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Versions: (draft-mathis-tcpm-proportional-rate-reduction) 00 01 02 03 04 RFC 6937

TCP Maintenance Working Group                                  M. Mathis
Internet-Draft                                              N. Dukkipati
Intended status: Experimental                                   Y. Cheng
Expires: April 26, 2012                                      Google, Inc
                                                        October 24, 2011


                  Proportional Rate Reduction for TCP
           draft-ietf-tcpm-proportional-rate-reduction-00.txt

Abstract

   This document describes an experimental algorithm, Proportional Rate
   Reduction (PPR) to improve the accuracy of the amount of data sent by
   TCP during loss recovery.  Standard Congestion Control requires that
   TCP and other protocols reduce their congestion window in response to
   losses.  This window reduction naturally occurs in the same round
   trip as the data retransmissions to repair the losses, and is
   implemented by choosing not to transmit any data in response to some
   ACKs arriving from the receiver.  Two widely deployed algorithms are
   used to implement this window reduction: Fast Recovery and Rate
   Halving.  Both algorithms are needlessly fragile under a number of
   conditions, particularly when there is a burst of losses that such
   that the number of ACKs returning to the sender is small.
   Proportional Rate Reduction avoids these excess window reductions
   such that at the end of recovery the actual window size will be as
   close as possible to ssthresh, the window size determined by the
   congestion control algorithm.  It is patterned after Rate Halving,
   but using the fraction that is appropriate for target window chosen
   by the congestion control algorithm.

Status of this Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on April 26, 2012.




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Copyright Notice

   Copyright (c) 2011 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
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   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.


Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Definitions  . . . . . . . . . . . . . . . . . . . . . . . . .  4
   3.  Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . .  5
     3.1.  Examples . . . . . . . . . . . . . . . . . . . . . . . . .  6
   4.  Properties . . . . . . . . . . . . . . . . . . . . . . . . . .  9
   5.  Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 11
   6.  Conclusion and Recommendations . . . . . . . . . . . . . . . . 12
   7.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 13
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 13
   9.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 13
   10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 13
   Appendix A.  Packet Conservation Bound . . . . . . . . . . . . . . 14
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 15




















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1.  Introduction

   This document describes an experimental algorithm, Proportional Rate
   Reduction (PPR) to improve the accuracy of the amount of data sent by
   TCP during loss recovery.

   Standard Congestion Control [RFC5681] requires that TCP (and other
   protocols) reduce their congestion window in response to losses.
   Fast Recovery, described in the same document, is the reference
   algorithm for making this adjustment.  It's stated goal is to recover
   TCP's self clock by relying on returning ACKs during recovery to
   clock more data into the network.  Fast Recovery adjusts the window
   by waiting for one half RTT of ACKs to pass before sending any data.
   It is fragile because it can not compensate for the implicit window
   reduction caused by the losses themselves, and is exposed to
   timeouts.  For example if half of the data or ACKs are lost, Fast
   Recovery's expected behavior would be wait for half window of ACKs to
   pass and then not receive any ACKs for the recovery and suffer a
   timeout.

   The rate-halving algorithm improves this situation by sending data on
   alternate ACKs during recovery, such that after one RTT the window
   has been halved.  Rate-having is implemented in Linux after only
   being informally published [RHweb], including from an uncompleted
   Internet-Draft [RHID].  Rate-halving does not adequately compensate
   for the implicit window reduction caused by the losses and also
   assumes a 50% window reduction, which was completely standard at the
   time it was written, but not appropriate for modern congestion
   control algorithms such as Cubic [CUBIC], which can reduce the window
   by less than 50%.  As a consequence rate-halving often allows the
   window to fall further than necessary, reducing performance and
   increasing the risk of timeouts if there are additional losses.

   Proportional Rate Reduction (PPR) avoids these excess window
   reductions such that at the end of recovery the actual window size
   will be as close as possible to, ssthresh, the window size determined
   by the congestion control algorithm.  It is patterned after Rate
   Halving, but using the fraction that is appropriate for target window
   chosen by the congestion control algorithm.  During PRR one of two
   additional reduction bound algorithms limits the total window
   reduction due to all mechanisms, including application stalls and the
   losses themselves.

   We describe two slightly different reduction bound algorithms:
   conservative reduction bound (CRB), which is strictly packet
   conserving; and a slow start reduction bound (SSRB), which is more
   aggressive than CRB by at most one segment per ACK.  PRR-CRB meets
   the strong conservative bound described in Appendix A, however in



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   real networks it does not perform as well as the algorithms described
   in RFC 3517, which prove to be non-conservative in a statistically
   significant number of cases.  SSRB offers a compromise by allowing
   TCP to send one additional segment per ACK relative to CRB in some
   situations.  Although SSRB is less aggressive than RFC 3517
   (transmitting fewer segments or taking more time to transmit them) it
   outperforms it, due to the lower probability of additional losses
   during recovery.

   PRR and both reduction bounds are based on common design principles,
   derived from Van Jacobson's packet conservation principle: segments
   delivered to the receiver are used as the clock to trigger sending
   the same number of segments back into the network.  As much as
   possible Proportional Rate Reduction and the reduction bound rely on
   this self clock process, and are only slightly affected by the
   accuracy of other estimators, such as pipe [RFC3517] and cwnd.  This
   is what gives the algorithms their precision in the presence of
   events that cause uncertainty in other estimators.

   We evaluated these and other algorithms in a large scale measurement
   study, summarized below.  The most important results from that study
   are presented in an companion paper [IMC11].  PRR+SSRB outperforms
   both RFC 3517 and Linux Rate Halving under authentic network traffic,
   even though it is less aggressive than RFC 3517.

   The algorithms are described as modifications to RFC 5681 [RFC5681],
   TCP Congestion Control, using concepts drawn from the pipe algorithm
   [RFC3517].  They are most accurate and more easily implemented with
   SACK [RFC2018], but they do not require SACK.


2.  Definitions

   The following terms, parameters and state variables are used as they
   are defined in earlier documents:

   RFC 3517: covered (as in "covered sequence numbers")

   RFC 5681: duplicate ACK, FlightSize, Sender Maximum Segment Size
   (SMSS)

   Voluntary window reductions: choosing not to send data in response to
   some ACKs, for the purpose of reducing the sending window size or
   data rate.

   We define some additional variables:

   SACKd: The total number of bytes that the scoreboard indicates have



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   been delivered to the receiver.  This can be computed by scanning the
   scoreboard and counting the total number of bytes covered by all sack
   blocks.  If SACK is not in use, SACKd is not defined.

   DeliveredData: The total number of bytes that the current ACK
   indicates have been delivered to the receiver.  When not in recovery,
   DeliveredData is the change in snd.una.  With SACK, DeliveredData can
   be computed precisely as the change in snd.una plus the (signed)
   change in SACKd.  In recovery without SACK, DeliveredData is
   estimated to be 1 SMSS on duplicate acknowledgements, and on a
   subsequent partial or full ACK, DeliveredData is estimated to be the
   change in snd.una, minus one SMSS for each preceding duplicate ACK.

   Note that DeliveredData is robust: for TCP using SACK, DeliveredData
   can be precisely computed anywhere in the network just by inspecting
   the returning ACKs.  The consequence of missing ACKs is that later
   ACKs will show a larger DeliveredData.  Furthermore, for any TCP
   (with or without SACK) the sum of DeliveredData must agree with the
   forward progress over the same time interval.

   We introduce a local variable "sndcnt", which indicates exactly how
   many bytes should be sent in response to each ACK.  Note that the
   decision of which data to send (e.g. retransmit missing data or send
   more new data) is out of scope for this document.


3.  Algorithms

   At the beginning of recovery initialize PRR state.  This assumes a
   modern congestion control algorithm, CongCtrlAlg(), that might set
   ssthresh to something other than FlightSize/2:

      ssthresh = CongCtrlAlg()  // Target cwnd after recovery
      prr_delivered = 0         // Total bytes delivered during recov
      prr_out = 0               // Total bytes sent during recovery
      RecoverFS = snd.nxt-snd.una // FlightSize at the start of recov

   On every ACK during recovery compute:













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      DeliveredData = delta(snd.una) + delta(SACKd)
      prr_delivered += DeliveredData
      pipe = (RFC 3517 pipe algorithm)
      if (pipe > ssthresh) {
         // Proportional Rate Reduction
         sndcnt = CEIL(prr_delivered * ssthresh / RecoverFS) - prr_out
      } else {
         // Two version of the reduction bound
         if (conservative) {    // PRR+CRB
           limit = prr_delivered - prr_out
         } else {               // PRR+SSRB
           limit = MAX(prr_delivered - prr_out, DeliveredData) + 1
         }
         // Attempt to catch up, as permitted by limit
         sndcnt = MIN(ssthresh - pipe, limit)
      }

   On any data transmission or retransmission:

         prr_out += (data sent) // strictly less than or equal to sndcnt

   The following examples will make these algorithms clearer.

3.1.  Examples

   We illustrate these algorithms by showing their different behaviors
   for two scenarios: TCP experiencing either a single loss or a burst
   of 15 consecutive losses.  In all cases we assume bulk data, standard
   AIMD congestion control (the ssthresh is set to FlightSize/2) and
   cwnd = FlightSize = pipe = 20 segments, so ssthresh will be set to 10
   at the beginning of recovery.  We also assume standard Fast
   Retransmit and Limited Transmit, so we send two new segments followed
   by one retransmit on the first 3 duplicate ACKs after the losses.

   Each of the diagrams below shows the per ACK response to the first
   round trip for the various recovery algorithms when the zeroth
   segment is lost.  The top line indicates the transmitted segment
   number triggering the ACKs, with an X for the lost segment. "cwnd"
   and "pipe" indicate the values of these algorithms after processing
   each returning ACK.  "Sent" indicates how much 'N'ew or
   'R'etransmitted data would be sent.  Note that the algorithms for
   deciding which data to send are out of scope of this document.

   When there is a single loss, PRR with either of the reduction bound
   algorithms has the same behavior.  We show "RB", a flag indicating
   which reduction bound subexpression ultimately determined the value
   of sndcnt.  When there is minimal losses "limit" (both algorithms)
   will always be larger than ssthresh - pipe, so the sndcnt will be



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   ssthresh - pipe indicated by "s" in the "RB" row.  Since PRR does not
   use cwnd during recovery it is not shown in the example.

   RFC 3517
   ack#   X  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19
   cwnd:    20 20 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
   pipe:    19 19 18 18 17 16 15 14 13 12 11 10 10 10 10 10 10 10 10
   sent:     N  N  R                          N  N  N  N  N  N  N  N


   Rate Halving (Linux)
   ack#   X  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19
   cwnd:    20 20 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11
   pipe:    19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11 10
   sent:     N  N  R     N     N     N     N     N     N     N     N


   PRR
   ack#   X  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19
   pipe:    19 19 18 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 10
   sent:     N  N  R     N     N     N     N     N     N        N  N
   RB:                                                          s  s

   Note that all three algorithms send same total amount of data.  RFC
   3517 experiences a "half-window of silence", while the Rate Halving
   and PRR spread the voluntary window reduction across an entire RTT.

   Next we consider the same initial conditions when the first 15
   packets (0-14) are lost.  During the remainder of the lossy RTT, only
   5 ACKs are returned to the sender.  We examine each of these
   algorithms in succession.




















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   RFC 3517
   ack#   X  X  X  X  X  X  X  X  X  X  X  X  X  X  X 15 16 17 18 19
   cwnd:                                              20 20 11 11 11
   pipe:                                              19 19  4 10 10
   sent:                                               N  N 7R  R  R


   Rate Halving (Linux)
   ack#   X  X  X  X  X  X  X  X  X  X  X  X  X  X  X 15 16 17 18 19
   cwnd:                                              20 20  5  5  5
   pipe:                                              19 19  4  4  4
   sent:                                               N  N  R  R  R


   PRR-CRB
   ack#   X  X  X  X  X  X  X  X  X  X  X  X  X  X  X 15 16 17 18 19
   pipe:                                              19 19  4  4  4
   sent:                                               N  N  R  R  R
   RB:                                                       f  f  f


   PRR-SSRB
   ack#   X  X  X  X  X  X  X  X  X  X  X  X  X  X  X 15 16 17 18 19
   pipe:                                              19 19  4  5  6
   sent:                                               N  N 2R 2R 2R
   RB:                                                       d  d  d



   In this specific situation, RFC 3517 is very non-conservative,
   because once fast retransmit is triggered (on the ACK for segment 17)
   TCP immediately retransmits sufficient data to bring pipe up to cwnd.
   Our measurement data (see Section 5) indicates that RFC 3517
   significantly outperforms Rate Halving, PRR-CRB and some other
   similarly conservative algorithms that we tested, suggesting that it
   is significantly common for the actual losses to exceed the window
   reduction determined by the congestion control algorithm.

   The Linux implementation of Rate Halving includes an early version of
   the conservative reduction bound [RHweb].  In this situation the five
   ACKs trigger exactly one transmission each (2 new data, 3 old data),
   and cwnd is set to 5.  At a window size of 5, it takes three round
   trips to retransmit all 15 lost segments.  Rate Halving does not
   raise the window at all during recovery, so when recovery finally
   completes, TCP will slowstart cwnd from 5 up to 10.  In this example,
   TCP operates at half of the window chosen by the congestion control
   for more than three RTTs, increasing the elapsed time and exposing it
   to timeouts in the event that there are additional losses.



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   PRR-CRB implements conservative reduction bound.  Since the total
   losses bring pipe below ssthresh, data is sent such that the total
   data transmitted, prr_out, follows the total data delivered to the
   receiver as reported by returning ACKs.  Transmission is controlled
   by the sending limit, which was set to prr_delivered - prr_out.  This
   is indicated by the RB:f tagging in the figure.  In this case PRR-CRB
   is exposed to exactly the same problems as Rate Halving, the excess
   window reduction causes it to take excessively long to recover the
   losses and exposes it to additional timeouts.

   PRR-SSRB increases the window by exactly 1 segment per ACK until pipe
   rises to sshthresh during recovery.  This is accomplished by setting
   limit to one greater than the data reported to have been delivered to
   the receiver on this ACK, implementing slowstart during recovery, and
   indicated by RB:d tagging in the figure.  Although increasing the
   window during recovery seems to be ill advised, it is important to
   remember that this actually less aggressive than permitted by RFC
   5681, which sends the same quantity of extra data as a single burst
   in response to the ACK that triggered Fast Retransmit

   Under less extreme conditions, when the total losses are smaller than
   the difference between Flight Size and ssthresh, PRR-CRB and PRR-SSRB
   have identical behaviours.


4.  Properties

   The following properties are common to both PRR-CRB and PRR-SSRB:

   Normally Proportional Rate Reduction will spread voluntary window
   reductions out evenly across a full RTT.  This has the potential to
   generally reduce the burstiness of Internet traffic, and could be
   considered to be a type of soft pacing.  Theoretically any pacing
   increases the probability that different flows are interleaved,
   reducing the opportunity for ACK compression and other phenomena that
   increase traffic burstiness.  However these effects have not been
   quantified.

   If there are minimal losses, Proportional Rate Reduction will
   converge to exactly the target window chosen by the congestion
   control algorithm.  Note that as TCP approaches the end of recovery
   prr_delivered will approach RecoverFS and sndcnt will be computed
   such that prr_out approaches ssthresh.

   Implicit window reductions due to multiple isolated losses during
   recovery cause later voluntary reductions to be skipped.  For small
   numbers of losses the window size ends at exactly the window chosen
   by the congestion control algorithm.



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   For burst losses, earlier voluntary window reductions can be undone
   by sending extra segments in response to ACKs arriving later during
   recovery.  Note that as long as some voluntary window reductions are
   not undone, the final value for pipe will be the same as ssthresh,
   the target cwnd value chosen by the congestion control algorithm.

   Proportional Rate Reduction with either reduction round improves the
   situation when there are application stalls (e.g. when the sending
   application does not queue data for transmission quickly enough or
   the receiver stops advancing rwnd).  When there is an application
   stall early during recovery prr_out will fall behind the sum of the
   transmissions permitted by sndcnt.  The missed opportunities to send
   due to stalls are treated like banked voluntary window reductions:
   specifically they cause prr_delivered-prr_out to be significantly
   positive.  If the application catches up while TCP is still in
   recovery, TCP will send a partial window burst to catch up to exactly
   where it would have been, had the application never stalled.
   Although this burst might be viewed as being hard on the network,
   this is exactly what happens every time there is a partial RTT
   application stall while not in recovery.  We have made the partial
   RTT stall behavior uniform in all states.  Changing this behavior is
   out of scope for this document.

   Proportional Rate Reduction with Reduction Bound is significantly
   less sensitive to errors of the pipe estimator.  While in recovery,
   pipe is intrinsically an estimator, using incomplete information to
   guess if un-SACKed segments are actually lost or out-of-order in the
   network.  Under some conditions pipe can have significant errors, for
   example when a burst of reordered data is presumed to be lost and is
   retransmitted, but then the original data arrives before the
   retransmission.  If the transmissions are regulated directly by pipe
   as they are in RFC 3517, then errors and discontinuities in the value
   of the pipe estimator can cause significant errors in the amount of
   data sent.  With Proportional Rate Reduction with Reduction Bound,
   pipe merely determines how sndcnt is computed from DeliveredData.
   Since short term errors in pipe are smoothed out across multiple ACKs
   and both Proportional Rate Reduction and the reduction bound converge
   to the same final window, errors in the pipe estimator have less
   impact on the final outcome.

   Under all conditions and sequences of events during recovery, PRR-CRB
   strictly bounds the data transmitted to be equal to or less than the
   amount of data delivered to the receiver.  We claim that this packet
   conservation bound is the most aggressive algorithm that does not
   lead to additional forced losses in some environments.  It has the
   property that if there is a standing queue at a bottleneck that is
   carrying no other traffic, the queue will maintain exactly constant
   length for the duration of the recovery (except for +1/-1 fluctuation



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   due to differences in packet arrival and exit times) .  See
   Appendix A for a detailed discussion of this property.

   Although the packet Packet Conserving Bound in very appealing for a
   number of reasons, our measurements summarized in Section 5
   demonstrate that it is less aggressive and does not perform as well
   as RFC3517, which permits large bursts of data when there are bursts
   of losses.  PRR-SSRB is a compromise that permits TCP to send one
   extra segment per ACK as compared to the packet conserving bound.
   From the perspective of the packet conserving bound, PRR-SSRB does
   indeed open the window during recovery, however it is significantly
   less aggressive than RFC3517 in the presence of burst losses.


5.  Measurements

   In a companion IMC11 paper [IMC11] we describe some measurements
   comparing the various strategies for reducing the window during
   recovery.  The results are summarized here.

   The various window reduction algorithms and extensive instrumentation
   were all implemented in Linux 2.6.  We used the uniform set of
   algorithms present in the base Linux implementation, including CUBIC
   [CUBIC], limited transmit [LT], threshold transmit from [FACK] and
   lost retransmission detection algorithms.  We confirmed that the
   behaviors of Rate Halving (the Linux default), RFC 3517 and PRR were
   authentic to their respective specifications and that performance and
   features were comparable to the kernels in production use.  The
   different window reduction algorithms were all present in the same
   kernel and could be selected with a sysctl, such that we had an
   absolutely uniform baseline for comparing them.

   Our experiments included an additional algorithm, PRR with an
   unlimited bound (PRR-UB), which sends ssthresh-pipe bursts when pipe
   falls below ssthresh.  This behavior parallels RFC 3517.

   An important detail of this configuration is that CUBIC only reduces
   the window by 30%, as opposed to the 50% reduction used by
   traditional congestion control algorithms.  This, in conjunction with
   using only standard algorithms to trigger Fast Retransmit,
   accentuates the tendency for RFC 3517 and PRR-UB to send a burst at
   the point when Fast Retransmit gets triggered if pipe is already
   below ssthresh.

   All experiments were performed on servers carrying production traffic
   for multiple Google services.

   In this configuration it is observed that for 32% of the recovery



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   events, pipe falls below ssthresh before Fast Retransmit is
   triggered, thus the various PRR algorithms start in the reduction
   bound phase, and RFC 3517 send bursts of segments with the fast
   retransmit.

   In the companion paper we observe that PRR-SSRB spends the least time
   in recovery of all the algorithms tested, largely because it
   experiences fewer timeouts once it is already in recovery.

   RFC 3517 experiences 29% more detected lost retransmissions and 2.6%
   more timeouts (presumably due to undetected lost retransmissions)
   than PRR-SSRB.  These results are representative of PRR-UB and other
   algorithms that send bursts when pipe falls below ssthresh.

   Rate Halving experiences 5% more timeouts and significantly smaller
   final cwnd values at the end of recovery.  The smaller cwnd sometimes
   causes the recovery itself to take extra round trips.  These results
   are representative of PRR-CRB and other algorithms that implement
   strict packet conservation during recovery.


6.  Conclusion and Recommendations

   Although the packet conserving bound is very appealing for a number
   of reasons, our measurements demonstrate that it is less aggressive
   and does not perform as well as RFC3517, which permits significant
   bursts of data when there are large bursts of losses.  PRR-SSRB is a
   compromise that permits TCP to send one extra segment per ACK as
   relative to the packet conserving bound.  From the perspective of the
   packet conserving bound, PRR-SSRB does indeed open the window during
   recovery, however it is significantly less aggressive than RFC3517 in
   the presence of burst losses.  Even so, it often out performs
   RFC3517, because it avoids some of the self inflicted losses caused
   by bursts from RFC3517.

   At this time we see no reason not to test and deploy PRR-SSRB on a
   large scale, indeed it already is.  Implementers worried about any
   potential impact of raising the window during recovery may want to
   optionally support PRR-CRB (which is actually simpler to implement)
   for comparison studies.

   One final comment about terminology: we expect that common usage will
   drop "slow start reduction bound" from the algorithm name.  This
   document needs to be pedantic about having distinct name for
   proportional rate reduction and every variant of the reduction bound.
   However, once paired they become one.





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7.  Acknowledgements

   This draft is based in part on previous incomplete work by Matt
   Mathis, Jeff Semke and Jamshid Mahdavi [RHID] and influenced by
   several discussion with John Heffner.

   Monia Ghobadi and Sivasankar Radhakrishnan helped analyze the
   experiments.


8.  Security Considerations

   Proportional Rate Reduction does not change the risk profile for TCP.

   Implementers that change PRR from counting bytes to segments have to
   be cautious about the effects of ACK splitting attacks[SPLIT], where
   the receiver acknowledges partial segments for the purpose of
   confusing the sender's congestion accounting.


9.  IANA Considerations

   This document makes no request of IANA.

   Note to RFC Editor: this section may be removed on publication as an
   RFC.


10.  References

   [RFC2018]  Mathis, M., Mahdavi, J., Floyd, S., and A. Romanow, "TCP
              Selective Acknowledgment Options", RFC 2018, October 1996.

   [RFC3517]  Blanton, E., Allman, M., Fall, K., and L. Wang, "A
              Conservative Selective Acknowledgment (SACK)-based Loss
              Recovery Algorithm for TCP", RFC 3517, April 2003.

   [RFC5681]  Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
              Control", RFC 5681, September 2009.

   [IMC11]    Dukkipati, N., Mathis, M., and Y. Cheng, "Proportional
              Rate Reduction for TCP", ACM Internet Measurement
              Conference IMC11, December 2011.

   [FACK]     Mathis, M. and J. Mahdavi, "Forward Acknowledgment:
              Refining TCP Congestion Control", ACM SIGCOMM SIGCOMM96,
              August 1996.




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   [RHID]     Mathis, M., Semke, J., Mahdavi, J., and K. Lahey, "The
              Rate-Halving Algorithm for TCP Congestion Control", draft-
              ratehalving (work in progress), June 1999.

   [RHweb]    Mathis, M. and J. Mahdavi, "TCP Rate-Halving with Bounding
              Parameters", Web publication , December 1997.

   [CUBIC]    Rhee, I. and L. Xu, "CUBIC: A new TCP-friendly high-speed
              TCP variant", PFLDnet 2005, Feb 2005.


Appendix A.  Packet Conservation Bound

   PRR-CRB meets a conservative, philosophically pure and aesthetically
   appealing notion of correct, described here.  However, in real
   networks it does not perform as well as the algorithms described in
   RFC 3517, which prove to be non-conservative in a statistically
   significant number of cases.

   Under all conditions and sequences of events during recovery, PRR-CRB
   strictly bounds the data transmitted to be equal to or less than the
   amount of data delivered to the receiver.  We claim that this packet
   conservation bound is the most aggressive algorithm that does not
   lead to additional forced losses in some environments.  It has the
   property that if there is a standing queue at a bottleneck that is
   carrying no other traffic, the queue will maintain exactly constant
   length for the entire recovery duration (except for +1/-1 fluctuation
   due to differences in packet arrival and exit times) .  Any less
   aggressive algorithm will result in a declining queue at the
   bottleneck.  Any more aggressive algorithm will result in an
   increasing queue or additional losses at the bottleneck.

   We demonstrate this property with a little thought experiment:

   Imagine a network path that has insignificant delays in both
   directions, except the processing time and queue at a single
   bottleneck in the forward path.  By insignificant delay, I mean when
   a packet is "served" at the head of the bottleneck queue, the
   following events happen in much less than one bottleneck packet time:
   the packet arrives at the receiver; the receiver sends an ACK; which
   arrives at the sender; the sender processes the ACK and sends some
   data; the data is queued at the bottleneck.

   If sndcnt is set to DeliveredData and nothing else is inhibiting
   sending data, then clearly the data arriving at the bottleneck queue
   will exactly replace the data that was served at the head of the
   queue, so the queue will have a constant length.  If queue is drop
   tail and full then the queue will stay exactly full.  Losses or



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   reordering on the ACK path only cause wider fluctuations in the queue
   size, but do not raise the peak size, independent of whether the data
   is in order or out-of-order (including loss recovery from an earlier
   RTT).  Any more aggressive algorithm which sends additional data will
   cause a queue overflow and loss.  Any less aggressive algorithm will
   under fill the queue.  Therefore setting sndcnt to DeliveredData is
   the most aggressive algorithm that does not cause forced losses in
   this simple network.  Relaxing the assumptions (e.g. making delays
   more authentic and adding more flows, delayed ACKs, etc) may
   increases the fine grained fluctuations in queue size but does not
   change it's basic behavior.

   Note that the congestion control algorithm implements a broader
   notion of optimal that includes appropriately sharing of the network.
   Typical congestion control algorithms are likely to reduce the data
   sent relative to the packet conserving bound implemented by PRR
   bringing TCP's actual window down to ssthresh.


Authors' Addresses

   Matt Mathis
   Google, Inc
   1600 Amphitheater Parkway
   Mountain View, California  93117
   USA

   Email: mattmathis@google.com


   Nandita Dukkipati
   Google, Inc
   1600 Amphitheater Parkway
   Mountain View, California  93117
   USA

   Email: nanditad@google.com


   Yuchung Cheng
   Google, Inc
   1600 Amphitheater Parkway
   Mountain View, California  93117
   USA

   Email: ycheng@google.com





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