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Versions: (draft-eggert-tcpm-rfc8312bis) 00 01 02

TCPM                                                               L. Xu
Internet-Draft                                                       UNL
Obsoletes: 8312 (if approved)                                      S. Ha
Intended status: Standards Track                                Colorado
Expires: 6 November 2021                                         I. Rhee
                                                                  Bowery
                                                                 V. Goel
                                                              Apple Inc.
                                                          L. Eggert, Ed.
                                                                  NetApp
                                                              5 May 2021


               CUBIC for Fast and Long-Distance Networks
                     draft-ietf-tcpm-rfc8312bis-02

Abstract

   CUBIC is a standard TCP congestion control algorithm that uses a
   cubic function instead of the linear window increase function on the
   sender side to improve scalability and stability over fast and long-
   distance networks.  CUBIC has been adopted as the default TCP
   congestion control algorithm by the Linux, Windows, and Apple stacks.

   This document updates the specification of CUBIC to include
   algorithmic improvements based on these implementations and recent
   academic work.  Based on the extensive deployment experience with
   CUBIC, it also moves the specification to the Standards Track,
   obsoleting [RFC8312].

Note to Readers

   Discussion of this draft takes place on the TCPM working group
   mailing list (mailto:tcpm@ietf.org), which is archived at
   https://mailarchive.ietf.org/arch/browse/tcpm/.

   Working Group information can be found at
   https://datatracker.ietf.org/wg/tcpm/; source code and issues list
   for this draft can be found at https://github.com/NTAP/rfc8312bis.

Note to the RFC Editor

   xml2rfc currently renders "<em></em>" in the XML by surrounding the
   corresponding text with underscores.  This is highly distracting;
   please manually remove the underscores when doing the final edits to
   the text version of this document.





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   (There is an issue open against xml2rfc to stop doing this in the
   future: https://trac.tools.ietf.org/tools/xml2rfc/trac/ticket/596)

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
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   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
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   time.  It is inappropriate to use Internet-Drafts as reference
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   This Internet-Draft will expire on 6 November 2021.

Copyright Notice

   Copyright (c) 2021 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 (https://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 to this document.  Code Components
   extracted from this document must 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.  Conventions . . . . . . . . . . . . . . . . . . . . . . . . .   4
   3.  Design Principles of CUBIC  . . . . . . . . . . . . . . . . .   4
     3.1.  Principle 1 for the CUBIC Increase Function . . . . . . .   5
     3.2.  Principle 2 for AIMD Friendliness . . . . . . . . . . . .   6
     3.3.  Principle 3 for RTT Fairness  . . . . . . . . . . . . . .   6
     3.4.  Principle 4 for the CUBIC Decrease Factor . . . . . . . .   7
   4.  CUBIC Congestion Control  . . . . . . . . . . . . . . . . . .   7
     4.1.  Definitions . . . . . . . . . . . . . . . . . . . . . . .   7
       4.1.1.  Constants of Interest . . . . . . . . . . . . . . . .   8
       4.1.2.  Variables of Interest . . . . . . . . . . . . . . . .   8
     4.2.  Window Increase Function  . . . . . . . . . . . . . . . .   9



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     4.3.  AIMD-Friendly Region  . . . . . . . . . . . . . . . . . .  11
     4.4.  Concave Region  . . . . . . . . . . . . . . . . . . . . .  12
     4.5.  Convex Region . . . . . . . . . . . . . . . . . . . . . .  12
     4.6.  Multiplicative Decrease . . . . . . . . . . . . . . . . .  13
     4.7.  Fast Convergence  . . . . . . . . . . . . . . . . . . . .  13
     4.8.  Timeout . . . . . . . . . . . . . . . . . . . . . . . . .  14
     4.9.  Spurious Congestion Events  . . . . . . . . . . . . . . .  15
     4.10. Slow Start  . . . . . . . . . . . . . . . . . . . . . . .  16
   5.  Discussion  . . . . . . . . . . . . . . . . . . . . . . . . .  16
     5.1.  Fairness to AIMD TCP  . . . . . . . . . . . . . . . . . .  17
     5.2.  Using Spare Capacity  . . . . . . . . . . . . . . . . . .  19
     5.3.  Difficult Environments  . . . . . . . . . . . . . . . . .  20
     5.4.  Investigating a Range of Environments . . . . . . . . . .  20
     5.5.  Protection against Congestion Collapse  . . . . . . . . .  21
     5.6.  Fairness within the Alternative Congestion Control
            Algorithm  . . . . . . . . . . . . . . . . . . . . . . .  21
     5.7.  Performance with Misbehaving Nodes and Outside
            Attackers  . . . . . . . . . . . . . . . . . . . . . . .  21
     5.8.  Behavior for Application-Limited Flows  . . . . . . . . .  21
     5.9.  Responses to Sudden or Transient Events . . . . . . . . .  21
     5.10. Incremental Deployment  . . . . . . . . . . . . . . . . .  21
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  21
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  22
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  22
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .  22
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  23
   Appendix A.  Acknowledgments  . . . . . . . . . . . . . . . . . .  25
   Appendix B.  Evolution of CUBIC . . . . . . . . . . . . . . . . .  25
     B.1.  Since draft-ietf-tcpm-rfc8312bis-01 . . . . . . . . . . .  25
     B.2.  Since draft-ietf-tcpm-rfc8312bis-00 . . . . . . . . . . .  25
     B.3.  Since draft-eggert-tcpm-rfc8312bis-03 . . . . . . . . . .  25
     B.4.  Since draft-eggert-tcpm-rfc8312bis-02 . . . . . . . . . .  25
     B.5.  Since draft-eggert-tcpm-rfc8312bis-01 . . . . . . . . . .  26
     B.6.  Since draft-eggert-tcpm-rfc8312bis-00 . . . . . . . . . .  26
     B.7.  Since RFC8312 . . . . . . . . . . . . . . . . . . . . . .  27
     B.8.  Since the Original Paper  . . . . . . . . . . . . . . . .  27
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  27

1.  Introduction

   CUBIC has been adopted as the default TCP congestion control
   algorithm in the Linux, Windows, and Apple stacks, and has been used
   and deployed globally.  Extensive, decade-long deployment experience
   in vastly different Internet scenarios has convincingly demonstrated
   that CUBIC is safe for deployment on the global Internet and delivers
   substantial benefits over traditional AIMD congestion control.  It is
   therefore to be regarded as the current standard for TCP congestion
   control.



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   The design of CUBIC was motivated by the well-documented problem
   traditional TCP has with low utilization over fast and long-distance
   networks [K03][RFC3649].  This problem arises from a slow increase of
   the congestion window following a congestion event in a network with
   a large bandwidth-delay product (BDP).  [HKLRX06] indicates that this
   problem is frequently observed even in the range of congestion window
   sizes over several hundreds of packets.  This problem is equally
   applicable to all Reno-style TCP standards and their variants,
   including TCP-Reno [RFC5681], TCP-NewReno [RFC6582][RFC6675], SCTP
   [RFC4960], and TFRC [RFC5348], which use the same linear increase
   function for window growth.  We refer to all Reno-style TCP standards
   and their variants collectively as "AIMD TCP" below because they use
   the Additive Increase and Multiplicative Decrease algorithm (AIMD).

   CUBIC, originally proposed in [HRX08], is a modification to the
   congestion control algorithm of traditional AIMD TCP to remedy this
   problem.  This document describes the most recent specification of
   CUBIC.  Specifically, CUBIC uses a cubic function instead of the
   linear window increase function of AIMD TCP to improve scalability
   and stability under fast and long-distance networks.

   Binary Increase Congestion Control (BIC-TCP) [XHR04], a predecessor
   of CUBIC, was selected as the default TCP congestion control
   algorithm by Linux in the year 2005 and had been used for several
   years by the Internet community at large.

   CUBIC uses a similar window increase function as BIC-TCP and is
   designed to be less aggressive and fairer to AIMD TCP in bandwidth
   usage than BIC-TCP while maintaining the strengths of BIC-TCP such as
   stability, window scalability, and round-trip time (RTT) fairness.

   In the following sections, we first briefly explain the design
   principles of CUBIC, then provide the exact specification of CUBIC,
   and finally discuss the safety features of CUBIC following the
   guidelines specified in [RFC5033].

2.  Conventions

   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.

3.  Design Principles of CUBIC

   CUBIC is designed according to the following design principles:




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   Principle 1:  For better network utilization and stability, CUBIC
      uses both the concave and convex profiles of a cubic function to
      increase the congestion window size, instead of using just a
      convex function.

   Principle 2:  To be AIMD-friendly, CUBIC is designed to behave like
      AIMD TCP in networks with short RTTs and small bandwidth where
      AIMD TCP performs well.

   Principle 3:  For RTT-fairness, CUBIC is designed to achieve linear
      bandwidth sharing among flows with different RTTs.

   Principle 4:  CUBIC appropriately sets its multiplicative window
      decrease factor in order to balance between the scalability and
      convergence speed.

3.1.  Principle 1 for the CUBIC Increase Function

   For better network utilization and stability, CUBIC [HRX08] uses a
   cubic window increase function in terms of the elapsed time from the
   last congestion event.  While most alternative congestion control
   algorithms to AIMD TCP increase the congestion window using convex
   functions, CUBIC uses both the concave and convex profiles of a cubic
   function for window growth.

   After a window reduction in response to a congestion event is
   detected by duplicate ACKs or Explicit Congestion Notification-Echo
   (ECN-Echo, ECE) ACKs [RFC3168], CUBIC remembers the congestion window
   size where it received the congestion event and performs a
   multiplicative decrease of the congestion window.  When CUBIC enters
   into congestion avoidance, it starts to increase the congestion
   window using the concave profile of the cubic function.  The cubic
   function is set to have its plateau at the remembered congestion
   window size, so that the concave window increase continues until
   then.  After that, the cubic function turns into a convex profile and
   the convex window increase begins.

   This style of window adjustment (concave and then convex) improves
   the algorithm stability while maintaining high network utilization
   [CEHRX07].  This is because the window size remains almost constant,
   forming a plateau around the remembered congestion window size of the
   last congestion event, where network utilization is deemed highest.
   Under steady state, most window size samples of CUBIC are close to
   that remembered congestion window size, thus promoting high network
   utilization and stability.






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   Note that congestion control algorithms that only use convex
   functions to increase the congestion window size have their maximum
   increments around the remembered congestion window size of the last
   congestion event, and thus introduce many packet bursts around the
   saturation point of the network, likely causing frequent global loss
   synchronizations.

3.2.  Principle 2 for AIMD Friendliness

   CUBIC promotes per-flow fairness to AIMD TCP.  Note that AIMD TCP
   performs well over paths with short RTTs and small bandwidths (or
   small BDPs).  There is only a scalability problem in networks with
   long RTTs and large bandwidths (or large BDPs).

   A congestion control algorithm designed to be friendly to AIMD TCP on
   a per-flow basis must increase its congestion window less
   aggressively in small BDP networks than in large BDP networks.

   The aggressiveness of CUBIC mainly depends on the maximum window size
   before a window reduction, which is smaller in small-BDP networks
   than in large-BDP networks.  Thus, CUBIC increases its congestion
   window less aggressively in small-BDP networks than in large-BDP
   networks.

   Furthermore, in cases when the cubic function of CUBIC would increase
   the congestion window less aggressively than AIMD TCP, CUBIC simply
   follows the window size of AIMD TCP to ensure that CUBIC achieves at
   least the same throughput as AIMD TCP in small-BDP networks.  We call
   this region where CUBIC behaves like AIMD TCP the "AIMD-friendly
   region".

3.3.  Principle 3 for RTT Fairness

   Two CUBIC flows with different RTTs have a throughput ratio that is
   linearly proportional to the inverse of their RTT ratio, where the
   throughput of a flow is approximately the size of its congestion
   window divided by its RTT.

   Specifically, CUBIC maintains a window increase rate independent of
   RTTs outside the AIMD-friendly region, and thus flows with different
   RTTs have similar congestion window sizes under steady state when
   they operate outside the AIMD-friendly region.









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   This notion of a linear throughput ratio is similar to that of AIMD
   TCP under high statistical multiplexing where packet loss is
   independent of individual flow rates.  However, under low statistical
   multiplexing, the throughput ratio of AIMD TCP flows with different
   RTTs is quadratically proportional to the inverse of their RTT ratio
   [XHR04].

   CUBIC always ensures a linear throughput ratio independent of the
   amount of statistical multiplexing.  This is an improvement over AIMD
   TCP.  While there is no consensus on particular throughput ratios for
   different RTT flows, we believe that over wired Internet paths, use
   of a linear throughput ratio seems more reasonable than equal
   throughputs (i.e., the same throughput for flows with different RTTs)
   or a higher-order throughput ratio (e.g., a quadratical throughput
   ratio of AIMD TCP under low statistical multiplexing environments).

3.4.  Principle 4 for the CUBIC Decrease Factor

   To balance between scalability and convergence speed, CUBIC sets the
   multiplicative window decrease factor to 0.7, whereas AIMD TCP uses
   0.5.

   While this improves the scalability of CUBIC, a side effect of this
   decision is slower convergence, especially under low statistical
   multiplexing.  This design choice is following the observation that
   HighSpeed TCP (HSTCP) [RFC3649] and other approaches (e.g., [GV02])
   made: the current Internet becomes more asynchronous with less
   frequent loss synchronizations under high statistical multiplexing.

   In such environments, even strict Multiplicative-Increase
   Multiplicative-Decrease (MIMD) can converge.  CUBIC flows with the
   same RTT always converge to the same throughput independent of
   statistical multiplexing, thus achieving intra-algorithm fairness.
   We also find that in environments with sufficient statistical
   multiplexing, the convergence speed of CUBIC is reasonable.

4.  CUBIC Congestion Control

   In this section, we discuss how the congestion window is updated
   during the different stages of the CUBIC congestion controller.

4.1.  Definitions

   The unit of all window sizes in this document is segments of the
   maximum segment size (MSS), and the unit of all times is seconds.






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4.1.1.  Constants of Interest

   β__cubic_: CUBIC multiplication decrease factor as described in
   Section 4.6.

   α__aimd_: CUBIC additive increase factor used in AIMD-friendly region
   as described in Section 4.3.

   _C_: constant that determines the aggressiveness of CUBIC in
   competing with other congestion control algorithms in high BDP
   networks.  Please see Section 5 for more explanation on how it is
   set.  The unit for _C_ is

                                  segment
                                  -------
                                        3
                                  second

4.1.2.  Variables of Interest

   This section defines the variables required to implement CUBIC:

   _RTT_: Smoothed round-trip time in seconds, calculated as described
   in [RFC6298].

   _cwnd_: Current congestion window in segments.

   _ssthresh_: Current slow start threshold in segments.

   _W_max_: Size of _cwnd_ in segments just before _cwnd_ was reduced in
   the last congestion event when fast convergence is disabled.
   However, if fast convergence is enabled, the size may be further
   reduced based on the current saturation point.

   _K_: The time period in seconds it takes to increase the congestion
   window size at the beginning of the current congestion avoidance
   stage to _W_max_.

   _current_time_: Current time of the system in seconds.

   _epoch_start_: The time in seconds at which the current congestion
   avoidance stage started.

   _cwnd_start_: The _cwnd_ at the beginning of the current congestion
   avoidance stage, i.e., at time _epoch_start_.






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   W_cubic(_t_): The congestion window in segments at time _t_ in
   seconds based on the cubic increase function, as described in
   Section 4.2.

   _target_: Target value of congestion window in segments after the
   next RTT, that is, W_cubic(_t_ + _RTT_), as described in Section 4.2.

   _W_est_: An estimate for the congestion window in segments in the
   AIMD-friendly region, that is, an estimate for the congestion window
   of AIMD TCP.

   _segments_acked_: Number of segments acked when an ACK is received.

4.2.  Window Increase Function

   CUBIC maintains the acknowledgment (ACK) clocking of AIMD TCP by
   increasing the congestion window only at the reception of an ACK.  It
   does not make any changes to the TCP Fast Recovery and Fast
   Retransmit algorithms [RFC6582][RFC6675].

   During congestion avoidance after a congestion event where a packet
   loss is detected by duplicate ACKs or by receiving packets carrying
   ECE flags [RFC3168], CUBIC changes the window increase function of
   AIMD TCP.

   CUBIC uses the following window increase function:

                                             3
                      W     (t) = C * (t - K)  + W
                       cubic                      max

                                  Figure 1

   where _t_ is the elapsed time in seconds from the beginning of the
   current congestion avoidance stage, that is,

                       t = current_time - epoch
                                               start

   and where _epoch_start_ is the time at which the current congestion
   avoidance stage starts. _K_ is the time period that the above
   function takes to increase the congestion window size at the
   beginning of the current congestion avoidance stage to _W_max_ if
   there are no further congestion events and is calculated using the
   following equation:






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                                  ________________
                                 /W    - cwnd
                             3  /  max       start
                         K = | /  ----------------
                             |/           C

                                  Figure 2

   where _cwnd_start_ is the congestion window at the beginning of the
   current congestion avoidance stage.  For example, right after a
   congestion event, _cwnd_start_ is equal to the new cwnd calculated as
   described in Section 4.6.

   Upon receiving an ACK during congestion avoidance, CUBIC computes the
   _target_ congestion window size after the next _RTT_ using Figure 1
   as follows, where _RTT_ is the smoothed round-trip time.  The lower
   and upper bounds below ensure that CUBIC's congestion window increase
   rate is non-decreasing and is less than the increase rate of slow
   start.

                  /
                  |                if W     (t + RTT) < cwnd
                  |cwnd                cubic
                  |
                  |
                  |
         target = <                if W     (t + RTT) > 1.5 * cwnd
                  |1.5 * cwnd          cubic
                  |
                  |
                  |W     (t + RTT)
                  | cubic          otherwise
                  \

   Depending on the value of the current congestion window size _cwnd_,
   CUBIC runs in three different regions:

   1.  The AIMD-friendly region, which ensures that CUBIC achieves at
       least the same throughput as AIMD TCP.

   2.  The concave region, if CUBIC is not in the AIMD-friendly region
       and _cwnd_ is less than _W_max_.

   3.  The convex region, if CUBIC is not in the AIMD-friendly region
       and _cwnd_ is greater than _W_max_.

   Below, we describe the exact actions taken by CUBIC in each region.




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4.3.  AIMD-Friendly Region

   AIMD TCP performs well in certain types of networks, for example,
   under short RTTs and small bandwidths (or small BDPs).  In these
   networks, CUBIC remains in the AIMD-friendly region to achieve at
   least the same throughput as AIMD TCP.

   The AIMD-friendly region is designed according to the analysis in
   [FHP00], which studies the performance of an AIMD algorithm with an
   additive factor of α__aimd_ (segments per _RTT_) and a multiplicative
   factor of β__aimd_, denoted by AIMD(α__aimd_, β__aimd_).
   Specifically, the average congestion window size of AIMD(α__aimd_,
   β__aimd_) can be calculated using Figure 3.  The analysis shows that
   AIMD(α__aimd_, β__aimd_) with

                                      1 - β
                                           cubic
                          α     = 3 * ----------
                           aimd       1 + β
                                           cubic

   achieves the same average window size as AIMD TCP that uses AIMD(1,
   0.5).

                                           ___________________
                                          /α     * (1 + β    )
                                         /  aimd         aimd
            AVG_AIMD(α    , β    ) = |  /  -------------------
                      aimd   aimd    | /   2 * (1 - β    ) * p
                                     |/              aimd

                                  Figure 3

   Based on the above analysis, CUBIC uses Figure 4 to estimate the
   window size _W_est_ of AIMD(α__aimd_, β__aimd_) with

                                      1 - β
                                           cubic
                          α     = 3 * ----------
                           aimd       1 + β
                                           cubic

                          β     = β
                           aimd    cubic







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   which achieves the same average window size as AIMD TCP.  When
   receiving an ACK in congestion avoidance (where _cwnd_ could be
   greater than or less than _W_max_), CUBIC checks whether W_cubic(_t_)
   is less than _W_est_. If so, CUBIC is in the AIMD-friendly region and
   _cwnd_ SHOULD be set to _W_est_ at each reception of an ACK.

   _W_est_ is set equal to _cwnd_start_ at the start of the congestion
   avoidance stage.  After that, on every ACK, _W_est_ is updated using
   Figure 4.

                                         segments_acked
                   W    = W    + α     * --------------
                    est    est    aimd        cwnd

                                  Figure 4

   Note that once _W_est_ reaches _W_max_, that is, _W_est_ >= _W_max_,
   α__aimd_ SHOULD be set to 1 to achieve the same congestion window
   increment as AIMD TCP, which uses AIMD(1, 0.5).

4.4.  Concave Region

   When receiving an ACK in congestion avoidance, if CUBIC is not in the
   AIMD-friendly region and _cwnd_ is less than _W_max_, then CUBIC is
   in the concave region.  In this region, _cwnd_ MUST be incremented by

                               target - cwnd
                               -------------
                                   cwnd

   for each received ACK, where _target_ is calculated as described in
   Section 4.2.

4.5.  Convex Region

   When receiving an ACK in congestion avoidance, if CUBIC is not in the
   AIMD-friendly region and _cwnd_ is larger than or equal to _W_max_,
   then CUBIC is in the convex region.

   The convex region indicates that the network conditions might have
   changed since the last congestion event, possibly implying more
   available bandwidth after some flow departures.  Since the Internet
   is highly asynchronous, some amount of perturbation is always
   possible without causing a major change in available bandwidth.







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   In this region, CUBIC is very careful.  The convex profile ensures
   that the window increases very slowly at the beginning and gradually
   increases its increase rate.  We also call this region the "maximum
   probing phase", since CUBIC is searching for a new _W_max_. In this
   region, _cwnd_ MUST be incremented by

                               target - cwnd
                               -------------
                                   cwnd

   for each received ACK, where _target_ is calculated as described in
   Section 4.2.

4.6.  Multiplicative Decrease

   When a packet loss is detected by duplicate ACKs or by receiving
   packets carrying ECE flags, CUBIC updates _W_max_ and reduces _cwnd_
   and _ssthresh_ immediately as described below.  An implementation MAY
   set a smaller _ssthresh_ than suggested below to accommodate rate-
   limited applications as described in [RFC7661].  For both packet loss
   and congestion detection through ECN, the sender MAY employ a Fast
   Recovery algorithm to gradually adjust the congestion window to its
   new reduced _ssthresh_ value.  The parameter β__cubic_ SHOULD be set
   to 0.7.

        ssthresh = cwnd * β         // new slow-start threshold
                           cubic

        ssthresh = max(ssthresh, 2) // threshold is at least 2 MSS


                                    // window reduction
        cwnd = ssthresh

   A side effect of setting β__cubic_ to a value bigger than 0.5 is
   slower convergence.  We believe that while a more adaptive setting of
   β__cubic_ could result in faster convergence, it will make the
   analysis of CUBIC much harder.

4.7.  Fast Convergence

   To improve convergence speed, CUBIC uses a heuristic.  When a new
   flow joins the network, existing flows need to give up some of their
   bandwidth to allow the new flow some room for growth, if the existing
   flows have been using all the network bandwidth.  To speed up this
   bandwidth release by existing flows, the following "Fast Convergence"
   mechanism SHOULD be implemented.




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   With Fast Convergence, when a congestion event occurs, we update
   _W_max_ as follows, before the window reduction as described in
   Section 4.6.

       /
       |       1 + β
       |            cubic if cwnd < W    and fast convergence is enabled,
       |cwnd * ----------            max
       |            2
W    = <
 max   |                  further reduce W
       |                                  max
       |
       |                  otherwise, remember cwnd before reduction
       \cwnd

   At a congestion event, if the current _cwnd_ is less than _W_max_,
   this indicates that the saturation point experienced by this flow is
   getting reduced because of a change in available bandwidth.  Then we
   allow this flow to release more bandwidth by reducing _W_max_
   further.  This action effectively lengthens the time for this flow to
   increase its congestion window, because the reduced _W_max_ forces
   the flow to plateau earlier.  This allows more time for the new flow
   to catch up to its congestion window size.

   Fast Convergence is designed for network environments with multiple
   CUBIC flows.  In network environments with only a single CUBIC flow
   and without any other traffic, Fast Convergence SHOULD be disabled.

4.8.  Timeout

   In case of a timeout, CUBIC follows AIMD TCP to reduce _cwnd_
   [RFC5681], but sets _ssthresh_ using β__cubic_ (same as in
   Section 4.6) in a way that is different from AIMD TCP [RFC5681].

   During the first congestion avoidance stage after a timeout, CUBIC
   increases its congestion window size using Figure 1, where _t_ is the
   elapsed time since the beginning of the current congestion avoidance,
   _K_ is set to 0, and _W_max_ is set to the congestion window size at
   the beginning of the current congestion avoidance stage.  In
   addition, for the AIMD-friendly region, _W_est_ SHOULD be set to the
   congestion window size at the beginning of the current congestion
   avoidance.








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4.9.  Spurious Congestion Events

   In cases where CUBIC reduces its congestion window in response to
   having detected packet loss via duplicate ACKs or timeouts, there is
   a possibility that the missing ACK would arrive after the congestion
   window reduction and a corresponding packet retransmission.  For
   example, packet reordering could trigger this behavior.  A high
   degree of packet reordering could cause multiple congestion window
   reduction events, where spurious losses are incorrectly interpreted
   as congestion signals, thus degrading CUBIC's performance
   significantly.

   When there is a congestion event, a CUBIC implementation SHOULD save
   the current value of the following variables before the congestion
   window reduction.

                       prior_cwnd = cwnd

                       prior_ssthresh = ssthresh

                       prior_W    = W
                              max    max

                       prior_K = K

                       prior_epoch      = epoch
                                  start        start

                       prior_W_{est} = W
                                        est

   CUBIC MAY implement an algorithm to detect spurious retransmissions,
   such as DSACK [RFC3708], Forward RTO-Recovery [RFC5682] or Eifel
   [RFC3522].  Once a spurious congestion event is detected, CUBIC
   SHOULD restore the original values of above mentioned variables as
   follows if the current _cwnd_ is lower than _prior_cwnd_. Restoring
   the original values ensures that CUBIC's performance is similar to
   what it would be without spurious losses.













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                                         \
            cwnd = prior_cwnd            |
                                         |
            ssthresh = prior_ssthresh    |
                                         |
            W    = prior_W               |
             max          max            |
                                         >if cwnd < prior_cwnd
            K = prior_K                  |
                                         |
            epoch      = prior_epoch     |
                 start              start|
                                         |
            W    = prior_W               |
             est          est            /

   In rare cases, when the detection happens long after a spurious loss
   event and the current _cwnd_ is already higher than _prior_cwnd_,
   CUBIC SHOULD continue to use the current and the most recent values
   of these variables.

4.10.  Slow Start

   CUBIC MUST employ a slow-start algorithm, when _cwnd_ is no more than
   _ssthresh_. Among the slow-start algorithms, CUBIC MAY choose the
   AIMD TCP slow start [RFC5681] in general networks, or the limited
   slow start [RFC3742] or hybrid slow start [HR08] for fast and long-
   distance networks.

   When CUBIC uses hybrid slow start [HR08], it may exit the first slow
   start without incurring any packet loss and thus _W_max_ is
   undefined.  In this special case, CUBIC switches to congestion
   avoidance and increases its congestion window size using Figure 1,
   where _t_ is the elapsed time since the beginning of the current
   congestion avoidance, _K_ is set to 0, and _W_max_ is set to the
   congestion window size at the beginning of the current congestion
   avoidance stage.

5.  Discussion

   In this section, we further discuss the safety features of CUBIC
   following the guidelines specified in [RFC5033].

   With a deterministic loss model where the number of packets between
   two successive packet losses is always _1/p_, CUBIC always operates
   with the concave window profile, which greatly simplifies the
   performance analysis of CUBIC.  The average window size of CUBIC can
   be obtained by the following function:



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                                  ________________      ____
                                 /C * (3 + β     )   3 /   4
                            4   /           cubic    |/ RTT
               AVG_W      = |  /  ---------------- * -------
                    cubic   | /   4 * (1 - β     )       __
                            |/              cubic     3 / 4
                                                      |/ p

                                  Figure 5

   With β__cubic_ set to 0.7, the above formula reduces to:

                                                  ____
                                     _______   3 /   4
                                 4  /C * 3.7   |/ RTT
                    AVG_W      = | / ------- * -------
                         cubic   |/    1.2         __
                                                3 / 4
                                                |/ p

                                  Figure 6

   We will determine the value of _C_ in the following subsection using
   Figure 6.

5.1.  Fairness to AIMD TCP

   In environments where AIMD TCP is able to make reasonable use of the
   available bandwidth, CUBIC does not significantly change this state.

   AIMD TCP performs well in the following two types of networks:

   1.  networks with a small bandwidth-delay product (BDP)

   2.  networks with a short RTTs, but not necessarily a small BDP

   CUBIC is designed to behave very similarly to AIMD TCP in the above
   two types of networks.  The following two tables show the average
   window sizes of AIMD TCP, HSTCP, and CUBIC.  The average window sizes
   of AIMD TCP and HSTCP are from [RFC3649].  The average window size of
   CUBIC is calculated using Figure 6 and the CUBIC AIMD-friendly region
   for three different values of _C_.









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   +=============+=======+========+================+=========+========+
   | Loss Rate P |  AIMD |  HSTCP | CUBIC (C=0.04) |   CUBIC |  CUBIC |
   |             |       |        |                | (C=0.4) |  (C=4) |
   +=============+=======+========+================+=========+========+
   |     1.0e-02 |    12 |     12 |             12 |      12 |     12 |
   +-------------+-------+--------+----------------+---------+--------+
   |     1.0e-03 |    38 |     38 |             38 |      38 |     59 |
   +-------------+-------+--------+----------------+---------+--------+
   |     1.0e-04 |   120 |    263 |            120 |     187 |    333 |
   +-------------+-------+--------+----------------+---------+--------+
   |     1.0e-05 |   379 |   1795 |            593 |    1054 |   1874 |
   +-------------+-------+--------+----------------+---------+--------+
   |     1.0e-06 |  1200 |  12280 |           3332 |    5926 |  10538 |
   +-------------+-------+--------+----------------+---------+--------+
   |     1.0e-07 |  3795 |  83981 |          18740 |   33325 |  59261 |
   +-------------+-------+--------+----------------+---------+--------+
   |     1.0e-08 | 12000 | 574356 |         105383 |  187400 | 333250 |
   +-------------+-------+--------+----------------+---------+--------+

        Table 1: AIMD TCP, HSTCP, and CUBIC with RTT = 0.1 seconds

   Table 1 describes the response function of AIMD TCP, HSTCP, and CUBIC
   in networks with _RTT_ = 0.1 seconds.  The average window size is in
   MSS-sized segments.

    +=============+=======+========+================+=========+=======+
    | Loss Rate P |  AIMD |  HSTCP | CUBIC (C=0.04) |   CUBIC | CUBIC |
    |             |       |        |                | (C=0.4) | (C=4) |
    +=============+=======+========+================+=========+=======+
    |     1.0e-02 |    12 |     12 |             12 |      12 |    12 |
    +-------------+-------+--------+----------------+---------+-------+
    |     1.0e-03 |    38 |     38 |             38 |      38 |    38 |
    +-------------+-------+--------+----------------+---------+-------+
    |     1.0e-04 |   120 |    263 |            120 |     120 |   120 |
    +-------------+-------+--------+----------------+---------+-------+
    |     1.0e-05 |   379 |   1795 |            379 |     379 |   379 |
    +-------------+-------+--------+----------------+---------+-------+
    |     1.0e-06 |  1200 |  12280 |           1200 |    1200 |  1874 |
    +-------------+-------+--------+----------------+---------+-------+
    |     1.0e-07 |  3795 |  83981 |           3795 |    5926 | 10538 |
    +-------------+-------+--------+----------------+---------+-------+
    |     1.0e-08 | 12000 | 574356 |          18740 |   33325 | 59261 |
    +-------------+-------+--------+----------------+---------+-------+

        Table 2: AIMD TCP, HSTCP, and CUBIC with RTT = 0.01 seconds






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   Table 2 describes the response function of AIMD TCP, HSTCP, and CUBIC
   in networks with _RTT_ = 0.01 seconds.  The average window size is in
   MSS-sized segments.

   Both tables show that CUBIC with any of these three _C_ values is
   more friendly to AIMD TCP than HSTCP, especially in networks with a
   short _RTT_ where AIMD TCP performs reasonably well.  For example, in
   a network with _RTT_ = 0.01 seconds and p=10^-6, AIMD TCP has an
   average window of 1200 packets.  If the packet size is 1500 bytes,
   then AIMD TCP can achieve an average rate of 1.44 Gbps.  In this
   case, CUBIC with _C_=0.04 or _C_=0.4 achieves exactly the same rate
   as AIMD TCP, whereas HSTCP is about ten times more aggressive than
   AIMD TCP.

   We can see that _C_ determines the aggressiveness of CUBIC in
   competing with other congestion control algorithms for bandwidth.
   CUBIC is more friendly to AIMD TCP, if the value of _C_ is lower.
   However, we do not recommend setting _C_ to a very low value like
   0.04, since CUBIC with a low _C_ cannot efficiently use the bandwidth
   in fast and long-distance networks.  Based on these observations and
   extensive deployment experience, we find _C_=0.4 gives a good balance
   between AIMD- friendliness and aggressiveness of window increase.
   Therefore, _C_ SHOULD be set to 0.4.  With _C_ set to 0.4, Figure 6
   is reduced to:

                                               ____
                                            3 /   4
                                            |/ RTT
                       AVG_W      = 1.054 * -------
                            cubic               __
                                             3 / 4
                                             |/ p

                                  Figure 7

   Figure 7 is then used in the next subsection to show the scalability
   of CUBIC.

5.2.  Using Spare Capacity

   CUBIC uses a more aggressive window increase function than AIMD TCP
   for fast and long-distance networks.

   The following table shows that to achieve the 10 Gbps rate, AIMD TCP
   requires a packet loss rate of 2.0e-10, while CUBIC requires a packet
   loss rate of 2.9e-8.





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      +===================+===========+=========+=========+=========+
      | Throughput (Mbps) | Average W |  AIMD P | HSTCP P | CUBIC P |
      +===================+===========+=========+=========+=========+
      |                 1 |       8.3 |  2.0e-2 |  2.0e-2 |  2.0e-2 |
      +-------------------+-----------+---------+---------+---------+
      |                10 |      83.3 |  2.0e-4 |  3.9e-4 |  2.9e-4 |
      +-------------------+-----------+---------+---------+---------+
      |               100 |     833.3 |  2.0e-6 |  2.5e-5 |  1.4e-5 |
      +-------------------+-----------+---------+---------+---------+
      |              1000 |    8333.3 |  2.0e-8 |  1.5e-6 |  6.3e-7 |
      +-------------------+-----------+---------+---------+---------+
      |             10000 |   83333.3 | 2.0e-10 |  1.0e-7 |  2.9e-8 |
      +-------------------+-----------+---------+---------+---------+

        Table 3: Required packet loss rate for AIMD TCP, HSTCP, and
                   CUBIC to achieve a certain throughput

   Table 3 describes the required packet loss rate for AIMD TCP, HSTCP,
   and CUBIC to achieve a certain throughput.  We use 1500-byte packets
   and an _RTT_ of 0.1 seconds.

   Our test results in [HKLRX06] indicate that CUBIC uses the spare
   bandwidth left unused by existing AIMD TCP flows in the same
   bottleneck link without taking away much bandwidth from the existing
   flows.

5.3.  Difficult Environments

   CUBIC is designed to remedy the poor performance of AIMD TCP in fast
   and long-distance networks.

5.4.  Investigating a Range of Environments

   There is decade-long deployment experience with CUBIC on the
   Internet.  CUBIC has also been extensively studied by using both NS-2
   simulation and testbed experiments, covering a wide range of network
   environments.  More information can be found in [HKLRX06].

   Same as AIMD TCP, CUBIC is a loss-based congestion control algorithm.
   Because CUBIC is designed to be more aggressive (due to a faster
   window increase function and bigger multiplicative decrease factor)
   than AIMD TCP in fast and long-distance networks, it can fill large
   drop-tail buffers more quickly than AIMD TCP and increases the risk
   of a standing queue [RFC8511].  In this case, proper queue sizing and
   management [RFC7567] could be used to reduce the packet queuing
   delay.





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5.5.  Protection against Congestion Collapse

   With regard to the potential of causing congestion collapse, CUBIC
   behaves like AIMD TCP, since CUBIC modifies only the window
   adjustment algorithm of AIMD TCP.  Thus, it does not modify the ACK
   clocking and timeout behaviors of AIMD TCP.

5.6.  Fairness within the Alternative Congestion Control Algorithm

   CUBIC ensures convergence of competing CUBIC flows with the same RTT
   in the same bottleneck links to an equal throughput.  When competing
   flows have different RTT values, their throughput ratio is linearly
   proportional to the inverse of their RTT ratios.  This is true
   independently of the level of statistical multiplexing on the link.

5.7.  Performance with Misbehaving Nodes and Outside Attackers

   This is not considered in the current CUBIC design.

5.8.  Behavior for Application-Limited Flows

   CUBIC does not increase its congestion window size if a flow is
   currently limited by the application instead of the congestion
   window.  In case of long periods during which _cwnd_ has not been
   updated due to such an application limit, such as idle periods, _t_
   in Figure 1 MUST NOT include these periods; otherwise, W_cubic(_t_)
   might be very high after restarting from these periods.

5.9.  Responses to Sudden or Transient Events

   If there is a sudden congestion, a routing change, or a mobility
   event, CUBIC behaves the same as AIMD TCP.

5.10.  Incremental Deployment

   CUBIC requires only changes to TCP senders, and it does not require
   any changes at TCP receivers.  That is, a CUBIC sender works
   correctly with the AIMD TCP receivers.  In addition, CUBIC does not
   require any changes to routers and does not require any assistance
   from routers.

6.  Security Considerations

   CUBIC makes no changes to the underlying security of TCP.  More
   information about TCP security concerns can be found in [RFC5681].






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7.  IANA Considerations

   This document does not require any IANA actions.

8.  References

8.1.  Normative References

   [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/rfc/rfc2119>.

   [RFC3168]  Ramakrishnan, K., Floyd, S., and D. Black, "The Addition
              of Explicit Congestion Notification (ECN) to IP",
              RFC 3168, DOI 10.17487/RFC3168, September 2001,
              <https://www.rfc-editor.org/rfc/rfc3168>.

   [RFC5033]  Floyd, S. and M. Allman, "Specifying New Congestion
              Control Algorithms", BCP 133, RFC 5033,
              DOI 10.17487/RFC5033, August 2007,
              <https://www.rfc-editor.org/rfc/rfc5033>.

   [RFC5348]  Floyd, S., Handley, M., Padhye, J., and J. Widmer, "TCP
              Friendly Rate Control (TFRC): Protocol Specification",
              RFC 5348, DOI 10.17487/RFC5348, September 2008,
              <https://www.rfc-editor.org/rfc/rfc5348>.

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

   [RFC6298]  Paxson, V., Allman, M., Chu, J., and M. Sargent,
              "Computing TCP's Retransmission Timer", RFC 6298,
              DOI 10.17487/RFC6298, June 2011,
              <https://www.rfc-editor.org/rfc/rfc6298>.

   [RFC6582]  Henderson, T., Floyd, S., Gurtov, A., and Y. Nishida, "The
              NewReno Modification to TCP's Fast Recovery Algorithm",
              RFC 6582, DOI 10.17487/RFC6582, April 2012,
              <https://www.rfc-editor.org/rfc/rfc6582>.

   [RFC6675]  Blanton, E., Allman, M., Wang, L., Jarvinen, I., Kojo, M.,
              and Y. Nishida, "A Conservative Loss Recovery Algorithm
              Based on Selective Acknowledgment (SACK) for TCP",
              RFC 6675, DOI 10.17487/RFC6675, August 2012,
              <https://www.rfc-editor.org/rfc/rfc6675>.




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   [RFC7567]  Baker, F., Ed. and G. Fairhurst, Ed., "IETF
              Recommendations Regarding Active Queue Management",
              BCP 197, RFC 7567, DOI 10.17487/RFC7567, July 2015,
              <https://www.rfc-editor.org/rfc/rfc7567>.

   [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/rfc/rfc8174>.

8.2.  Informative References

   [CEHRX07]  Cai, H., Eun, D., Ha, S., Rhee, I., and L. Xu, "Stochastic
              Ordering for Internet Congestion Control and its
              Applications", IEEE INFOCOM 2007 - 26th IEEE International
              Conference on Computer Communications,
              DOI 10.1109/infcom.2007.111, 2007,
              <https://doi.org/10.1109/infcom.2007.111>.

   [FHP00]    Floyd, S., Handley, M., and J. Padhye, "A Comparison of
              Equation-Based and AIMD Congestion Control", May 2000,
              <https://www.icir.org/tfrc/aimd.pdf>.

   [GV02]     Gorinsky, S. and H. Vin, "Extended Analysis of Binary
              Adjustment Algorithms", Technical Report TR2002-29,
              Department of Computer Sciences, The University of
              Texas at Austin, 11 August 2002,
              <http://www.cs.utexas.edu/ftp/techreports/tr02-39.ps.gz>.

   [HKLRX06]  Ha, S., Kim, Y., Le, L., Rhee, I., and L. Xu, "A Step
              toward Realistic Performance Evaluation of High-Speed TCP
              Variants", International Workshop on Protocols for Fast
              Long-Distance Networks, February 2006,
              <https://pfld.net/2006/paper/s2_03.pdf>.

   [HR08]     Ha, S. and I. Rhee, "Hybrid Slow Start for High-Bandwidth
              and Long-Distance Networks", International Workshop
              on Protocols for Fast Long-Distance Networks, March 2008,
              <http://www.hep.man.ac.uk/g/GDARN-IT/pfldnet2008/paper/
              Sangate_Ha%20Final.pdf>.

   [HRX08]    Ha, S., Rhee, I., and L. Xu, "CUBIC: a new TCP-friendly
              high-speed TCP variant", ACM SIGOPS Operating Systems
              Review Vol. 42, pp. 64-74, DOI 10.1145/1400097.1400105,
              July 2008, <https://doi.org/10.1145/1400097.1400105>.







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   [K03]      Kelly, T., "Scalable TCP: improving performance in
              highspeed wide area networks", ACM SIGCOMM Computer
              Communication Review Vol. 33, pp. 83-91,
              DOI 10.1145/956981.956989, April 2003,
              <https://doi.org/10.1145/956981.956989>.

   [RFC3522]  Ludwig, R. and M. Meyer, "The Eifel Detection Algorithm
              for TCP", RFC 3522, DOI 10.17487/RFC3522, April 2003,
              <https://www.rfc-editor.org/rfc/rfc3522>.

   [RFC3649]  Floyd, S., "HighSpeed TCP for Large Congestion Windows",
              RFC 3649, DOI 10.17487/RFC3649, December 2003,
              <https://www.rfc-editor.org/rfc/rfc3649>.

   [RFC3708]  Blanton, E. and M. Allman, "Using TCP Duplicate Selective
              Acknowledgement (DSACKs) and Stream Control Transmission
              Protocol (SCTP) Duplicate Transmission Sequence Numbers
              (TSNs) to Detect Spurious Retransmissions", RFC 3708,
              DOI 10.17487/RFC3708, February 2004,
              <https://www.rfc-editor.org/rfc/rfc3708>.

   [RFC3742]  Floyd, S., "Limited Slow-Start for TCP with Large
              Congestion Windows", RFC 3742, DOI 10.17487/RFC3742, March
              2004, <https://www.rfc-editor.org/rfc/rfc3742>.

   [RFC4960]  Stewart, R., Ed., "Stream Control Transmission Protocol",
              RFC 4960, DOI 10.17487/RFC4960, September 2007,
              <https://www.rfc-editor.org/rfc/rfc4960>.

   [RFC5682]  Sarolahti, P., Kojo, M., Yamamoto, K., and M. Hata,
              "Forward RTO-Recovery (F-RTO): An Algorithm for Detecting
              Spurious Retransmission Timeouts with TCP", RFC 5682,
              DOI 10.17487/RFC5682, September 2009,
              <https://www.rfc-editor.org/rfc/rfc5682>.

   [RFC7661]  Fairhurst, G., Sathiaseelan, A., and R. Secchi, "Updating
              TCP to Support Rate-Limited Traffic", RFC 7661,
              DOI 10.17487/RFC7661, October 2015,
              <https://www.rfc-editor.org/rfc/rfc7661>.

   [RFC8312]  Rhee, I., Xu, L., Ha, S., Zimmermann, A., Eggert, L., and
              R. Scheffenegger, "CUBIC for Fast Long-Distance Networks",
              RFC 8312, DOI 10.17487/RFC8312, February 2018,
              <https://www.rfc-editor.org/rfc/rfc8312>.







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   [RFC8511]  Khademi, N., Welzl, M., Armitage, G., and G. Fairhurst,
              "TCP Alternative Backoff with ECN (ABE)", RFC 8511,
              DOI 10.17487/RFC8511, December 2018,
              <https://www.rfc-editor.org/rfc/rfc8511>.

   [SXEZ19]   Sun, W., Xu, L., Elbaum, S., and D. Zhao, "Model-Agnostic
              and Efficient Exploration of Numerical State Space of
              Real-World TCP Congestion Control Implementations", USENIX
              NSDI 2019, February 2019,
              <https://www.usenix.org/system/files/nsdi19-sun.pdf>.

   [XHR04]    Xu, L., Harfoush, K., and I. Rhee, "Binary Increase
              Congestion Control (BIC) for Fast Long-Distance Networks",
              IEEE INFOCOM 2004, DOI 10.1109/infcom.2004.1354672, March
              2004, <https://doi.org/10.1109/infcom.2004.1354672>.

Appendix A.  Acknowledgments

   Richard Scheffenegger and Alexander Zimmermann originally co-authored
   [RFC8312].

Appendix B.  Evolution of CUBIC

B.1.  Since draft-ietf-tcpm-rfc8312bis-01

   *  address Michael Scharf's editorial suggestions. (#59
      (https://github.com/NTAP/rfc8312bis/issues/59))

   *  add "Note to the RFC Editor" about removing underscores

B.2.  Since draft-ietf-tcpm-rfc8312bis-00

   *  use updated xml2rfc with better text rendering of subscripts

B.3.  Since draft-eggert-tcpm-rfc8312bis-03

   *  fix spelling nits

   *  rename to draft-ietf

   *  define _W_max_ more clearly

B.4.  Since draft-eggert-tcpm-rfc8312bis-02

   *  add definition for segments_acked and alpha__aimd_. (#47
      (https://github.com/NTAP/rfc8312bis/issues/47))





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   *  fix a mistake in _W_max_ calculation in the fast convergence
      section. (#51 (https://github.com/NTAP/rfc8312bis/issues/51))

   *  clarity on setting _ssthresh_ and _cwnd_start_ during
      multiplicative decrease. (#53 (https://github.com/NTAP/rfc8312bis/
      issues/53))

B.5.  Since draft-eggert-tcpm-rfc8312bis-01

   *  rename TCP-Friendly to AIMD-Friendly and rename Standard TCP to
      AIMD TCP to avoid confusion as CUBIC has been widely used on the
      Internet. (#38 (https://github.com/NTAP/rfc8312bis/issues/38))

   *  change introductory text to reflect the significant broader
      deployment of CUBIC on the Internet. (#39
      (https://github.com/NTAP/rfc8312bis/issues/39))

   *  rephrase introduction to avoid referring to variables that have
      not been defined yet.

B.6.  Since draft-eggert-tcpm-rfc8312bis-00

   *  acknowledge former co-authors (#15
      (https://github.com/NTAP/rfc8312bis/issues/15))

   *  prevent _cwnd_ from becoming less than two (#7
      (https://github.com/NTAP/rfc8312bis/issues/7))

   *  add list of variables and constants (#5
      (https://github.com/NTAP/rfc8312bis/issues/5), #6
      (https://github.com/NTAP/rfc8312bis/issues/6))

   *  update _K_'s definition and add bounds for CUBIC _target_ _cwnd_
      [SXEZ19] (#1 (https://github.com/NTAP/rfc8312bis/issues/1), #14
      (https://github.com/NTAP/rfc8312bis/issues/14))

   *  update _W_est_ to use AIMD approach (#20
      (https://github.com/NTAP/rfc8312bis/issues/20))

   *  set alpha__aimd_ to 1 once _W_est_ reaches _W_max_ (#2
      (https://github.com/NTAP/rfc8312bis/issues/2))

   *  add Vidhi as co-author (#17 (https://github.com/NTAP/rfc8312bis/
      issues/17))

   *  note for Fast Recovery during _cwnd_ decrease due to congestion
      event (#11 (https://github.com/NTAP/rfc8312bis/issues/11))




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   *  add section for spurious congestion events (#23
      (https://github.com/NTAP/rfc8312bis/issues/23))

   *  initialize _W_est_ after timeout and remove variable
      _W_(last_max)_ (#28 (https://github.com/NTAP/rfc8312bis/
      issues/28))

B.7.  Since RFC8312

   *  converted to Markdown and xml2rfc v3

   *  updated references (as part of the conversion)

   *  updated author information

   *  various formatting changes

   *  move to Standards Track

B.8.  Since the Original Paper

   CUBIC has gone through a few changes since the initial release
   [HRX08] of its algorithm and implementation.  Below we highlight the
   differences between its original paper and [RFC8312].

   *  The original paper [HRX08] includes the pseudocode of CUBIC
      implementation using Linux's pluggable congestion control
      framework, which excludes system-specific optimizations.  The
      simplified pseudocode might be a good source to start with and
      understand CUBIC.

   *  [HRX08] also includes experimental results showing its performance
      and fairness.

   *  The definition of beta__cubic_ constant was changed in [RFC8312].
      For example, beta__cubic_ in the original paper was the window
      decrease constant while [RFC8312] changed it to CUBIC
      multiplication decrease factor.  With this change, the current
      congestion window size after a congestion event in [RFC8312] was
      beta__cubic_ * _W_max_ while it was (1-beta__cubic_) * _W_max_ in
      the original paper.

   *  Its pseudocode used _W_(last_max)_ while [RFC8312] used _W_max_.

   *  Its AIMD-friendly window was _W_tcp_ while [RFC8312] used _W_est_.

Authors' Addresses




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   Lisong Xu
   University of Nebraska-Lincoln
   Department of Computer Science and Engineering
   Lincoln, NE 68588-0115
   United States of America

   Email: xu@unl.edu
   URI:   https://cse.unl.edu/~xu/


   Sangtae Ha
   University of Colorado at Boulder
   Department of Computer Science
   Boulder, CO 80309-0430
   United States of America

   Email: sangtae.ha@colorado.edu
   URI:   https://netstech.org/sangtaeha/


   Injong Rhee
   Bowery Farming
   151 W 26TH Street, 12TH Floor
   New York, NY 10001
   United States of America

   Email: injongrhee@gmail.com


   Vidhi Goel
   Apple Inc.
   One Apple Park Way
   Cupertino, California 95014
   United States of America

   Email: vidhi_goel@apple.com


   Lars Eggert (editor)
   NetApp
   Stenbergintie 12 B
   FI-02700 Kauniainen
   Finland

   Email: lars@eggert.org
   URI:   https://eggert.org/





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