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Versions: (RFC 8312) 00 01

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


                 CUBIC for Fast Long-Distance Networks
                    draft-eggert-tcpm-rfc8312bis-01

Abstract

   CUBIC is an extension to the current TCP standards.  It differs from
   the current TCP standards only in the congestion control algorithm on
   the sender side.  In particular, it uses a cubic function instead of
   a linear window increase function of the current TCP standards to
   improve scalability and stability under fast and long-distance
   networks.  CUBIC and its predecessor algorithm have been adopted as
   defaults by Linux and have been used for many years.  This document
   provides a specification of CUBIC to enable third-party
   implementations and to solicit community feedback through
   experimentation on the performance of CUBIC.

   This documents obsoletes [RFC8312], updating the specification of
   CUBIC to conform to the current Linux version.

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.

Status of This Memo

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





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   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
   4.  CUBIC Congestion Control  . . . . . . . . . . . . . . . . . .   6
     4.1.  Definitions . . . . . . . . . . . . . . . . . . . . . . .   6
       4.1.1.  Constants of Interest . . . . . . . . . . . . . . . .   6
       4.1.2.  Variables of Interest . . . . . . . . . . . . . . . .   7
     4.2.  Window Increase Function  . . . . . . . . . . . . . . . .   8
     4.3.  TCP-Friendly Region . . . . . . . . . . . . . . . . . . .   9
     4.4.  Concave Region  . . . . . . . . . . . . . . . . . . . . .  11
     4.5.  Convex Region . . . . . . . . . . . . . . . . . . . . . .  11
     4.6.  Multiplicative Decrease . . . . . . . . . . . . . . . . .  12
     4.7.  Fast Convergence  . . . . . . . . . . . . . . . . . . . .  12
     4.8.  Timeout . . . . . . . . . . . . . . . . . . . . . . . . .  13
     4.9.  Spurious Congestion Events  . . . . . . . . . . . . . . .  13
     4.10. Slow Start  . . . . . . . . . . . . . . . . . . . . . . .  15
   5.  Discussion  . . . . . . . . . . . . . . . . . . . . . . . . .  15
     5.1.  Fairness to Standard TCP  . . . . . . . . . . . . . . . .  16
     5.2.  Using Spare Capacity  . . . . . . . . . . . . . . . . . .  18
     5.3.  Difficult Environments  . . . . . . . . . . . . . . . . .  19



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     5.4.  Investigating a Range of Environments . . . . . . . . . .  19
     5.5.  Protection against Congestion Collapse  . . . . . . . . .  19
     5.6.  Fairness within the Alternative Congestion Control
            Algorithm  . . . . . . . . . . . . . . . . . . . . . . .  19
     5.7.  Performance with Misbehaving Nodes and Outside
            Attackers  . . . . . . . . . . . . . . . . . . . . . . .  19
     5.8.  Behavior for Application-Limited Flows  . . . . . . . . .  19
     5.9.  Responses to Sudden or Transient Events . . . . . . . . .  20
     5.10. Incremental Deployment  . . . . . . . . . . . . . . . . .  20
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  20
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  20
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  20
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .  20
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  21
   Appendix A.  Acknowledgements . . . . . . . . . . . . . . . . . .  23
   Appendix B.  Evolution of CUBIC . . . . . . . . . . . . . . . . .  23
     B.1.  Since draft-eggert-tcpm-rfc8312bis-00 . . . . . . . . . .  23
     B.2.  Since RFC8312 . . . . . . . . . . . . . . . . . . . . . .  24
     B.3.  Since the Original Paper  . . . . . . . . . . . . . . . .  24
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  25

1.  Introduction

   The low utilization problem of TCP in fast long-distance networks is
   well documented in [K03] and [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, which we refer to
   collectively as "Standard TCP" below.

   CUBIC, originally proposed in [HRX08], is a modification to the
   congestion control algorithm of Standard TCP to remedy this problem.
   This document describes the most recent specification of CUBIC.
   Specifically, CUBIC uses a cubic function instead of a linear window
   increase function of Standard 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 has 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 Standard TCP in bandwidth usage than BIC-TCP



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   while maintaining the strengths of BIC-TCP such as stability, window
   scalability, and RTT fairness.  CUBIC has already replaced BIC-TCP as
   the default TCP congestion control algorithm in Linux and has been
   deployed globally by Linux.  Through extensive testing in various
   Internet scenarios, we believe that CUBIC is safe for testing and
   deployment in the global Internet.

   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:

   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 TCP-friendly, CUBIC is designed to behave like
      Standard TCP in networks with short RTTs and small bandwidth where
      Standard 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.

   Principle 1: 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 Standard 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) ACKs



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   [RFC3168], CUBIC registers the congestion window size where it got
   the congestion event as _W_(max)_ and performs a multiplicative
   decrease of congestion window.  After it 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 _W_(max)_ so that the concave window increase
   continues until the window size becomes _W_(max)_. 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 _W_(max)_ where
   network utilization is deemed highest.  Under steady state, most
   window size samples of CUBIC are close to _W_(max)_, thus promoting
   high network utilization and stability.  Note that those congestion
   control algorithms using only convex functions to increase the
   congestion window size have the maximum increments around _W_(max)_,
   and thus introduce a large number of packet bursts around the
   saturation point of the network, likely causing frequent global loss
   synchronizations.

   Principle 2: CUBIC promotes per-flow fairness to Standard TCP.  Note
   that Standard TCP performs well under short RTT and small bandwidth
   (or small BDP) networks.  There is only a scalability problem in
   networks with long RTTs and large bandwidth (or large BDP).  An
   alternative congestion control algorithm to Standard TCP designed to
   be friendly to Standard TCP on a per-flow basis must operate to
   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 increases its congestion window less
   aggressively than Standard TCP, CUBIC simply follows the window size
   of Standard TCP to ensure that CUBIC achieves at least the same
   throughput as Standard TCP in small BDP networks.  We call this
   region where CUBIC behaves like Standard TCP, the "TCP-friendly
   region".

   Principle 3: Two CUBIC flows with different RTTs have their
   throughput ratio 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 of the
   TCP-friendly region, and thus flows with different RTTs have similar
   congestion window sizes under steady state when they operate outside
   the TCP-friendly region.  This notion of a linear throughput ratio is



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   similar to that of Standard TCP under high statistical multiplexing
   environments where packet losses are independent of individual flow
   rates.  However, under low statistical multiplexing environments, the
   throughput ratio of Standard TCP flows with different RTTs is
   quadratically proportional to the inverse of their RTT ratio [XHR04].
   CUBIC always ensures the linear throughput ratio independent of the
   levels of statistical multiplexing.  This is an improvement over
   Standard TCP.  While there is no consensus on particular throughput
   ratios of different RTT flows, we believe that under wired Internet,
   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 Standard TCP under low statistical multiplexing
   environments).

   Principle 4: To balance between the scalability and convergence
   speed, CUBIC sets the multiplicative window decrease factor to 0.7
   while Standard 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 environments.  This
   design choice is following the observation that the author of
   HighSpeed TCP (HSTCP) [RFC3649] has made along with other researchers
   (e.g., [GV02]): the current Internet becomes more asynchronous with
   less frequent loss synchronizations with high statistical
   multiplexing.  Under this environment, 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 under the environments with sufficient statistical
   multiplexing, the convergence speed of CUBIC flows 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.

4.1.1.  Constants of Interest

   β__(cubic)_: CUBIC multiplication decrease factor as described in
   Section 4.6.






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   _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

   Variables required to implement CUBIC are described in this section.

   _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_ is reduced
   in the last congestion event.

   _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 starts.

   _cwnd_(start)_: The _cwnd_ at the beginning of the current congestion
   avoidance stage, i.e., at time _epoch_(start)_.

   W_(cubic)(_t_): Target value of 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
   TCP-friendly region, that is, an estimate for the congestion window
   using the AIMD approach similar to TCP-NewReno congestion controller.




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4.2.  Window Increase Function

   CUBIC maintains the acknowledgment (ACK) clocking of Standard TCP by
   increasing the congestion window only at the reception of an ACK.  It
   does not make any change to the fast recovery and retransmit of TCP,
   such as TCP-NewReno [RFC6582][RFC6675].  During congestion avoidance
   after a congestion event where a packet loss is detected by duplicate
   ACKs or a network congestion is detected by ACKs with ECN-Echo flags
   [RFC3168], CUBIC changes the window increase function of Standard
   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:

                                  ________________
                                 /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. _cwnd_(start)_ is calculated as
   described in Section 4.6 when a congestion event is detected,
   although implementations can further adjust _cwnd_(start)_ based on
   other fast recovery mechanisms.  In special cases, if _cwnd_(start)_
   is greater than _W_(max)_, _K_ is set to 0.





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   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 modes.

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

   2.  The concave region, if CUBIC is not in the TCP-friendly region
       and _cwnd_ is less than _W_(max)_.

   3.  The convex region, if CUBIC is not in the TCP-friendly region and
       _cwnd_ is greater than _W_(max)_.

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

4.3.  TCP-Friendly Region

   Standard TCP performs well in certain types of networks, for example,
   under short RTT and small bandwidth (or small BDP) networks.  In
   these networks, we use the TCP-friendly region to ensure that CUBIC
   achieves at least the same throughput as Standard TCP.










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   The TCP-friendly region is designed according to the analysis
   described in [FHP00].  The analysis studies the performance of an
   Additive Increase and Multiplicative Decrease (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 Standard 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

   which achieves the same average window size as Standard TCP.  When
   receiving an ACK in congestion avoidance (_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 TCP-friendly region and
   _cwnd_ SHOULD be set to _W_(est)_ at each reception of an ACK.

   _W_(est)_ is set equal to _cwnd_ at the start of the congestion
   avoidance stage.  After that, on every ACK, _W_(est)_ is updated
   using Figure 4.



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                                         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 size as standard TCP that uses AIMD.

4.4.  Concave Region

   When receiving an ACK in congestion avoidance, if CUBIC is not in the
   TCP-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
   TCP-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 been perturbed 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.  In this region, CUBIC is being
   very careful by very slowly increasing its window size.  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.






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4.6.  Multiplicative Decrease

   When a packet loss is detected by duplicate ACKs or a network
   congestion is detected by receiving packets marked with ECN-Echo
   (ECE), CUBIC updates its _W_(max)_ and reduces its _cwnd_ and
   _ssthresh_ immediately as below.  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 value.  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.  This adaptive adjustment of
   β__(cubic)_ is an item for the next version of CUBIC.

4.7.  Fast Convergence

   To improve the convergence speed of CUBIC, we add a heuristic in
   CUBIC.  When a new flow joins the network, existing flows in the
   network 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
   bandwidth of the network.  To speed up this bandwidth release by
   existing flows, the following mechanism called "fast convergence"
   SHOULD be implemented.

   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   , further reduce W
           |W    * ----------            max                  max
    W    = < max        2
     max   |
           |                  otherwise, remember cwnd before reduction
           \cwnd





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   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 the 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 have the plateau earlier.  This allows more time for the
   new flow to catch up to its congestion window size.

   The 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, the fast convergence SHOULD
   be disabled.

4.8.  Timeout

   In case of timeout, CUBIC follows Standard TCP to reduce _cwnd_
   [RFC5681], but sets _ssthresh_ using β__(cubic)_ (same as in
   Section 4.6) that is different from Standard TCP [RFC5681].

   During the first congestion avoidance 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.  In addition,
   for the tcp-friendliness region, _W_(est)_ should be set to the
   congestion window size at the beginning of the current congestion
   avoidance.

4.9.  Spurious Congestion Events

   For the case where CUBIC reduces its congestion window in response to
   detection of packet loss via duplicate ACKs or timeout, there is a
   possibility that the missing ACK would arrive after the congestion
   window reduction and the corresponding packet retransmission.  For
   example, packet reordering which is common in networks could trigger
   this behavior.  A high degree of packet reordering could cause
   multiple events of congestion window reduction 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.







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                       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
   to the original values ensures that CUBIC's performance is similar to
   what it would be if there were no spurious losses.

                                         \
            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 the _prior_cwnd_,
   CUBIC SHOULD continue to use the current and the most recent values
   of these variables.








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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
   standard TCP slow start [RFC5681] in general networks, or the limited
   slow start [RFC3742] or hybrid slow start [HR08] for fast and long-
   distance networks.

   In the case when CUBIC runs the 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.

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:

                                  ________________      ____
                                 /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 is reduced to:

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




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                                  Figure 6

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

5.1.  Fairness to Standard TCP

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

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

   +=============+=======+========+================+=========+========+
   | Loss Rate P |   TCP |  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: Standard TCP, HSTCP, and CUBIC with RTT = 0.1 seconds

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



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    +=============+=======+========+================+=========+=======+
    | Loss Rate P |   TCP |  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: Standard TCP, HSTCP, and CUBIC with RTT = 0.01 seconds

   Table 2 describes the response function of Standard 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 TCP than HSTCP, especially in networks with a short
   _RTT_ where TCP performs reasonably well.  For example, in a network
   with _RTT_ = 0.01 seconds and p=10^-6, TCP has an average window of
   1200 packets.  If the packet size is 1500 bytes, then 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 Standard TCP, whereas HSTCP
   is about ten times more aggressive than Standard 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 Standard 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 long-_RTT_ and high-bandwidth networks.  Based on these
   observations and our experiments, we find _C_=0.4 gives a good
   balance between TCP- 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:







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                                               ____
                                            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 Standard
   TCP under long-_RTT_ and high-bandwidth networks.

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

      +===================+===========+=========+=========+=========+
      | Throughput (Mbps) | Average W |   TCP 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 Standard TCP, HSTCP,
                 and CUBIC to achieve a certain throughput

   Table 3 describes the required packet loss rate for Standard 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 Standard TCP flows in the same
   bottleneck link without taking away much bandwidth from the existing
   flows.




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5.3.  Difficult Environments

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

5.4.  Investigating a Range of Environments

   CUBIC has been extensively studied by using both NS-2 simulation and
   test-bed experiments covering a wide range of network environments.
   More information can be found in [HKLRX06].

   Same as Standard 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 Standard TCP in fast and long-distance networks, it can
   fill large drop-tail buffers more quickly than Standard TCP and
   increase 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.

5.5.  Protection against Congestion Collapse

   With regard to the potential of causing congestion collapse, CUBIC
   behaves like Standard TCP since CUBIC modifies only the window
   adjustment algorithm of TCP.  Thus, it does not modify the ACK
   clocking and Timeout behaviors of Standard 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 independent of the level of statistical multiplexing in the
   link.

5.7.  Performance with Misbehaving Nodes and Outside Attackers

   This is not considered in the current CUBIC.

5.8.  Behavior for Application-Limited Flows

   CUBIC does not raise its congestion window size if the flow is
   currently limited by the application instead of the congestion
   window.  In case of long periods when _cwnd_ has not been updated due
   to the application rate 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.



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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 Standard TCP.

5.10.  Incremental Deployment

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

6.  Security Considerations

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

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/info/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/info/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/info/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/info/rfc5348>.





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   [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>.

   [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/info/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/info/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/info/rfc6675>.

   [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/info/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/info/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>.




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   [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>.

   [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/info/rfc3522>.

   [RFC3649]  Floyd, S., "HighSpeed TCP for Large Congestion Windows",
              RFC 3649, DOI 10.17487/RFC3649, December 2003,
              <https://www.rfc-editor.org/info/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/info/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/info/rfc3742>.

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






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   [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/info/rfc5682>.

   [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/info/rfc8312>.

   [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/info/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.  Acknowledgements

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

Appendix B.  Evolution of CUBIC

B.1.  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/5))






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   *  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/rfc8312bis11/issues/11))

   *  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.2.  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.3.  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.




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   *  [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 TCP friendly window was W_(tcp) while [RFC8312] used
      _W_(est)_.

Authors' Addresses

   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






Xu, et al.                Expires 6 August 2021                [Page 25]


Internet-Draft                    CUBIC                    February 2021


   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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