path: root/doc/rfc/rfc8312.txt

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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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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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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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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   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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   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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   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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   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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   +--------+-----------+-----------+------------+-----------+---------+
   |   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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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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   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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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>.






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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>.

   [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.




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   [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.


















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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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