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Changing the Default QUIC ACK Policy
draft-fairhurst-quic-ack-scaling-01

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Authors Gorry Fairhurst , Ana Custura , Tom Jones
Last updated 2020-03-05 (Latest revision 2020-01-29)
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draft-fairhurst-quic-ack-scaling-01
Internet Engineering Task Force                             G. Fairhurst
Internet-Draft                                                A. Custura
Intended status: Informational                                  T. Jones
Expires: September 6, 2020                        University of Aberdeen
                                                          March 05, 2020

                  Changing the Default QUIC ACK Policy
                  draft-fairhurst-quic-ack-scaling-01

Abstract

   ACKs are used by transport protocols to confirm delivery of packets.
   The transmission of ACKs consumes resources at the receiver, in the
   network and at the sender.  On network paths where there is
   significant path asymmetry, acknowledgments of data receipt can
   reduce the efficient use of network capacity.  This effect occurs
   when the return capacity is significantly more constrained than the
   forward capacity, or the cost of transmission per packet is a
   significant component of the total transmission cost.  In these
   cases, reducing the ratio of acknowledgements to data can improve
   link utilization and reduce link transmission costs.  It can also
   reduce processing overhead at the sender and receiver.

   This document proposes a change to the default acknowledgement policy
   of the QUIC transport protocol to improve performance over paths with
   appreciable asymmetry.

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 https://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 September 6, 2020.

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Copyright Notice

   Copyright (c) 2020 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
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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Motivation  . . . . . . . . . . . . . . . . . . . . . . . . .   3
     2.1.  ACK Ratio Impact on Asymmetric Paths  . . . . . . . . . .   3
     2.2.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   3
     2.3.  Adapting the ACK Ratio in Current Transport
           Specifications  . . . . . . . . . . . . . . . . . . . . .   3
     2.4.  Adapting the ACK Ratio in the Network . . . . . . . . . .   4
   3.  Updating the Default ACK Ratio for QUIC . . . . . . . . . . .   4
     3.1.  Considerations Updating the Default QUIC ACK Policy . . .   5
     3.2.  During Slow Start . . . . . . . . . . . . . . . . . . . .   6
     3.3.  After Slow Start  . . . . . . . . . . . . . . . . . . . .   6
     3.4.  When Encountering Loss/Congestion . . . . . . . . . . . .   6
   4.  Recommended ACK Policy  . . . . . . . . . . . . . . . . . . .   6
     4.1.  Further Tuning of the ACK Policy  . . . . . . . . . . . .   7
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   7
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   7
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   7
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .   7
     7.2.  Informative References  . . . . . . . . . . . . . . . . .   8
   Appendix A.  Summary of Recommended ACK Policy for TCP  . . . . .   9
   Appendix B.  Experiments Exploring an ACK Ratio of 1:10 . . . . .  10
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   The current design of QUIC [I-D.ietf-quic-transport] currently
   proposes a default acknowledgement (ACK) ratio of 1:2 (at least one
   ACK for every 2 ack-eliciting packets) inspired by current
   recommendations for TCP, Appendix A, see.  This document proposes an
   increase in the ratio of ACK packets to data packets from 1:2 to 1:10
   for QUIC flows.

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2.  Motivation

   When the characteristics of the forward and return paths are not
   symmetric, the transmission of ACKs can adversely impact either
   transport performance or the cost of sending data across a link.

2.1.  ACK Ratio Impact on Asymmetric Paths

   TCP Performance Implications of Network Path Asymmetry [RFC3449]
   describes a series of problems and mitigations when transports use an
   asymmetric path.  Performance problems arise in several access
   networks, including bandwidth-asymmetric networks (such as broadband
   satellite access, DOCSIS cable networks, cellular mobile, WiFi, etc).

   Where the ACK rate is limited by the capacity of the return path,
   this constrains the maxium throughput for the forward path.  The ACK
   traffic also competes for capacity and/or transmission opportunities
   with other traffic that shares a constrained return path.  This
   motivates the need to reduce the volume of ACK traffic (increase the
   number of segments/packets that are acknowledged by each ACK).

   Capacity is not the only asymmetric path constraint.  Sending ACKs
   can consume significant transmission resources and the cost of
   transmitting ACKs can become a significant part of the cost of
   transmission when using a network segment.  In many wireless
   technologies, there is appreciable overhead for the transmission of
   each packet burst (data and ACK).  There can also be associated costs
   (e.g. in radio resource management and transmission scheduling) that
   are often different for the forward and return paths because they use
   different technologies or configurations.  This provides an incentive
   to reduce the rate of ACK traffic.

2.2.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

2.3.  Adapting the ACK Ratio in Current Transport Specifications

   Various methods have been proposed to modify the ACK Ratio used by
   transport protocols.  Two examples follow:

   ACK-CC [RFC5690] proposed a method to control the rate of ACKs to
   avoid the return path from becoming congested, but this did not
   achieve wide-scale deployment.

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   The Datagram Congestion Control Protocol (DCCP) [RFC4340] has methods
   to control the ACK ratio at the receiver.  DCCP specifies a TCP-
   friendly congestion control [RFC4341], which includes the ability to
   use signaling to allow this sender to adjust the receiver ACK ratio
   within certain parameters.  This also was not widely used.

   End-to-end transport methods do not have a way to detect and account
   for the cost of ACK transmission, and are difficult to tune to adapt
   to delays introduced by the path (especially when fair-queueing and
   other link scheduling methods hide the effects of increased ACK
   traffic).  They therefore only provide a partial mitigation to the
   impacts when sending ACKs over asymmetric paths.

2.4.  Adapting the ACK Ratio in the Network

   An alternative approach has been deployed for TCP that uses a
   middlebox in the network to thin the rate of ACKs.  This method is
   used with paths that exhibit significant ACK symmetry to improve
   performance of TCP when it uses an ACK Ratio of 1:2 [RFC3449].
   Performance Enhancing Proxies (PEPs) can implement these functions
   when they detect/know an upstream link is filled with TCP ACKs.

   Removing redundant ACKs (also known as "ACK Thinning") leads to TCP
   stretch ACKs (where a single ACK acknowledges more than two TCP
   segments).  The introduction of TCP Appropriate Byte Counting (ABC)
   i[RFC3465] partly mitigates the impact of stretch ACKs, and also
   recommends burst mitigation techniques at a TCP sender.

   These methods only work when ACKs can be observed by a device in the
   network.  QUIC uses an encrypted feedback packet to communicate an
   ACK.  The use of encryption intentionally prevents such in-network
   optimisations.  Compared to TCP, performance of QUIC is therefore
   disadvantaged when QUIC uses an ACK Ratio of 1:2.

   QUIC ACKs are also significantly larger in size than TCP ACKS (e.g.,
   1.5-2 times), which means additional processing overhead and link
   usage for all Internet paths, with a significant impact on asymmetric
   links, where this can also limit throughput.

3.  Updating the Default ACK Ratio for QUIC

   Any ACK policy that changes the ACK ratio from 1:2 needs to
   compensate for three issues:

   o  A reduced frequency of feedback can increase the time to detect
      congestion, impacting the congestion control algorithm.  QUIC
      mitigates this by using PTO-based retransmission.

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   o  A reduced frequency of feedback can increase the time to detect
      loss, impacting the loss recovery algorithm, and potentially
      leading to cases of spurious retransmission;

   o  A reduced ACK rate can lead to bursts of acknowledged packets, and
      introduces a need for burst mitigation at the sender;

3.1.  Considerations Updating the Default QUIC ACK Policy

   The QUIC transport protocol currently specifies a maximum ACK Delay,
   which is communicated by the sender to indicate the maximum time an
   endpoint will delay sending acknowledgments.  A default of 25
   milliseconds is recommended and QUIC currently recommends a default
   ACK Ratio of 1:2 [I-D.ietf-quic-transport].

   This document proposes changing the default QUIC behaviour to send an
   ACK for at least every 10 received packets.  Further background to
   the proposed method is detailed in the Annexe (Appendix B).

   The ACK Delay timer ensures ACKs are not unduly delayed.  The effect
   of a large delay could be significant when a stretched ACK
   acknowledges more packets, and therefore the proposed method also
   ensures feedback at least four times per RTT (less important when the
   RTT is greater than 100ms and the ACK Delay forms a small part of the
   total RTT).

   Loss detection can be impacted by delayed acknowledgments.  Although
   timer-based methods (e.g., using the QUIC Probe Timeout (PTO), see
   section 5.1 of [I-D.ietf-quic-recovery]) can reduce the reliance on
   ACKs to detect loss, prompt communication of ACK ranges after loss is
   still important to efficient loss recovery.

   Since the introduction of the specification to allow a larger TCP
   Initial Window (IW) [RFC6928], there has been deployment experience
   using TCP with an IW of 10 segments at startup.  QUIC continues this
   practice, which in part motivates the need for a QUIC transport
   protocol to operate when a burst of acknowledgements for up to ten
   packets is received.  QUIC therefore transport recommends the use of
   pacing to mitigate packet bursts being generated by a sender (see
   section 6.8 of [I-D.ietf-quic-recovery]).

   The proposed method seeks to allow QUIC to effectively operate over
   asymmetric paths.

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3.2.  During Slow Start

   Some congestion controllers can benefit from frequent feedback during
   an initial slow start period, where the sender is probing for
   available path capacity.  This update therefore does not change the
   recommended ACK Ratio during the initial part of slow start.  This
   ensures stretch ACKs do not impact the initial rate of growth for the
   congestion window.

   A suitable method might send an ACK frame for every received ack-
   eliciting packets for the first 100 received packets if max_ack_delay
   time has passed since the oldest unacknowledged data was received.

   A receiver typically has no understanding of the senders congestion
   control state.  The number 100 reflects a trade-off, corresponding to
   an appreciable opening of the sender's congestion window.

   A congestion controller typically re-enters slow start after
   congestion is detected.  The need to probe to re-establish a working
   congestion window is helped by the ACK policy after loss.

3.3.  After Slow Start

   A receiver sends an ACK if a period more than
   MIN(max_ack_delay,min_rtt/4) has passed since receiving the oldest
   unacknowledged data OR it has accumulated 10 unacknowledged packets.

3.4.  When Encountering Loss/Congestion

   Following detected loss or congestion, a receiver sends ACKs
   according to section 13.2.1 of QUIC transport
   [I-D.ietf-quic-transport].

4.  Recommended ACK Policy

   The max_ack_delay needs to be set so that at least several samples
   can be generated per RTT to estimate the path RTT.

   A QUIC receiver can generate one ACK frame for every received ack-
   eliciting packet.  TCP recommends that a receiver generates an ACK
   corresponding to every second MSS of received data, Section 4.2 of
   RFC 5681 [RFC5681], however RFC 3449 [RFC3449] also notes the need
   for, and deployment of, methods to further reduce the number of TCP
   ACKs in networks with asymmetric paths.

   An ACK frame SHOULD be generated for at least every tenth ack-
   eliciting packet.  The maximum of receiving not more than 10 ack-

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   eliciting packets is derived from the recommended TCP Initial Window
   [RFC6928].

   Using an appropriate value for max_ack_delay, or ensuring a minimum
   number of ACKs per RTT (e.g 8) would mitigate the effect of ACK loss
   on RTT estimation and aids performance for low-rate interactive
   applications.

4.1.  Further Tuning of the ACK Policy

   In situations where the default method is not sufficient, the ACK
   Ratio might be further tuned by server, as described in
   [I-D.iyengar-quic-delayed-ack].  This could also permit the ACK
   method to be adapted to match the behaviour of new congestion control
   algorithms.  Reducing the rate of ACKs can also lower the
   computational effort required to process ACKs at the sender and
   receiver.  For instance, this could reduce the workload for high
   speed network interfaces by reducing the rate of cache ejection for
   Generic Receiver Offload (GRO).

5.  IANA Considerations

   This memo includes no request to IANA.

6.  Security Considerations

   The security considerations for the QUIC transport protocol are
   described in [I-D.ietf-quic-transport].

7.  References

7.1.  Normative References

   [I-D.ietf-quic-recovery]
              Iyengar, J. and I. Swett, "QUIC Loss Detection and
              Congestion Control", draft-ietf-quic-recovery-26 (work in
              progress), February 2020.

   [I-D.ietf-quic-transport]
              Iyengar, J. and M. Thomson, "QUIC: A UDP-Based Multiplexed
              and Secure Transport", draft-ietf-quic-transport-27 (work
              in progress), February 2020.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

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   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

7.2.  Informative References

   [I-D.iyengar-quic-delayed-ack]
              Iyengar, J. and I. Swett, "Sender Control of
              Acknowledgement Delays in QUIC", draft-iyengar-quic-
              delayed-ack-00 (work in progress), January 2020.

   [RFC1122]  Braden, R., Ed., "Requirements for Internet Hosts -
              Communication Layers", STD 3, RFC 1122,
              DOI 10.17487/RFC1122, October 1989,
              <https://www.rfc-editor.org/info/rfc1122>.

   [RFC2525]  Paxson, V., Allman, M., Dawson, S., Fenner, W., Griner,
              J., Heavens, I., Lahey, K., Semke, J., and B. Volz, "Known
              TCP Implementation Problems", RFC 2525,
              DOI 10.17487/RFC2525, March 1999,
              <https://www.rfc-editor.org/info/rfc2525>.

   [RFC3449]  Balakrishnan, H., Padmanabhan, V., Fairhurst, G., and M.
              Sooriyabandara, "TCP Performance Implications of Network
              Path Asymmetry", BCP 69, RFC 3449, DOI 10.17487/RFC3449,
              December 2002, <https://www.rfc-editor.org/info/rfc3449>.

   [RFC3465]  Allman, M., "TCP Congestion Control with Appropriate Byte
              Counting (ABC)", RFC 3465, DOI 10.17487/RFC3465, February
              2003, <https://www.rfc-editor.org/info/rfc3465>.

   [RFC4340]  Kohler, E., Handley, M., and S. Floyd, "Datagram
              Congestion Control Protocol (DCCP)", RFC 4340,
              DOI 10.17487/RFC4340, March 2006,
              <https://www.rfc-editor.org/info/rfc4340>.

   [RFC4341]  Floyd, S. and E. Kohler, "Profile for Datagram Congestion
              Control Protocol (DCCP) Congestion Control ID 2: TCP-like
              Congestion Control", RFC 4341, DOI 10.17487/RFC4341, March
              2006, <https://www.rfc-editor.org/info/rfc4341>.

   [RFC5681]  Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
              Control", RFC 5681, DOI 10.17487/RFC5681, September 2009,
              <https://www.rfc-editor.org/info/rfc5681>.

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   [RFC5690]  Floyd, S., Arcia, A., Ros, D., and J. Iyengar, "Adding
              Acknowledgement Congestion Control to TCP", RFC 5690,
              DOI 10.17487/RFC5690, February 2010,
              <https://www.rfc-editor.org/info/rfc5690>.

   [RFC6928]  Chu, J., Dukkipati, N., Cheng, Y., and M. Mathis,
              "Increasing TCP's Initial Window", RFC 6928,
              DOI 10.17487/RFC6928, April 2013,
              <https://www.rfc-editor.org/info/rfc6928>.

Appendix A.  Summary of Recommended ACK Policy for TCP

   RFC 5681 [RFC5681] clarifies the TCP ACK frequency described in
   RFC 1122 [RFC1122] to recommend the ACK policy for a TCP receiver:
   "an ACK SHOULD be generated for at least every second full-sized
   segment, and MUST be generated within 500 ms of the arrival of the
   first unacknowledged packet".

   The TCP sender regards reception of an ACK as a positive indication
   that data has been received across the path.  The congestion control
   algorithm uses this to increase the size of the congestion window,
   cwnd RFC 5681 [RFC5681].

   To reduce the ACK Rate, a receiver can delay sending an ACK for a
   period of time called the ACK Delay.  This can increase network
   efficiency.  When the receiver delays ACKs, this reduces the rate of
   growth of the cwnd.  TCP implementations often use heuristics such as
   DAAS (Delayed ACK after Slow Start) to mitigate this.  This allows
   the receiver to estimate when the sender could be in the slow start
   phase of cwnd growth, and for a period of time sends an ACK for each
   received segment/packet (i.e., an ACK Ratio of 1:1).

   ACKs can be lost on the return path (either through packet loss, or
   by intentional thinning of the ACK stream).  If a sender does not
   receive an ACK for every second segment, a stretch ACK has occurred.
   RFC2525 [RFC2525] describes the significance of stretch ACK
   violations:

   "this behavior will cause TCP senders to generate burstier traffic,
   which can degrade performance in congested environments.  In
   addition, generating fewer ACKs increases the amount of time needed
   by the slow start algorithm to open the congestion window to an
   appropriate point, which diminishes performance in environments with
   large bandwidth-delay products.  Finally, generating fewer ACKs may
   cause needless retransmission timeouts in lossy environments, as it
   increases the possibility that an entire window of ACKs is lost,
   forcing a retransmission timeout."

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   RFC 3465 [RFC3465] further discusses the issue of bursts that may be
   caused by the interaction between ACK processing and congestion
   control.  This motivates a need to deal with bursts within TCP.  TCP
   senders can mitigate bursts by using Appropriate Byte Counting (ABC),
   which increases the congestion window in proportion to the amount of
   data sent into the network, rather than upon the arrival of each ACK.
   (This also defends against ACK Splitting, where multiple ACKs are
   received for parts of the same segment/packet).

   There are other scenarios where a change to the TCP ACK policy would
   have improved performance.  However, the design of TCP, and
   ossification of the protocol has made it hard for new mechanisms to
   be deployed.  QUIC does not suffer from these design constraints.

Appendix B.  Experiments Exploring an ACK Ratio of 1:10

   The performance of QUIC is at a disadvantage compared to other
   transport protocols if designs use a conservative ACK Ratio, because
   QUIC can not modified by in-network middleboxes (such as used for TCP
   ACK Thinning).  We argue that a default ratio of 1:2 is too
   conservative.

   We used an experimental approach to examine a change to QUIC's ACK
   Policy <http://erg.abdn.ac.uk/~downloads/ackscaling.pdf>.  This
   updated the default ACK Ratio from 1:2 to 1:10.  Our tests show that
   this did not negatively impact the protocol.  This reduced the amount
   of IP, UDP and ACK overhead by a factor of approximately 5.  The
   implemented congestion control, was also not negatively impacted.
   These experiments were performed in January 2020 based on available
   implementations at that time.

   Unlike TCP, QUIC sends other types of data frames in addition to ACK
   frames, increasing the total overhead on the return path.  On
   asymmetrical paths an ACK Ratio of 1:10 may still reduce the ACK
   traffic, helping to avoid return path capacity limits impacting the
   ability to use the forward path capacity.

   Figure 1 presents a table with a set of asymmetric scenarios.  The
   columns present the rate of ACK traffic required (in kbps) to fill
   each of the forward paths.  The table shows the results for TCP
   (without a PEP), both for lossless communication.  It considers the
   period after loss, when ACKs communicate the loss information.  It
   also shows the impact of using an ACK Ratio of 1:10 with QUIC.

   An ACK Ratio of 1:10 reduces the utilisation of the return path.
   Scenarios where the ACK traffic exceeds the return link capacity
   (i.e.  where this limits the forward path capacity that can be used)
   are marked with a star.  Note that the QUIC figure does not include

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   the encryption overhead, which would be dependent on the ciphers
   chosen.  This would add several additional bytes for every QUIC
   packet.

   +-------------------+-------------+---------------+-----------------+
   |                   |  10/2 Mbps  |  50/10 Mbps   |   250/3 Mbps    |
   +-------------------+-------------+---------------+-----------------+
   | TCP no loss       | 133 - 346   | 650 -1,730    | 3250 - 8,650*   |
   | TCP loss          | 346 - 560   | 1,730 - 2,800 | 8,650 - 14,000* |
   | QUIC 1:2 no loss  | 144 - 438   | 720 - 2,190   | 3,600 - 10,950* |
   | QUIC 1:2 loss     | 290 - *     | 1450 - *      | 7,250 - *       |
   | QUIC 1:10 no loss | 28.8 - 87.6 | 144 - 438     | 720 - 2,190     |
   +-------------------+-------------+---------------+-----------------+

   Figure 1: ACK traffic required to fill the forward path in different
      loss and asymmetry scenarios.  The QUIC figures do not include
                           encryption overhead.

   Figure 2 presents a table with the numbers of packets sent by two
   QUIC implementations using a 1:2 and a 1:10 ACK Ratio.  This shows
   between a four and five time reduction in the number of packets sent.

    +-------------------------------+----------------+----------------+
    |                               |   Chromium     |     Quicly     |
    |                               |   Draft 23     |    Draft 23    |
    +-------------------------------+----------------+----------------+
    | Packets sent                  | 77,419         | 83,238         |
    | Packets on return path (1:2)  | 39,089 (50.4%) | 41,108 (49.3%) |
    | Packets on return path (1:10) | 10,409 (13.4%) | 9650 (11.5%)   |
    +-------------------------------+----------------+----------------+

     Figure 2: Number of packets sent and received during a 100MB QUIC
       transfer using different ACK ratios, for two implementations

   Figure 3 presents a table with the number of bytes sent by one of the
   QUIC implementations using a 1:2 and a 1:10 ACK Ratio.  This shows a
   reduction in the number of bytes on the return path from 2.7 to 0.7%
   of the total bytes sent.  In these scenarios, this is sufficient to
   take full advantage of the forward path capacity.

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           +---------------------------------+----------------+
           |                                 |    Chromium    |
           |                                 |    Draft 23    |
           +---------------------------------+----------------+
           | Bytes sent                      | 110M           |
           | Bytes on return path (1:2 AR)   | 3,056KB (2.7%) |
           | Bytes on return path (1:10 AR)  | 810KB (0.7%)   |
           +---------------------------------+----------------+

    Figure 3: Number of bytes sent and received during a 100MB Chromium
                 QUIC transfer using different ACK ratios

   The number of bytes and packets reduces as expected when using an ACK
   Ratio of 1:10, without any increase in loss, on a high-latency path
   with an asymmetry of 5:1.  This offers a clear benefit for paths that
   are capacity-constrained, as well as paths which would benefit from a
   reduction in the ACK Rate.

Authors' Addresses

   Godred Fairhurst
   University of Aberdeen
   School of Engineering
   Fraser Noble Building
   Aberdeen  AB24 3UE
   UK

   Email: gorry@erg.abdn.ac.uk

   Ana Custura
   University of Aberdeen
   School of Engineering
   Fraser Noble Building
   Aberdeen  AB24 3UE
   UK

   Email: ana@erg.abdn.ac.uk

   Tom Jones
   University of Aberdeen
   School of Engineering
   Fraser Noble Building
   Aberdeen  AB24 3UE
   UK

   Email: tom@erg.abdn.ac.uk

Fairhurst, et al.       Expires September 6, 2020              [Page 12]