CUBIC for Fast Long-Distance Networks
draft-ietf-tcpm-cubic-06

Versions: (draft-zimmermann-tcpm-cubic) 00 01 02           Informational
          03 04 05 06                                                   
TCP Maintenance and Minor Extensions (TCPM) WG                   I. Rhee
Internet-Draft                                                      NCSU
Intended status: Informational                                     L. Xu
Expires: March 21, 2018                                              UNL
                                                                   S. Ha
                                                                Colorado
                                                           A. Zimmermann

                                                               L. Eggert
                                                                  NetApp
                                                        R. Scheffenegger
                                                      September 17, 2017


                 CUBIC for Fast Long-Distance Networks
                        draft-ietf-tcpm-cubic-06

Abstract

   CUBIC is an extension to the current TCP standards.  The protocol
   differs from the current TCP standards only in the congestion window
   adjustment function in 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 default by Linux and have been used for many years.
   This document provides a specification of CUBIC to enable third party
   implementation and to solicit the community feedback through
   experimentation on the performance of CUBIC.

Status of This Memo

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

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on March 21, 2018.





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Copyright Notice

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   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Conventions . . . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Design principle of CUBIC . . . . . . . . . . . . . . . . . .   4
   4.  CUBIC Congestion Control  . . . . . . . . . . . . . . . . . .   5
     4.1.  Window growth function  . . . . . . . . . . . . . . . . .   6
     4.2.  TCP-friendly region . . . . . . . . . . . . . . . . . . .   7
     4.3.  Concave region  . . . . . . . . . . . . . . . . . . . . .   7
     4.4.  Convex region . . . . . . . . . . . . . . . . . . . . . .   7
     4.5.  Multiplicative decrease . . . . . . . . . . . . . . . . .   8
     4.6.  Fast convergence  . . . . . . . . . . . . . . . . . . . .   8
     4.7.  Timeout . . . . . . . . . . . . . . . . . . . . . . . . .   9
     4.8.  Slowstart . . . . . . . . . . . . . . . . . . . . . . . .   9
   5.  Discussion  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     5.1.  Fairness to standard TCP  . . . . . . . . . . . . . . . .  10
     5.2.  Using Spare Capacity  . . . . . . . . . . . . . . . . . .  12
     5.3.  Difficult Environments  . . . . . . . . . . . . . . . . .  12
     5.4.  Investigating a Range of Environments . . . . . . . . . .  13
     5.5.  Protection against Congestion Collapse  . . . . . . . . .  13
     5.6.  Fairness within the Alternative Congestion Control
           Algorithm.  . . . . . . . . . . . . . . . . . . . . . . .  13
     5.7.  Performance with Misbehaving Nodes and Outside Attackers   13
     5.8.  Behavior for Application-Limited Flows  . . . . . . . . .  13
     5.9.  Responses to Sudden or Transient Events . . . . . . . . .  14
     5.10. Incremental Deployment  . . . . . . . . . . . . . . . . .  14
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  14
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  14
   8.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  14
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  14
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  14
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  15
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  16



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1.  Introduction

   The low utilization problem of TCP in fast long-distance networks is
   well documented in [K03][RFC3649].  This problem arises from a slow
   increase of congestion window following a congestion event in a
   network with a large bandwidth delay product (BDP).  Our experience
   [HKLRX06] indicates that this problem is frequently observed even in
   the range of congestion window sizes over several hundreds of packets
   (each packet is sized around 1000 bytes) especially under a network
   path with over 100ms round-trip times (RTTs).  This problem is
   equally applicable to all Reno style TCP standards and their
   variants, including TCP-RENO [RFC5681], TCP-NewReno
   [RFC6582][RFC6675], SCTP [RFC4960], TFRC [RFC5348] that use the same
   linear increase function for window growth, which we refer to
   collectively as Standard TCP below.

   CUBIC [HRX08] is a modification to the congestion control mechanism
   of Standard TCP, in particular, to the window increase function of
   Standard TCP senders, to remedy this problem.  Specifically, it uses
   a cubic function instead of a linear window increase function of the
   Standrad TCP to improve scalability and stability under fast and long
   distance networks.

   BIC-TCP, a predecessor of CUBIC, has been selected as default TCP
   congestion control algorithm by Linux in the year 2005 and been used
   for several years by the Internet community at large.  CUBIC uses a
   similar window growth function as BIC-TCP and is designed to be less
   aggressive and fairer to 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 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 ensuing sections, we first brefly explain the design principle
   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", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].







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3.  Design principle of CUBIC

   CUBIC [HRX08] uses a cubic window increase function in terms of the
   elapsed time from the last congestion event.  While most alternative
   algorithms to Standard TCP uses a convex increase function where
   during congestion avoidance the window increment is always
   increasing, CUBIC uses both the concave and convex profiles of a
   cubic function for window increase.  After a window reduction
   following a loss event detected by duplicate ACKs, it registers the
   window size where it got the loss event as W_max and performs a
   multiplicative decrease of congestion window and the regular fast
   recovery and retransmit of Standard TCP.  After it enters into
   congestion avoidance from fast recovery, it starts to increase the
   window using the concave profile of the cubic function.  The cubic
   function is set to have its plateau at W_max so the concave growth
   continues until the window size becomes W_max.  After that, the cubic
   function turns into a convex profile and the convex window growth
   begins.  This style of window adjustment (concave and then convex)
   improves protocol and network 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 and under steady state, most window
   size samples of CUBIC are close to W_max, thus promoting high network
   utilization and protocol stability.  Note that protocols with convex
   increase functions have the maximum increments around W_max and
   introduces a large number of packet bursts around the saturation
   point of the network, likely causing frequent global loss
   synchronizations.

   Another notable feature of CUBIC is that its window increase rate is
   mostly independent of RTT, and follows a (cubic) function of the
   elapsed time from the beginning of congestion avoidance.  This
   feature promotes per-flow fairness to Standard TCP as well as RTT-
   fairness.  Note that Standard TCP performs well under short RTT and
   small bandwidth (or small BDP) networks.  Only in a large long RTT
   and large bandwidth (or large BDP) networks, it has the scalability
   problem.  An alternative protocol to Standard TCP designed to be
   friendly to Standard TCP at a per-flow basis must operate to increase
   its window much less aggressively in small BDP networks than in large
   BDP networks.  In CUBIC, its window growth rate is slowest around the
   inflection point of the cubic function and this function does not
   depend on RTT.  In a smaller BDP network where Standard TCP flows are
   working well, the absolute amount of the window decrease at a loss
   event is always smaller because of the multiplicative decrease.
   Therefore, in CUBIC, the starting window size after a loss event from
   which the window starts to increase, is smaller in a smaller BDP
   network, thus falling nearer to the plateau of the cubic function
   where the growth rate is slowest.  By setting appropriate values of



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   the cubic function parameters, CUBIC sets its growth rate always no
   faster than Standard TCP around its inflection point.  When the cubic
   function grows slower than the window of Standard TCP, CUBIC simply
   follows the window size of Standard TCP to ensure fairness to
   Standard TCP in a small BDP network.  We call this region where CUBIC
   behaves like Standard TCP, the TCP-friendly region.

   CUBIC maintains the same window growth rate independent of RTTs
   outside of the TCP-friendly region, and flows with different RTTs
   have the similar window sizes under steady state when they operate
   outside the TCP-friendly region.  This ensures CUBIC flows with
   different RTTs to have their bandwidth shares (approximately, window/
   RTT) linearly proportional to the inverse of their RTT ratio (the
   longer RTT, the smaller the share).  This behavior is the same as
   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
   bandwidth share ratio of Standard TCP flows with different RTTs is
   squarely proportional to the inverse of their RTT ratio [XHR04].
   CUBIC always ensures the linear ratio independent of the levels of
   statistical multiplexing.  This is an improvement over Standard TCP.
   While there is no consensus on a particular bandwidth share ratios of
   different RTT flows, we believe that under wired Internet, use of the
   linear share notion seems more reasonable than equal share or a
   higher order shares.  HTCP [LS08] currently uses the equal share.

   CUBIC sets the multiplicative window decrease factor to 0.7 while
   Standard TCP uses 0.5.  While this improves the scalability of the
   protocol, 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 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 share of bandwidth independent of statistical
   multiplexing, thus achieving intra-protocol 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.






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4.1.  Window growth function

   CUBIC maintains the acknowledgment (ACK) clocking of Standard TCP by
   increasing congestion window only at the reception of ACK.  The
   protocol does not make any change to the fast recovery and retransmit
   of TCP, such as TCP-NewReno [RFC6582] [RFC6675].  During congestion
   avoidance after fast recovery, CUBIC changes the window update
   algorithm of Standard TCP.  Suppose that W_max is the window size
   before the window is reduced in the last fast retransmit and
   recovery.

   The window growth function of CUBIC uses the following function:

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

   where C is a constant fixed to determine the aggressiveness of window
   growth in high BDP networks, t is the elapsed time from the last
   window reduction that is measured right after the fast recovery in
   response to duplicate ACKs or after the congestion window reduction
   in response to ECN-Echo ACKs, and K is the time period that the above
   function takes to increase the current window size to W_max if there
   is no further loss event and is calculated by 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 packet loss detected by duplicate ACKs or a network
   congestion detected by ECN-Echo ACKs occurs, CUBIC reduces its
   current window 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.

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

   Depending on the value of the current 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 the 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.



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   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 the 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 (segment per RTT) and a
   multiplicative factor of beta_aimd, denoted by AIMD(alpha_aimd,
   beta_aimd).  Specifically, the average 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 the 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 the 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(t).  If so, CUBIC is in the TCP-friendly region and cwnd
   SHOULD be set to W_est(t) at each reception of 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 the protocol is not
   in the TCP-friendly region and cwnd is less than W_max, then the
   protocol 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 the current window size of CUBIC is larger than W_max, it passes
   the plateau of the cubic function after which CUBIC follows the
   convex profile of the cubic function.  Since cwnd is larger than the



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   previous saturation point W_max, this indicates that the network
   conditions might have been perturbed since the last loss 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 phase, 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 growth rate.  We also call this phase as 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 detected by duplicate ACKs or a network congestion
   detected by ECN-Echo ACKs occurs, CUBIC updates its W_max, cwnd, and
   ssthresh (slow start threshold) 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
      cwnd = cwnd * beta_cubic;     // window reduction

   A side effect of setting beta_cubic to a bigger value 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 the protocol 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 the
   protocol.  When a new flow joins the network, existing flows in the
   network need to give up their bandwidth shares to allow the flow some
   room for growth if the existing flows have been using all the
   bandwidth of the network.  To increase this release of bandwidth by
   existing flows, the following mechanism called fast convergence
   SHOULD be implemented.

   With fast convergence, when a loss event occurs, before a window
   reduction of congestion window, a flow remembers the last value of
   W_max before it updates W_max for the current loss event.  Let us
   call the last value of W_max to be W_last_max.







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      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 loss 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 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 its 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.

4.7.  Timeout

   In case of timeout, CUBIC follows the standard TCP to reduce cwnd,
   but sets ssthresh using beta_cubic (same as in Section 4.5).

4.8.  Slowstart

   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 high-bandwidth
   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
   K is set to 0 and W_max is set to the window size when CUBIC just
   exits the slow start.

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 lost events is always 1/p, CUBIC always operates with



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   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.

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 RTT, 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 size of standard TCP, HSTCP, and CUBIC.  The average
   window size of standard TCP and HSTCP is from [RFC3649].  The average
   window size of CUBIC is calculated by using Eq. 6 and CUBIC TCP
   friendly mode for three different values of C.



















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   +----------+-------+--------+-------------+-------------+-----------+
   |     Loss |   TCP |  HSTCP |       CUBIC |       CUBIC |     CUBIC |
   |   Rate P |       |        |    (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 |
   +----------+-------+--------+-------------+-------------+-----------+

   Response function of standard TCP, HSTCP, and CUBIC in networks with
   RTT = 0.1 seconds.  The average window size is in MSS-sized segments.

                                  Table 1

   +--------+-----------+-----------+------------+-----------+---------+
   |   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 |
   +--------+-----------+-----------+------------+-----------+---------+

   Response function of standard TCP, HSTCP, and CUBIC in networks with
       RTT = 0.01 seconds.  The average window size is in MSS-sized
                                 segments.

                                  Table 2

   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 protocols for the bandwidth.  CUBIC is more friendly to



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   the Standard TCP, if the value of C is lower.  However, we do not
   recommend to set 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 growth.  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.

5.2.  Using Spare Capacity

   CUBIC uses a more aggressive window growth function than Standard TCP
   under long RTT and high bandwidth networks.

   The following table shows that to achieve 10Gbps 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  |
      +------------------+-----------+---------+---------+---------+

      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.

                                  Table 3

   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 long-
   distance networks.




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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
   faster window growth 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[KWAF16].  In this case, proper
   queue sizing and management [RFC7567] could be used to reduce the
   packet queueing 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 bandwidth share.  When
   competing flows have different RTTs, their bandwidth shares are
   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.








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5.9.  Responses to Sudden or Transient Events

   In case that 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 does not require
   any assistant of routers.

6.  Security Considerations

   This proposal makes no changes to the underlying security of TCP.

7.  IANA Considerations

   There are no IANA considerations regarding this document.

8.  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.

9.  References

9.1.  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>.

   [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>.




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   [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>.

   [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>.

9.2.  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 , 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 , February 2006.



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   [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 , 2008.

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

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

   [KWAF16]   Khademi, N., Welzl, M., Armitage, G., and G. Fairhurst,
              "TCP Alternative Backoff with ECN (ABE)", Internet-draft,
              IETF work-in-progress draft-khademi-tcpm-
              alternativebackoff-ecn-01 , October 2016.

   [LS08]     Leith, D. and R. Shorten, "H-TCP: TCP Congestion Control
              for High Bandwidth-Delay Product Paths", Internet-draft
              draft-leith-tcp-htcp-06 , April 2008.

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

Authors' Addresses

   Injong Rhee
   North Carolina State University
   Department of Computer Science
   Raleigh, NC  27695-7534
   US

   Email: rhee@ncsu.edu


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

   Email: xu@unl.edu








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   Sangtae Ha
   University of Colorado at Boulder
   Department of Computer Science
   Boulder, CO  80309-0430
   US

   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

   Email: rscheff@gmx.at























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