revised TFRC
   for connections with alternating busy and idle periods, alternating
   idle and data-limited periods, or with idle or data-limited periods
   during slow-start.

C.6.  Evaluating TFRC's Response to Idle Periods

   In this section we focus on evaluating Revised TFRC's response to
   idle or data-limited periods.

   One drawback to Standard TFRC's strict response to idle or data-
   limited periods is that it could be seen as encouraging applications
   to pad their sending rate during idle or data-limited periods, by
   sending dummy data when there was no other data to send.  Because
   Revised TFRC has a less strict response to data-limited periods than



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   that of Standard TFRC, Revised TFRC also could be seen as giving
   applications less of an incentive to pad their sending rates during
   data-limited periods.  Work in progress, such as Faster Restart
   [KFS07], can also decrease an application's incentive to pad its
   sending rate, by allowing faster start-up after idle periods.
   Further research would be useful to understand, in more detail, the
   interaction between TCP or TFRC's congestion control mechanisms, and
   an application's incentive to pad its sending rate during idle or
   data-limited periods.

   TCP Congestion Window Validation, described in Appendix C.1 above, is
   an Experimental standard specifying that the TCP sender slowly
   reduces the congestion window during an idle or data-limited period
   [RFC2861].  While TFRC and Revised TFRC's responses to idle periods
   are roughly similar to those of TCP with Congestion Window
   Validation, Revised TFRC's response to data-limited periods is less
   conservative than those of TCP with Congestion Window Validation (and
   Standard TFRC's response to data-limited periods was considerably
   *more* conservative than those of Congestion Window Validation).
   Future work could include modifications to this document so that the
   response of Revised TFRC to a data-limited period includes a slow
   reduction of the allowed sending rate; Section C specifies a possible
   mechanism for this.  Such a modification would be particularly
   compelling if Congestion Window Validation became a Proposed Standard
   in the IETF for TCP.

References

Normative References

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

   [RFC3448]    Handley, M., Floyd, S., Padhye, J., and J. Widmer, "TCP
                Friendly Rate Control (TFRC): Protocol Specification",
                RFC 3448, January 2003.

Informative References

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

   [CCID-4]     Floyd, S., and E. Kohler, "Profile for DCCP Congestion
                Control ID 4: the Small-Packet Variant of TFRC
                Congestion Control", Work in Progress, February 2008.




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   [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.

   [FF99]       Floyd, S., and K. Fall, Promoting the Use of End-to-End
                Congestion Control in the Internet, IEEE/ACM
                Transactions on Networking, August 1999.

   [KFS07]      E. Kohler, S. Floyd, and A. Sathiaseelan, "Faster
                Restart for TCP Friendly Rate Control (TFRC)", Work in
                Progress, November 2007.

   [MAF05]      A. Medina, M. Allman, and S. Floyd, "Measuring the
                Evolution of Transport Protocols in the Internet", ACM
                Computer Communications Review, April 2005.

   [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.

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

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

   [RFC2581bis] Allman, M., Paxson, V., and W. Stevens, "TCP Congestion
                Control", Work in Progress, April 2008.

   [RFC2861]    Handley, M., Padhye, J., and S. Floyd, "TCP Congestion
                Window Validation", RFC 2861, June 2000.

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

   [RFC3168]    Ramakrishnan, K., Floyd, S., and D. Black, "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.





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   [RFC3448Err] RFC 3448 Errata,
                <http://www.rfc-editor.org/errata_search.php?rfc=3448>.

   [RFC3540]    Spring, N., Wetherall, D., and D. Ely, "Robust Explicit
                Congestion Notification (ECN) Signaling with Nonces",
                RFC 3540, 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.

   [RFC4828]    Floyd, S. and E. Kohler, "TCP Friendly Rate Control
                (TFRC): The Small-Packet (SP) Variant", RFC 4828, April
                2007.

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




























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Authors' Addresses

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

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

   Jitendra Padhye
   Microsoft Research
   EMail: padhye@microsoft.com

   Joerg Widmer
   DoCoMo Euro-Labs
   Landsberger Strasse 312
   80687 Munich
   Germany
   EMail: widmer@acm.org

























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Full Copyright Statement

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