    Internet Engineering Task Force (IETF)                           I. Rhee
    Request for Comments: 8312                                          NCSU
    Category: Informational                                            L. Xu
    ISSN: 2070-1721                                                      UNL
                                                                       S. Ha
                                                                    Colorado
                                                               A. Zimmermann

                                                                   L. Eggert
                                                            R. Scheffenegger
                                                                      NetApp
                                                               February 2018

                     CUBIC for Fast Long-Distance Networks

    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.

    Status of This Memo

       This document is not an Internet Standards Track specification; it is
       published for informational purposes.

       This document is a product of the Internet Engineering Task Force
       (IETF).  It represents the consensus of the IETF community.  It has
       received public review and has been approved for publication by the
       Internet Engineering Steering Group (IESG).  Not all documents
       approved by the IESG are a candidate for any level of Internet
       Standard; see Section 2 of RFC 7841.

       Information about the current status of this document, any errata,
       and how to provide feedback on it may be obtained at
       https://www.rfc-editor.org/info/rfc8312.

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    RFC 8312                          CUBIC                    February 2018

    Copyright Notice

       Copyright (c) 2018 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 .....................................................3
       3. Design Principles of CUBIC ......................................4
       4. CUBIC Congestion Control ........................................6
          4.1. Window Increase Function ...................................6
          4.2. TCP-Friendly Region ........................................7
          4.3. Concave Region .............................................8
          4.4. Convex Region ..............................................8
          4.5. Multiplicative Decrease ....................................8
          4.6. Fast Convergence ...........................................9
          4.7. Timeout ...................................................10
          4.8. Slow Start ................................................10
       5. Discussion .....................................................10
          5.1. Fairness to Standard TCP ..................................11
          5.2. Using Spare Capacity ......................................13
          5.3. Difficult Environments ....................................13
          5.4. Investigating a Range of Environments .....................13
          5.5. Protection against Congestion Collapse ....................14
          5.6. Fairness within the Alternative Congestion Control
               Algorithm .................................................14
          5.7. Performance with Misbehaving Nodes and Outside Attackers ..14
          5.8. Behavior for Application-Limited Flows ....................14
          5.9. Responses to Sudden or Transient Events ...................14
          5.10. Incremental Deployment ...................................14
       6. Security Considerations ........................................15
       7. IANA Considerations ............................................15
       8. References .....................................................15
          8.1. Normative References ......................................15
          8.2. Informative References ....................................16
       Acknowledgements ..................................................17
       Authors' Addresses ................................................18

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    RFC 8312                          CUBIC                    February 2018

    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
       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.

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    RFC 8312                          CUBIC                    February 2018

    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
       [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.

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    RFC 8312                          CUBIC                    February 2018

       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
       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

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    RFC 8312                          CUBIC                    February 2018

       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

       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.
       Let cwnd denote the congestion window size of a flow, and ssthresh
       denote the slow-start threshold.

    4.1.  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.  Suppose that W_max is the window size just before the window is
       reduced in the last congestion event.

       CUBIC uses the following window increase function:

           W_cubic(t) = C*(t-K)^3 + W_max (Eq. 1)

       where C is a constant fixed to determine the aggressiveness of window
       increase in high BDP networks, t is the elapsed time from the
       beginning of the current congestion avoidance, and K is the time
       period that the above function takes to increase the current window
       size to W_max if there are no further congestion events and is
       calculated using the following equation:

           K = cubic_root(W_max*(1-beta_cubic)/C) (Eq. 2)

       where beta_cubic is the CUBIC multiplication decrease factor, that
       is, when a congestion event is detected, CUBIC reduces its cwnd to
       W_cubic(0)=W_max*beta_cubic.  We discuss how we set beta_cubic in
       Section 4.5 and how we set C in Section 5.

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    RFC 8312                          CUBIC                    February 2018

       Upon receiving an ACK during congestion avoidance, CUBIC computes the
       window increase rate during the next RTT period using Eq. 1.  It sets
       W_cubic(t+RTT) as the candidate target value of the congestion
       window, where RTT is the weighted average RTT calculated by Standard
       TCP.

       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.

    4.2.  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.

       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 alpha_aimd (segments per RTT) and a
       multiplicative factor of beta_aimd, denoted by AIMD(alpha_aimd,
       beta_aimd).  Specifically, the average congestion window size of
       AIMD(alpha_aimd, beta_aimd) can be calculated using Eq. 3.  The
       analysis shows that AIMD(alpha_aimd, beta_aimd) with
       alpha_aimd=3*(1-beta_aimd)/(1+beta_aimd) achieves the same average
       window size as Standard TCP that uses AIMD(1, 0.5).

           AVG_W_aimd = [ alpha_aimd * (1+beta_aimd) /
                          (2*(1-beta_aimd)*p) ]^0.5 (Eq. 3)

       Based on the above analysis, CUBIC uses Eq. 4 to estimate the window
       size W_est of AIMD(alpha_aimd, beta_aimd) with
       alpha_aimd=3*(1-beta_cubic)/(1+beta_cubic) and beta_aimd=beta_cubic,
       which achieves the same average window size as Standard TCP.  When
       receiving an ACK in congestion avoidance (cwnd could be greater than

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    RFC 8312                          CUBIC                    February 2018

       or less than W_max), CUBIC checks whether W_cubic(t) is less than
       W_est(t).  If so, CUBIC is in the TCP-friendly region and cwnd SHOULD
       be set to W_est(t) at each reception of an ACK.

           W_est(t) = W_max*beta_cubic +
                       [3*(1-beta_cubic)/(1+beta_cubic)] * (t/RTT) (Eq. 4)

    4.3.  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
       (W_cubic(t+RTT) - cwnd)/cwnd for each received ACK, where
       W_cubic(t+RTT) is calculated using Eq. 1.

    4.4.  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
       (W_cubic(t+RTT) - cwnd)/cwnd for each received ACK, where
       W_cubic(t+RTT) is calculated using Eq. 1.

    4.5.  Multiplicative Decrease

       When a packet loss is detected by duplicate ACKs or a network
       congestion is detected by ECN-Echo ACKs, CUBIC updates its W_max,
       cwnd, and ssthresh as follows.  Parameter beta_cubic SHOULD be set to
       0.7.

          W_max = cwnd;                 // save window size before reduction
          ssthresh = cwnd * beta_cubic; // new slow-start threshold
          ssthresh = max(ssthresh, 2);  // threshold is at least 2 MSS
          cwnd = cwnd * beta_cubic;     // window reduction

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       A side effect of setting beta_cubic to a value bigger than 0.5 is
       slower convergence.  We believe that while a more adaptive setting of
       beta_cubic could result in faster convergence, it will make the
       analysis of CUBIC much harder.  This adaptive adjustment of
       beta_cubic is an item for the next version of CUBIC.

    4.6.  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, before the
       window reduction of the congestion window, a flow remembers the last
       value of W_max before it updates W_max for the current congestion
       event.  Let us call the last value of W_max to be W_last_max.

          if (W_max < W_last_max){ // should we make room for others
              W_last_max = W_max;             // remember the last W_max
              W_max = W_max*(1.0+beta_cubic)/2.0; // further reduce W_max
          } else {
              W_last_max = W_max              // remember the last W_max
          }

       At a congestion event, if the current value of W_max is less than
       W_last_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.

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    4.7.  Timeout

       In case of timeout, CUBIC follows Standard TCP to reduce cwnd
       [RFC5681], but sets ssthresh using beta_cubic (same as in
       Section 4.5) that is different from Standard TCP [RFC5681].

       During the first congestion avoidance after a timeout, CUBIC
       increases its congestion window size using Eq. 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.

    4.8.  Slow Start

       CUBIC MUST employ a slow-start algorithm, when the 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 Eq. 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:

           AVG_W_cubic = [C*(3+beta_cubic)/(4*(1-beta_cubic))]^0.25 *
                           (RTT^0.75) / (p^0.75) (Eq. 5)

       With beta_cubic set to 0.7, the above formula is reduced to:

           AVG_W_cubic = (C*3.7/1.2)^0.25 * (RTT^0.75) / (p^0.75) (Eq. 6)

       We will determine the value of C in the following subsection using
       Eq. 6.

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    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 Eq. 6 and the CUBIC
       TCP-friendly region for three different values of C.

       +--------+----------+-----------+------------+-----------+----------+
       |   Loss |  Average |   Average |      CUBIC |     CUBIC |    CUBIC |
       | Rate P |    TCP W |   HSTCP W |   (C=0.04) |   (C=0.4) |    (C=4) |
       +--------+----------+-----------+------------+-----------+----------+
       |  10^-2 |       12 |        12 |         12 |        12 |       12 |
       |  10^-3 |       38 |        38 |         38 |        38 |       59 |
       |  10^-4 |      120 |       263 |        120 |       187 |      333 |
       |  10^-5 |      379 |      1795 |        593 |      1054 |     1874 |
       |  10^-6 |     1200 |     12279 |       3332 |      5926 |    10538 |
       |  10^-7 |     3795 |     83981 |      18740 |     33325 |    59261 |
       |  10^-8 |    12000 |    574356 |     105383 |    187400 |   333250 |
       +--------+----------+-----------+------------+-----------+----------+

                                      Table 1

       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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    RFC 8312                          CUBIC                    February 2018

       +--------+-----------+-----------+------------+-----------+---------+
       |   Loss |   Average |   Average |      CUBIC |     CUBIC |   CUBIC |
       | Rate P |     TCP W |   HSTCP W |   (C=0.04) |   (C=0.4) |   (C=4) |
       +--------+-----------+-----------+------------+-----------+---------+
       |  10^-2 |        12 |        12 |         12 |        12 |      12 |
       |  10^-3 |        38 |        38 |         38 |        38 |      38 |
       |  10^-4 |       120 |       263 |        120 |       120 |     120 |
       |  10^-5 |       379 |      1795 |        379 |       379 |     379 |
       |  10^-6 |      1200 |     12279 |       1200 |      1200 |    1874 |
       |  10^-7 |      3795 |     83981 |       3795 |      5926 |   10538 |
       |  10^-8 |     12000 |    574356 |      18740 |     33325 |   59261 |
       +--------+-----------+-----------+------------+-----------+---------+

                                      Table 2

       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, Eq. 6 is reduced to:

          AVG_W_cubic = 1.054 * (RTT^0.75) / (p^0.75) (Eq. 7)

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

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    RFC 8312                          CUBIC                    February 2018

    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

       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.

    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

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    RFC 8312                          CUBIC                    February 2018

       increase the risk of a standing queue [KWAF17].  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 RTTs, 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 Eq. 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 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.

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    RFC 8312                          CUBIC                    February 2018

    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>.

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

       [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>.

       [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>.

    Rhee, et al.                  Informational                    [Page 15]

    RFC 8312                          CUBIC                    February 2018

       [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>.

       [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", In Proceedings of IEEE INFOCOM,
                  DOI 10.1109/INFCOM.2007.111, May 2007.

       [FHP00]    Floyd, S., Handley, M., and J. Padhye, "A Comparison of
                  Equation-Based and AIMD Congestion Control", May 2000.

       [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, August 2002.

       [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.

       [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.

    Rhee, et al.                  Informational                    [Page 16]

    RFC 8312                          CUBIC                    February 2018

       [HRX08]    Ha, S., Rhee, I., and L. Xu, "CUBIC: A New TCP-Friendly
                  High-Speed TCP Variant", ACM SIGOPS Operating System
                  Review, DOI 10.1145/1400097.1400105, July 2008.

       [K03]      Kelly, T., "Scalable TCP: Improving Performance in
                  HighSpeed Wide Area Networks", ACM SIGCOMM
                  Computer Communication Review, DOI 10.1145/956981.956989,
                  April 2003.

       [KWAF17]   Khademi, N., Welzl, M., Armitage, G., and G. Fairhurst,
                  "TCP Alternative Backoff with ECN (ABE)", Work in
                  Progress, draft-ietf-tcpm-alternativebackoff-ecn-05,
                  December 2017.

       [XHR04]    Xu, L., Harfoush, K., and I. Rhee, "Binary Increase
                  Congestion Control for Fast, Long Distance Networks", In
                  Proceedings of IEEE INFOCOM,
                  DOI 10.1109/INFCOM.2004.1354672, March 2004.

    Acknowledgements

       Alexander Zimmermann and Lars Eggert have received funding from the
       European Union's Horizon 2020 research and innovation program
       2014-2018 under grant agreement No. 644866 (SSICLOPS).  This document
       reflects only the authors' views and the European Commission is not
       responsible for any use that may be made of the information it
       contains.

       The work of Lisong Xu was partially supported by the National Science
       Foundation (NSF) under Grant No. 1526253.  Any opinions, findings,
       and conclusions or recommendations expressed in this material are
       those of the authors and do not necessarily reflect the views of the
       NSF.

    Rhee, et al.                  Informational                    [Page 17]

    RFC 8312                          CUBIC                    February 2018

    Authors' Addresses

       Injong Rhee
       North Carolina State University
       Department of Computer Science
       Raleigh, NC  27695-7534
       United States of America
       Email: rhee@ncsu.edu

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

       Email: xu@unl.edu

       Sangtae Ha
       University of Colorado at Boulder
       Department of Computer Science
       Boulder, CO  80309-0430
       United States of America
       Email: sangtae.ha@colorado.edu

       Alexander Zimmermann
       Phone: +49 175 5766838
       Email: alexander.zimmermann@rwth-aachen.de

       Lars Eggert
       NetApp
       Sonnenallee 1
       Kirchheim  85551
       Germany
       Phone: +49 151 12055791
       Email: lars@netapp.com

       Richard Scheffenegger
       NetApp
       Am Europlatz 2
       Vienna  1120
       Austria
       Email: rs.ietf@gmx.at

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