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rfc:rfc8312

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.

Rhee, et al. Informational [Page 1] 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

Rhee, et al. Informational [Page 2] 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.

Rhee, et al. Informational [Page 3] 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.

Rhee, et al. Informational [Page 4] 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

Rhee, et al. Informational [Page 5] 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.

Rhee, et al. Informational [Page 6] 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

Rhee, et al. Informational [Page 7] 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

Rhee, et al. Informational [Page 8] RFC 8312 CUBIC February 2018

 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.

Rhee, et al. Informational [Page 9] RFC 8312 CUBIC February 2018

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.

Rhee, et al. Informational [Page 10] RFC 8312 CUBIC February 2018

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.

Rhee, et al. Informational [Page 11] 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.

Rhee, et al. Informational [Page 12] 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

Rhee, et al. Informational [Page 13] 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.

Rhee, et al. Informational [Page 14] 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

Rhee, et al. Informational [Page 18]

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