rfc9438.original   rfc9438.txt 
TCPM L. Xu Internet Engineering Task Force (IETF) L. Xu
Internet-Draft UNL Request for Comments: 9438 UNL
Obsoletes: 8312 (if approved) S. Ha Obsoletes: 8312 S. Ha
Updates: 5681 (if approved) Colorado Updates: 5681 Colorado
Intended status: Standards Track I. Rhee Category: Standards Track I. Rhee
Expires: 4 August 2023 Bowery ISSN: 2070-1721 Bowery
V. Goel V. Goel
Apple Inc. Apple Inc.
L. Eggert, Ed. L. Eggert, Ed.
NetApp NetApp
31 January 2023 August 2023
CUBIC for Fast and Long-Distance Networks CUBIC for Fast and Long-Distance Networks
draft-ietf-tcpm-rfc8312bis-15
Abstract Abstract
CUBIC is a standard TCP congestion control algorithm that uses a CUBIC is a standard TCP congestion control algorithm that uses a
cubic function instead of a linear congestion window increase cubic function instead of a linear congestion window increase
function to improve scalability and stability over fast and long- function to improve scalability and stability over fast and long-
distance networks. CUBIC has been adopted as the default TCP distance networks. CUBIC has been adopted as the default TCP
congestion control algorithm by the Linux, Windows, and Apple stacks. congestion control algorithm by the Linux, Windows, and Apple stacks.
This document updates the specification of CUBIC to include This document updates the specification of CUBIC to include
algorithmic improvements based on these implementations and recent algorithmic improvements based on these implementations and recent
academic work. Based on the extensive deployment experience with academic work. Based on the extensive deployment experience with
CUBIC, it also moves the specification to the Standards Track, CUBIC, this document also moves the specification to the Standards
obsoleting RFC 8312. This also requires updating RFC 5681, to allow Track and obsoletes RFC 8312. This document also updates RFC 5681,
for CUBIC's occasionally more aggressive sending behavior. to allow for CUBIC's occasionally more aggressive sending behavior.
About This Document
This note is to be removed before publishing as an RFC.
Status information for this document may be found at
https://datatracker.ietf.org/doc/draft-ietf-tcpm-rfc8312bis/.
Discussion of this document takes place on the TCPM Working Group
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Source for this draft and an issue tracker can be found at
https://github.com/NTAP/rfc8312bis.
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Table of Contents Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4 1. Introduction
2. Conventions . . . . . . . . . . . . . . . . . . . . . . . . . 6 2. Conventions
3. Design Principles of CUBIC . . . . . . . . . . . . . . . . . 6 3. Design Principles of CUBIC
3.1. Principle 1 for the CUBIC Increase Function . . . . . . . 7 3.1. Principle 1 for the CUBIC Increase Function
3.2. Principle 2 for Reno-Friendliness . . . . . . . . . . . . 7 3.2. Principle 2 for Reno-Friendliness
3.3. Principle 3 for RTT Fairness . . . . . . . . . . . . . . 8 3.3. Principle 3 for RTT-Fairness
3.4. Principle 4 for the CUBIC Decrease Factor . . . . . . . . 8 3.4. Principle 4 for the CUBIC Decrease Factor
4. CUBIC Congestion Control . . . . . . . . . . . . . . . . . . 9 4. CUBIC Congestion Control
4.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 9 4.1. Definitions
4.1.1. Constants of Interest . . . . . . . . . . . . . . . . 9 4.1.1. Constants of Interest
4.1.2. Variables of Interest . . . . . . . . . . . . . . . . 10 4.1.2. Variables of Interest
4.2. Window Increase Function . . . . . . . . . . . . . . . . 11 4.2. Window Increase Function
4.3. Reno-Friendly Region . . . . . . . . . . . . . . . . . . 12 4.3. Reno-Friendly Region
4.4. Concave Region . . . . . . . . . . . . . . . . . . . . . 14 4.4. Concave Region
4.5. Convex Region . . . . . . . . . . . . . . . . . . . . . . 14 4.5. Convex Region
4.6. Multiplicative Decrease . . . . . . . . . . . . . . . . . 15 4.6. Multiplicative Decrease
4.7. Fast Convergence . . . . . . . . . . . . . . . . . . . . 16 4.7. Fast Convergence
4.8. Timeout . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.8. Timeout
4.9. Spurious Congestion Events . . . . . . . . . . . . . . . 17 4.9. Spurious Congestion Events
4.9.1. Spurious timeout . . . . . . . . . . . . . . . . . . 18 4.9.1. Spurious Timeouts
4.9.2. Spurious loss detected by acknowledgments . . . . . . 18 4.9.2. Spurious Fast Retransmits
4.10. Slow Start . . . . . . . . . . . . . . . . . . . . . . . 19 4.10. Slow Start
5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 20 5. Discussion
5.1. Fairness to Reno . . . . . . . . . . . . . . . . . . . . 21 5.1. Fairness to Reno
5.2. Using Spare Capacity . . . . . . . . . . . . . . . . . . 23 5.2. Using Spare Capacity
5.3. Difficult Environments . . . . . . . . . . . . . . . . . 24 5.3. Difficult Environments
5.4. Investigating a Range of Environments . . . . . . . . . . 24 5.4. Investigating a Range of Environments
5.5. Protection against Congestion Collapse . . . . . . . . . 24 5.5. Protection against Congestion Collapse
5.6. Fairness within the Alternative Congestion Control 5.6. Fairness within the Alternative Congestion Control
Algorithm . . . . . . . . . . . . . . . . . . . . . . . 25 Algorithm
5.7. Performance with Misbehaving Nodes and Outside 5.7. Performance with Misbehaving Nodes and Outside Attackers
Attackers . . . . . . . . . . . . . . . . . . . . . . . 25 5.8. Behavior for Application-Limited Flows
5.8. Behavior for Application-Limited Flows . . . . . . . . . 25 5.9. Responses to Sudden or Transient Events
5.9. Responses to Sudden or Transient Events . . . . . . . . . 25 5.10. Incremental Deployment
5.10. Incremental Deployment . . . . . . . . . . . . . . . . . 26 6. Security Considerations
6. Security Considerations . . . . . . . . . . . . . . . . . . . 26 7. IANA Considerations
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 26 8. References
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.1. Normative References
8.1. Normative References . . . . . . . . . . . . . . . . . . 26 8.2. Informative References
8.2. Informative References . . . . . . . . . . . . . . . . . 28 Appendix A. Evolution of CUBIC since the Original Paper
Appendix A. Acknowledgments . . . . . . . . . . . . . . . . . . 31 Appendix B. Proof of the Average CUBIC Window Size
Appendix B. Evolution of CUBIC . . . . . . . . . . . . . . . . . 32 Acknowledgments
B.1. Since draft-ietf-tcpm-rfc8312bis-14 . . . . . . . . . . . 32 Authors' Addresses
B.2. Since draft-ietf-tcpm-rfc8312bis-13 . . . . . . . . . . . 32
B.3. Since draft-ietf-tcpm-rfc8312bis-12 . . . . . . . . . . . 32
B.4. Since draft-ietf-tcpm-rfc8312bis-11 . . . . . . . . . . . 32
B.5. Since draft-ietf-tcpm-rfc8312bis-10 . . . . . . . . . . . 32
B.6. Since draft-ietf-tcpm-rfc8312bis-09 . . . . . . . . . . . 32
B.7. Since draft-ietf-tcpm-rfc8312bis-08 . . . . . . . . . . . 32
B.8. Since draft-ietf-tcpm-rfc8312bis-07 . . . . . . . . . . . 33
B.9. Since draft-ietf-tcpm-rfc8312bis-06 . . . . . . . . . . . 33
B.10. Since draft-ietf-tcpm-rfc8312bis-05 . . . . . . . . . . . 33
B.11. Since draft-ietf-tcpm-rfc8312bis-04 . . . . . . . . . . . 33
B.12. Since draft-ietf-tcpm-rfc8312bis-03 . . . . . . . . . . . 34
B.13. Since draft-ietf-tcpm-rfc8312bis-02 . . . . . . . . . . . 34
B.14. Since draft-ietf-tcpm-rfc8312bis-01 . . . . . . . . . . . 35
B.15. Since draft-ietf-tcpm-rfc8312bis-00 . . . . . . . . . . . 35
B.16. Since draft-eggert-tcpm-rfc8312bis-03 . . . . . . . . . . 35
B.17. Since draft-eggert-tcpm-rfc8312bis-02 . . . . . . . . . . 35
B.18. Since draft-eggert-tcpm-rfc8312bis-01 . . . . . . . . . . 35
B.19. Since draft-eggert-tcpm-rfc8312bis-00 . . . . . . . . . . 36
B.20. Since RFC8312 . . . . . . . . . . . . . . . . . . . . . . 36
B.21. Since the Original Paper . . . . . . . . . . . . . . . . 37
Appendix C. Proof of the Average CUBIC Window Size . . . . . . . 37
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 40
1. Introduction 1. Introduction
CUBIC has been adopted as the default TCP congestion control CUBIC has been adopted as the default TCP congestion control
algorithm in the Linux, Windows, and Apple stacks, and has been used algorithm in the Linux, Windows, and Apple stacks, and has been used
and deployed globally. Extensive, decade-long deployment experience and deployed globally. Extensive, decade-long deployment experience
in vastly different Internet scenarios has convincingly demonstrated in vastly different Internet scenarios has convincingly demonstrated
that CUBIC is safe for deployment on the global Internet and delivers that CUBIC is safe for deployment on the global Internet and delivers
substantial benefits over classical Reno congestion control substantial benefits over classical Reno congestion control
[RFC5681]. It is therefore to be regarded as the currently most [RFC5681]. It is therefore to be regarded as the currently most
widely deployed standard for TCP congestion control. CUBIC can also widely deployed standard for TCP congestion control. CUBIC can also
be used for other transport protocols such as QUIC [RFC9000] and SCTP be used for other transport protocols such as QUIC [RFC9000] and the
[RFC9260] as a default congestion controller. Stream Control Transmission Protocol (SCTP) [RFC9260] as a default
congestion controller.
The design of CUBIC was motivated by the well-documented problem The design of CUBIC was motivated by the well-documented problem
classical Reno TCP has with low utilization over fast and long- classical Reno TCP has with low utilization over fast and long-
distance networks [K03][RFC3649]. This problem arises from a slow distance networks [K03] [RFC3649]. This problem arises from a slow
increase of the congestion window following a congestion event in a increase of the congestion window (cwnd) following a congestion event
network with a large bandwidth-delay product (BDP). [HLRX07] in a network with a large bandwidth-delay product (BDP). [HLRX07]
indicates that this problem is frequently observed even in the range indicates that this problem is frequently observed even in the range
of congestion window sizes over several hundreds of packets. This of congestion window sizes over several hundreds of packets. This
problem is equally applicable to all Reno-style standards and their problem is equally applicable to all Reno-style standards and their
variants, including TCP-Reno [RFC5681], TCP-NewReno variants, including TCP-Reno [RFC5681], TCP-NewReno [RFC6582]
[RFC6582][RFC6675], SCTP [RFC9260], TFRC [RFC5348], and QUIC [RFC6675], SCTP [RFC9260], TCP Friendly Rate Control (TFRC)
congestion control [RFC9002], which use the same linear increase [RFC5348], and QUIC congestion control [RFC9002], which use the same
function for window growth. All Reno-style standards and their linear increase function for window growth. All Reno-style standards
variants are collectively referred to as "Reno" in this document. and their variants are collectively referred to as "Reno" in this
document.
CUBIC, originally proposed in [HRX08], is a modification to the CUBIC, originally proposed in [HRX08], is a modification to the
congestion control algorithm of classical Reno to remedy this congestion control algorithm of classical Reno to remedy this
problem. Specifically, CUBIC uses a cubic function instead of the problem. Specifically, CUBIC uses a cubic function instead of the
linear window increase function of Reno to improve scalability and linear window increase function of Reno to improve scalability and
stability under fast and long-distance networks. stability under fast and long-distance networks.
This document updates the specification of CUBIC to include This document updates the specification of CUBIC to include
algorithmic improvements based on the Linux, Windows, and Apple algorithmic improvements based on the Linux, Windows, and Apple
implementations and recent academic work. Based on the extensive implementations and recent academic work. Based on the extensive
deployment experience with CUBIC, it also moves the specification to deployment experience with CUBIC, it also moves the specification to
the Standards Track, obsoleting [RFC8312]. This requires an update the Standards Track, obsoleting [RFC8312]. This requires an update
to Section 3 of [RFC5681], which limits the aggressiveness of Reno to Section 3 of [RFC5681], which limits the aggressiveness of Reno
TCP implementations. Since CUBIC is occasionally more aggressive TCP implementations. Since CUBIC is occasionally more aggressive
than the [RFC5681] algorithms, this document updates the first than the algorithms defined in [RFC5681], this document updates the
paragraph of Section 3 of [RFC5681], replacing it with a normative first paragraph of Section 3 of [RFC5681], replacing it with a
reference to guideline (1) in Section 3 of [RFC5033], which allows normative reference to guideline (1) in Section 3 of [RFC5033], which
for CUBIC's behavior as defined in this document. allows for CUBIC's behavior as defined in this document.
Specifically, CUBIC may increase the congestion window more Specifically, CUBIC may increase the congestion window more
aggressively than Reno during the congestion avoidance phase. aggressively than Reno during the congestion avoidance phase.
According to [RFC5681], during congestion avoidance, the sender must According to [RFC5681], during congestion avoidance, the sender must
not increment cwnd by more than SMSS bytes once per RTT, whereas not increment cwnd by more than Sender Maximum Segment Size (SMSS)
CUBIC may increase cwnd much more aggressively. Additionally, CUBIC bytes once per round-trip time (RTT), whereas CUBIC may increase cwnd
recommends the HyStart++ algorithm [I-D.ietf-tcpm-hystartplusplus] much more aggressively. Additionally, CUBIC recommends the HyStart++
for slow start, which allows for cwnd increases of more than SMSS algorithm [RFC9406] for slow start, which allows for cwnd increases
bytes for incoming acknowledgments during slow start, while this of more than SMSS bytes for incoming acknowledgments during slow
behavior is not allowed as part of [RFC5681] standard. start, while this behavior is not allowed as part of the standard
behavior prescribed by [RFC5681].
Binary Increase Congestion Control (BIC-TCP) [XHR04], a predecessor Binary Increase Congestion Control (BIC-TCP) [XHR04], a predecessor
of CUBIC, was selected as the default TCP congestion control of CUBIC, was selected as the default TCP congestion control
algorithm by Linux in the year 2005 and had been used for several algorithm by Linux in the year 2005 and had been used for several
years by the Internet community at large. years by the Internet community at large.
CUBIC uses a similar window increase function as BIC-TCP and is CUBIC uses a window increase function similar to BIC-TCP and is
designed to be less aggressive and fairer to Reno in bandwidth usage designed to be less aggressive and fairer to Reno in bandwidth usage
than BIC-TCP while maintaining the strengths of BIC-TCP such as than BIC-TCP while maintaining the strengths of BIC-TCP such as
stability, window scalability, and round-trip time (RTT) fairness. stability, window scalability, and RTT-fairness.
[RFC5033] documents the IETF's best current practices for specifying [RFC5033] documents the IETF's best current practices for specifying
new congestion control algorithms, specifically, ones that differ new congestion control algorithms, specifically those that differ
from the general congestion control principles outlined in [RFC2914]. from the general congestion control principles outlined in [RFC2914].
It describes what type of evaluation is expected by the IETF to It describes what type of evaluation is expected by the IETF to
understand the suitability of a new congestion control algorithm and understand the suitability of a new congestion control algorithm and
the process to enable a specification to be approved for widespread the process of enabling a specification to be approved for widespread
deployment in the global Internet. deployment in the global Internet.
There are areas in which CUBIC differs from the congestion control There are areas in which CUBIC differs from the congestion control
algorithms previously published in standards-track RFCs; those algorithms previously published in Standards Track RFCs; those
changes are specified in this document. However, it is not obvious changes are specified in this document. However, it is not obvious
that these changes go beyond the general congestion control that these changes go beyond the general congestion control
principles outlined in [RFC2914], so the process in [RFC5033] may not principles outlined in [RFC2914], so the process documented in
apply. [RFC5033] may not apply.
Also, the wide deployment of CUBIC on the Internet was driven by Also, the wide deployment of CUBIC on the Internet was driven by
direct adoption in most of the popular operating systems, and did not direct adoption in most of the popular operating systems and did not
follow the practices documented in [RFC5033]. However, due to the follow the practices documented in [RFC5033]. However, due to the
resulting Internet-scale deployment experience over a long period of resulting Internet-scale deployment experience over a long period of
time, the IETF has determined that CUBIC may be published as a time, the IETF determined that CUBIC could be published as a
standards-track specification. This decision by the IETF does not Standards Track specification. This decision by the IETF does not
alter the general guidance in [RFC2914]. alter the general guidance provided in [RFC2914].
The following sections first briefly explain the design principles of The following sections
CUBIC, provide the exact specification of CUBIC, and finally discuss
the safety features of CUBIC following the guidelines specified in 1. briefly explain the design principles of CUBIC,
[RFC5033].
2. provide the exact specification of CUBIC, and
3. discuss the safety features of CUBIC, following the guidelines
specified in [RFC5033].
2. Conventions 2. Conventions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in "OPTIONAL" in this document are to be interpreted as described in
BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here. capitals, as shown here.
3. Design Principles of CUBIC 3. Design Principles of CUBIC
skipping to change at page 6, line 43 skipping to change at line 231
convex function. convex function.
Principle 2: To be Reno-friendly, CUBIC is designed to behave like Principle 2: To be Reno-friendly, CUBIC is designed to behave like
Reno in networks with short RTTs and small bandwidth where Reno Reno in networks with short RTTs and small bandwidth where Reno
performs well. performs well.
Principle 3: For RTT-fairness, CUBIC is designed to achieve linear Principle 3: For RTT-fairness, CUBIC is designed to achieve linear
bandwidth sharing among flows with different RTTs. bandwidth sharing among flows with different RTTs.
Principle 4: CUBIC appropriately sets its multiplicative window Principle 4: CUBIC appropriately sets its multiplicative window
decrease factor in order to balance between the scalability and decrease factor in order to achieve a balance between scalability
convergence speed. and convergence speed.
3.1. Principle 1 for the CUBIC Increase Function 3.1. Principle 1 for the CUBIC Increase Function
For better network utilization and stability, CUBIC [HRX08] uses a For better network utilization and stability, CUBIC [HRX08] uses a
cubic window increase function in terms of the elapsed time from the cubic window increase function in terms of the elapsed time from the
last congestion event. While most alternative congestion control last congestion event. While most congestion control algorithms that
algorithms to Reno increase the congestion window using convex provide alternatives to Reno increase the congestion window using
functions, CUBIC uses both the concave and convex profiles of a cubic convex functions, CUBIC uses both the concave and convex profiles of
function for window growth. a cubic function for window growth.
After a window reduction in response to a congestion event detected After a window reduction in response to a congestion event detected
by duplicate ACKs, Explicit Congestion Notification-Echo (ECN-Echo, by duplicate acknowledgments (ACKs), Explicit Congestion
ECE) ACKs [RFC3168], TCP RACK [RFC8985] or QUIC loss detection Notification-Echo (ECN-Echo (ECE)) ACKs [RFC3168], RACK-TLP for TCP
[RFC9002], CUBIC remembers the congestion window size at which it [RFC8985], or QUIC loss detection [RFC9002], CUBIC remembers the
received the congestion event and performs a multiplicative decrease congestion window size at which it received the congestion event and
of the congestion window. When CUBIC enters into congestion performs a multiplicative decrease of the congestion window. When
avoidance, it starts to increase the congestion window using the CUBIC enters into congestion avoidance, it starts to increase the
concave profile of the cubic function. The cubic function is set to congestion window using the concave profile of the cubic function.
have its plateau at the remembered congestion window size, so that The cubic function is set to have its plateau at the remembered
the concave window increase continues until then. After that, the congestion window size, so that the concave window increase continues
cubic function turns into a convex profile and the convex window until then. After that, the cubic function turns into a convex
increase begins. profile and the convex window increase begins.
This style of window adjustment (concave and then convex) improves This style of window adjustment (concave and then convex) improves
the algorithm stability while maintaining high network utilization algorithm stability while maintaining high network utilization
[CEHRX09]. This is because the window size remains almost constant, [CEHRX09]. This is because the window size remains almost constant,
forming a plateau around the remembered congestion window size of the forming a plateau around the remembered congestion window size of the
last congestion event, where network utilization is deemed highest. last congestion event, where network utilization is deemed highest.
Under steady state, most window size samples of CUBIC are close to Under steady state, most window size samples of CUBIC are close to
that remembered congestion window size, thus promoting high network that remembered congestion window size, thus promoting high network
utilization and stability. utilization and stability.
Note that congestion control algorithms that only use convex Note that congestion control algorithms that only use convex
functions to increase the congestion window size have their maximum functions to increase the congestion window size have their maximum
increments around the remembered congestion window size of the last increments around the remembered congestion window size of the last
congestion event, and thus introduce many packet bursts around the congestion event and thus introduce many packet bursts around the
saturation point of the network, likely causing frequent global loss saturation point of the network, likely causing frequent global loss
synchronizations. synchronizations.
3.2. Principle 2 for Reno-Friendliness 3.2. Principle 2 for Reno-Friendliness
CUBIC promotes per-flow fairness to Reno. Note that Reno performs CUBIC promotes per-flow fairness to Reno. Note that Reno performs
well over paths with small bandwidth-delay products, and only well over paths with small BDPs and only experiences problems when
experiences problems when attempting to increase bandwidth attempting to increase bandwidth utilization on paths with large
utilization on paths with large bandwidth-delay products. BDPs.
A congestion control algorithm designed to be friendly to Reno on a A congestion control algorithm designed to be friendly to Reno on a
per-flow basis must increase its congestion window less aggressively per-flow basis must increase its congestion window less aggressively
in small-BDP networks than in large-BDP networks. in small-BDP networks than in large-BDP networks.
The aggressiveness of CUBIC mainly depends on the maximum window size The aggressiveness of CUBIC mainly depends on the maximum window size
before a window reduction, which is smaller in small-BDP networks before a window reduction, which is smaller in small-BDP networks
than in large-BDP networks. Thus, CUBIC increases its congestion than in large-BDP networks. Thus, CUBIC increases its congestion
window less aggressively in small-BDP networks than in large-BDP window less aggressively in small-BDP networks than in large-BDP
networks. networks.
Furthermore, in cases when the cubic function of CUBIC would increase Furthermore, in cases when the cubic function of CUBIC would increase
the congestion window less aggressively than Reno, CUBIC simply the congestion window less aggressively than Reno, CUBIC simply
follows the window size of Reno to ensure that CUBIC achieves at follows the window size of Reno to ensure that CUBIC achieves at
least the same throughput as Reno in small-BDP networks. The region least the same throughput as Reno in small-BDP networks. The region
where CUBIC behaves like Reno is called the "Reno-friendly region". where CUBIC behaves like Reno is called the "Reno-friendly region".
3.3. Principle 3 for RTT Fairness 3.3. Principle 3 for RTT-Fairness
Two CUBIC flows with different RTTs have a throughput ratio that is Two CUBIC flows with different RTTs have a throughput ratio that is
linearly proportional to the inverse of their RTT ratio, where the linearly proportional to the inverse of their RTT ratio, where the
throughput of a flow is approximately the size of its congestion throughput of a flow is approximately the size of its congestion
window divided by its RTT. window divided by its RTT.
Specifically, CUBIC maintains a window increase rate independent of Specifically, CUBIC maintains a window increase rate that is
RTTs outside the Reno-friendly region, and thus flows with different independent of RTTs outside the Reno-friendly region, and thus flows
RTTs have similar congestion window sizes under steady state when with different RTTs have similar congestion window sizes under steady
they operate outside the Reno-friendly region. state when they operate outside the Reno-friendly region.
This notion of a linear throughput ratio is similar to that of Reno This notion of a linear throughput ratio is similar to that of Reno
under an asynchronous loss model, where flows with different RTTs under an asynchronous loss model, where flows with different RTTs
have the same packet loss rate but experience loss events at have the same packet loss rate but experience loss events at
different times. However, under a synchronous loss model, where different times. However, under a synchronous loss model, where
flows with different RTTs experience loss events at the same time but flows with different RTTs experience loss events at the same time but
have different packet loss rates, the throughput ratio of Reno flows have different packet loss rates, the throughput ratio of Reno flows
with different RTTs is quadratically proportional to the inverse of with different RTTs is quadratically proportional to the inverse of
their RTT ratio [XHR04]. their RTT ratio [XHR04].
CUBIC always ensures a linear throughput ratio independent of the CUBIC always ensures a linear throughput ratio that is independent of
loss environment. This is an improvement over Reno. While there is the loss environment. This is an improvement over Reno. While there
no consensus on the optimal throughput ratio for different RTT flows, is no consensus on the optimal throughput ratio for different RTT
over wired Internet paths, use of a linear throughput ratio seems flows, over wired Internet paths, use of a linear throughput ratio
more reasonable than equal throughputs (i.e., the same throughput for seems more reasonable than equal throughputs (i.e., the same
flows with different RTTs) or a higher-order throughput ratio (e.g., throughput for flows with different RTTs) or a higher-order
a quadratical throughput ratio of Reno in synchronous loss throughput ratio (e.g., a quadratic throughput ratio of Reno in
environments). synchronous loss environments).
3.4. Principle 4 for the CUBIC Decrease Factor 3.4. Principle 4 for the CUBIC Decrease Factor
To balance between scalability and convergence speed, CUBIC sets the To achieve a balance between scalability and convergence speed, CUBIC
multiplicative window decrease factor to 0.7, whereas Reno uses 0.5. sets the multiplicative window decrease factor to 0.7, whereas Reno
uses 0.5.
While this improves the scalability of CUBIC, a side effect of this While this improves the scalability of CUBIC, a side effect of this
decision is slower convergence, especially under low statistical decision is slower convergence, especially under low statistical
multiplexing. This design choice is following the observation that multiplexing. This design choice is following the observation that
HighSpeed TCP (HSTCP) [RFC3649] and other approaches (e.g., [GV02]) HighSpeed TCP (HSTCP) [RFC3649] and other approaches (e.g., [GV02])
made: the current Internet becomes more asynchronous with less made: the current Internet becomes more asynchronous with less
frequent loss synchronizations under high statistical multiplexing. frequent loss synchronizations under high statistical multiplexing.
In such environments, even strict Multiplicative-Increase In such environments, even strict Multiplicative-Increase
Multiplicative-Decrease (MIMD) can converge. CUBIC flows with the Multiplicative-Decrease (MIMD) can converge. CUBIC flows with the
same RTT always converge to the same throughput independent of same RTT always converge to the same throughput independently of
statistical multiplexing, thus achieving intra-algorithm fairness. statistical multiplexing, thus achieving intra-algorithm fairness.
In environments with sufficient statistical multiplexing, the In environments with sufficient statistical multiplexing, the
convergence speed of CUBIC is reasonable. convergence speed of CUBIC is reasonable.
4. CUBIC Congestion Control 4. CUBIC Congestion Control
This section discusses how the congestion window is updated during This section discusses how the congestion window is updated during
the different stages of the CUBIC congestion controller. the different stages of the CUBIC congestion controller.
4.1. Definitions 4.1. Definitions
The unit of all window sizes in this document is segments of the 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. SMSS, and the unit of all times is seconds. Implementations can use
Implementations can use bytes to express window sizes, which would bytes to express window sizes, which would require factoring in the
require factoring in the maximum segment size wherever necessary and SMSS wherever necessary and replacing _segments_acked_ (Figure 4)
replacing _segments_acked_ with the number of bytes acknowledged in with the number of acknowledged bytes.
Figure 4.
4.1.1. Constants of Interest 4.1.1. Constants of Interest
β__cubic_: CUBIC multiplicative decrease factor as described in * β__cubic_: CUBIC multiplicative decrease factor as described in
Section 4.6. Section 4.6.
α__cubic_: CUBIC additive increase factor used in Reno-friendly * α__cubic_: CUBIC additive increase factor used in the Reno-
region as described in Section 4.3. friendly region as described in Section 4.3.
_C_: constant that determines the aggressiveness of CUBIC in * _C_: Constant that determines the aggressiveness of CUBIC in
competing with other congestion control algorithms in high-BDP competing with other congestion control algorithms in high-BDP
networks. Please see Section 5 for more explanation on how it is networks. Please see Section 5 for more explanation on how it is
set. The unit for _C_ is set. The unit for _C_ is
segment segment
─────── ───────
3 3
second second
4.1.2. Variables of Interest 4.1.2. Variables of Interest
This section defines the variables required to implement CUBIC: This section defines the variables required to implement CUBIC:
_RTT_: Smoothed round-trip time in seconds, calculated as described * _RTT_: Smoothed round-trip time in seconds, calculated as
in [RFC6298]. described in [RFC6298].
_cwnd_: Current congestion window in segments. * _cwnd_: Current congestion window in segments.
_ssthresh_: Current slow start threshold in segments. * _ssthresh_: Current slow start threshold in segments.
_cwnd_prior_: Size of _cwnd_ in segments at the time of setting * _cwnd_prior_: Size of _cwnd_ in segments at the time of setting
_ssthresh_ most recently, either upon exiting the first slow start, _ssthresh_ most recently, either upon exiting the first slow start
or just before _cwnd_ was reduced in the last congestion event. or just before _cwnd_ was reduced in the last congestion event.
_W_max_: Size of _cwnd_ in segments just before _cwnd_ was reduced in * _W_max_: Size of _cwnd_ in segments just before _cwnd_ was reduced
the last congestion event when fast convergence is disabled (same as in the last congestion event when fast convergence is disabled
_cwnd_prior_ on a congestion event). However, if fast convergence is (same as _cwnd_prior_ on a congestion event). However, if fast
enabled, _W_max_ may be further reduced based on the current convergence is enabled, _W_max_ may be further reduced based on
saturation point. the current saturation point.
_K_: The time period in seconds it takes to increase the congestion * _K_: The time period in seconds it takes to increase the
window size at the beginning of the current congestion avoidance congestion window size at the beginning of the current congestion
stage to _W_max_. avoidance stage to _W_max_.
_t_current_: Current time of the system in seconds. * _t_current_: Current time of the system in seconds.
_t_epoch_: The time in seconds at which the current congestion * _t_epoch_: The time in seconds at which the current congestion
avoidance stage started. avoidance stage started.
_cwnd_epoch_: The _cwnd_ at the beginning of the current congestion * _cwnd_epoch_: The _cwnd_ at the beginning of the current
avoidance stage, i.e., at time _t_epoch_. congestion avoidance stage, i.e., at time _t_epoch_.
W_cubic(_t_): The congestion window in segments at time _t_ in * W_cubic(_t_): The congestion window in segments at time _t_ in
seconds based on the cubic increase function, as described in seconds based on the cubic increase function, as described in
Section 4.2. Section 4.2.
_target_: Target value of congestion window in segments after the * _target_: Target value of the congestion window in segments after
next RTT, that is, W_cubic(_t_ + _RTT_), as described in Section 4.2. the next RTT -- that is, W_cubic(_t_ + _RTT_), as described in
Section 4.2.
_W_est_: An estimate for the congestion window in segments in the * _W_est_: An estimate for the congestion window in segments in the
Reno-friendly region, that is, an estimate for the congestion window Reno-friendly region -- that is, an estimate for the congestion
of Reno. window of Reno.
_segments_acked_: Number of MSS-sized segments acked when a "new ACK" * _segments_acked_: Number of SMSS-sized segments acked when a "new
is received, i.e., an ACK that cumulatively acknowledges the delivery ACK" is received, i.e., an ACK that cumulatively acknowledges the
of new data. This number will be a decimal value when a new ACK delivery of previously unacknowledged data. This number will be a
acknowledges an amount of data that is not MSS-sized. Specifically, decimal value when a new ACK acknowledges an amount of data that
it can be less than 1 when a new ACK acknowledges a segment smaller is not SMSS-sized. Specifically, it can be less than 1 when a new
than the MSS. ACK acknowledges a segment smaller than the SMSS.
4.2. Window Increase Function 4.2. Window Increase Function
CUBIC maintains the acknowledgment (ACK) clocking of Reno by CUBIC maintains the ACK clocking of Reno by increasing the congestion
increasing the congestion window only at the reception of a new ACK. window only at the reception of a new ACK. It does not make any
It does not make any changes to the TCP Fast Recovery and Fast changes to the TCP Fast Recovery and Fast Retransmit algorithms
Retransmit algorithms [RFC6582][RFC6675]. [RFC6582] [RFC6675].
During congestion avoidance, after a congestion event is detected by During congestion avoidance, after a congestion event is detected as
mechanisms described in Section 3.1, CUBIC uses a window increase described in Section 3.1, CUBIC uses a window increase function
function different from Reno. different from Reno.
CUBIC uses the following window increase function: CUBIC uses the following window increase function:
3 3
W (t) = C * (t - K) + W W (t) = C * (t - K) + W
cubic max cubic max
Figure 1 Figure 1
where _t_ is the elapsed time in seconds from the beginning of the where _t_ is the elapsed time in seconds from the beginning of the
current congestion avoidance stage, that is, current congestion avoidance stage -- that is,
t = t - t t = t - t
current epoch current epoch
and where _t_epoch_ is the time at which the current congestion and where _t_epoch_ is the time at which the current congestion
avoidance stage starts. _K_ is the time period that the above avoidance stage starts. _K_ is the time period that the above
function takes to increase the congestion window size at the function takes to increase the congestion window size at the
beginning of the current congestion avoidance stage to _W_max_ if beginning of the current congestion avoidance stage to _W_max_ if
there are no further congestion events and is calculated using the there are no further congestion events. _K_ is calculated using the
following equation: following equation:
┌────────────────┐ ┌────────────────┐
3 │W - cwnd 3 │W - cwnd
╲ │ max epoch ╲ │ max epoch
K = ╲ │──────────────── K = ╲ │────────────────
╲│ C ╲│ C
Figure 2 Figure 2
skipping to change at page 12, line 48 skipping to change at line 511
To summarize, CUBIC computes both W_cubic(_t_) and _W_est_ (see To summarize, CUBIC computes both W_cubic(_t_) and _W_est_ (see
Section 4.3) on receiving a new ACK in congestion avoidance and Section 4.3) on receiving a new ACK in congestion avoidance and
chooses the larger of the two values. chooses the larger of the two values.
The next sections describe the exact actions taken by CUBIC in each The next sections describe the exact actions taken by CUBIC in each
region. region.
4.3. Reno-Friendly Region 4.3. Reno-Friendly Region
Reno performs well in certain types of networks, for example, under Reno performs well in certain types of networks -- for example, under
short RTTs and small bandwidths (or small BDPs). In these networks, short RTTs and small bandwidths (or small BDPs). In these networks,
CUBIC remains in the Reno-friendly region to achieve at least the CUBIC remains in the Reno-friendly region to achieve at least the
same throughput as Reno. same throughput as Reno.
The Reno-friendly region is designed according to the analysis in The Reno-friendly region is designed according to the analysis
[FHP00], which studies the performance of an AIMD algorithm with an discussed in [FHP00], which studies the performance of an AIMD
additive factor of α (segments per _RTT_) and a multiplicative factor algorithm with an additive factor of α (segments per _RTT_) and a
of β, denoted by AIMD(α, β). _p_ is the packet loss rate. multiplicative factor of β, denoted by AIMD(α, β). _p_ is the packet
Specifically, the average congestion window size of AIMD(α, β) can be loss rate. Specifically, the average congestion window size of
calculated using Figure 3. AIMD(α, β) can be calculated using Figure 3.
┌───────────────┐ ┌───────────────┐
│ α * (1 + β) │ α * (1 + β)
AVG_AIMD(α, β) = ╲ │─────────────── AVG_AIMD(α, β) = ╲ │───────────────
╲│2 * (1 - β) * p ╲│2 * (1 - β) * p
Figure 3 Figure 3
By the same analysis, to achieve a similar average window size as By the same analysis, to achieve an average window size similar to
Reno that uses AIMD(1, 0.5), α must be equal to, Reno that uses AIMD(1, 0.5), α must be equal to
1 - β 1 - β
3 * ───── 3 * ─────
1 + β 1 + β
Thus, CUBIC uses Figure 4 to estimate the window size _W_est_ in the Thus, CUBIC uses Figure 4 to estimate the window size _W_est_ in the
Reno-friendly region with Reno-friendly region with
1 - β 1 - β
cubic cubic
α = 3 * ────────── α = 3 * ──────────
cubic 1 + β cubic 1 + β
cubic cubic
which achieves approximately the same average window size as Reno in which achieves approximately the same average window size as Reno in
many cases. The model used to calculate α__cubic_ is not absolutely many cases. The model used to calculate α__cubic_ is not absolutely
precise, but analysis and simulation in [AIMD-friendliness], as well precise, but analysis and simulation as discussed in
as over a decade of experience with CUBIC in the public Internet, [AIMD-friendliness], as well as over a decade of experience with
show that this approach produces acceptable levels of rate fairness CUBIC in the public Internet, show that this approach produces
between CUBIC and Reno flows. Also, no significant drawbacks of the acceptable levels of rate fairness between CUBIC and Reno flows.
model have been reported. However, it would be beneficial to see Also, no significant drawbacks of the model have been reported.
continued detailed analysis on it. When receiving a new ACK in However, continued detailed analysis of this approach would be
congestion avoidance (where _cwnd_ could be greater than or less than beneficial. When receiving a new ACK in congestion avoidance (where
_W_max_), CUBIC checks whether W_cubic(_t_) is less than _W_est_. If _cwnd_ could be greater than or less than _W_max_), CUBIC checks
so, CUBIC is in the Reno-friendly region and _cwnd_ SHOULD be set to whether W_cubic(_t_) is less than _W_est_. If so, CUBIC is in the
_W_est_ at each reception of a new ACK. Reno-friendly region and _cwnd_ SHOULD be set to _W_est_ at each
reception of a new ACK.
_W_est_ is set equal to _cwnd_epoch_ at the start of the congestion _W_est_ is set equal to _cwnd_epoch_ at the start of the congestion
avoidance stage. After that, on every new ACK, _W_est_ is updated avoidance stage. After that, on every new ACK, _W_est_ is updated
using Figure 4. Note that this equation uses _segments_acked_ and using Figure 4. Note that this equation uses _segments_acked_ and
_cwnd_ is measured in segments. An implementation that measures _cwnd_ is measured in segments. An implementation that measures
_cwnd_ in bytes should adjust the equation accordingly using number _cwnd_ in bytes should adjust the equation accordingly using the
of acknowledged bytes and MSS. Also note that this equation works number of acknowledged bytes and the SMSS. Also note that this
for connections with enabled or disabled Delayed ACKs [RFC5681], as equation works for connections with enabled or disabled delayed ACKs
_segments_acked_ will be different based on the segments actually [RFC5681], as _segments_acked_ will be different based on the
acknowledged by a new ACK. segments actually acknowledged by a new ACK.
segments_acked segments_acked
W = W + α * ────────────── W = W + α * ──────────────
est est cubic cwnd est est cubic cwnd
Figure 4 Figure 4
Once _W_est_ has grown to reach the _cwnd_ at the time of most Once _W_est_ has grown to reach the _cwnd_ at the time of most
recently setting _ssthresh_, that is, _W_est_ >= _cwnd_prior_, the recently setting _ssthresh_ -- that is, _W_est_ >= _cwnd_prior_ --
sender SHOULD set α__cubic_ to 1 to ensure that it can achieve the the sender SHOULD set α__cubic_ to 1 to ensure that it can achieve
same congestion window increment rate as Reno, which uses AIMD(1, the same congestion window increment rate as Reno, which uses AIMD(1,
0.5). 0.5).
The next two sections assume that CUBIC is not in the Reno-friendly The next two sections assume that CUBIC is not in the Reno-friendly
region and uses the window increase function described in region and uses the window increase function described in
Section 4.2. Although _cwnd_ is incremented in the same way for both Section 4.2. Although _cwnd_ is incremented in the same way for both
concave and convex regions, they are discussed separately to analyze concave and convex regions, they are discussed separately to analyze
and understand the difference between the two regions. and understand the difference between the two regions.
4.4. Concave Region 4.4. Concave Region
skipping to change at page 15, line 5 skipping to change at line 614
When receiving a new ACK in congestion avoidance, if CUBIC is not in When receiving a new ACK in congestion avoidance, if CUBIC is not in
the Reno-friendly region and _cwnd_ is larger than or equal to the Reno-friendly region and _cwnd_ is larger than or equal to
_W_max_, then CUBIC is in the convex region. _W_max_, then CUBIC is in the convex region.
The convex region indicates that the network conditions might have The convex region indicates that the network conditions might have
changed since the last congestion event, possibly implying more changed since the last congestion event, possibly implying more
available bandwidth after some flow departures. Since the Internet available bandwidth after some flow departures. Since the Internet
is highly asynchronous, some amount of perturbation is always is highly asynchronous, some amount of perturbation is always
possible without causing a major change in available bandwidth. possible without causing a major change in available bandwidth.
Unless it is overridden by the AIMD window increase, CUBIC is very Unless the cwnd is overridden by the AIMD window increase, CUBIC will
careful in this region. The convex profile aims to increase the behave cautiously when operating in this region. The convex profile
window very slowly at the beginning when _cwnd_ is around _W_max_ and aims to increase the window very slowly at the beginning when _cwnd_
then gradually increases its rate of increase. This region is also is around _W_max_ and then gradually increases its rate of increase.
called the "maximum probing phase", since CUBIC is searching for a This region is also called the "maximum probing phase", since CUBIC
new _W_max_. In this region, _cwnd_ MUST be incremented by is searching for a new _W_max_. In this region, _cwnd_ MUST be
incremented by
target - cwnd target - cwnd
───────────── ─────────────
cwnd cwnd
for each received new ACK, where _target_ is calculated as described for each received new ACK, where _target_ is calculated as described
in Section 4.2. in Section 4.2.
4.6. Multiplicative Decrease 4.6. Multiplicative Decrease
When a congestion event is detected by mechanisms described in When a congestion event is detected by the mechanisms described in
Section 3.1, CUBIC updates _W_max_ and reduces _cwnd_ and _ssthresh_ Section 3.1, CUBIC updates _W_max_ and reduces _cwnd_ and _ssthresh_
immediately as described below. In case of packet loss, the sender immediately, as described below. In the case of packet loss, the
MUST reduce _cwnd_ and _ssthresh_ immediately upon entering loss sender MUST reduce _cwnd_ and _ssthresh_ immediately upon entering
recovery, similar to [RFC5681] (and [RFC6675]). Note that other loss recovery, similar to [RFC5681] (and [RFC6675]). Note that other
mechanisms, such as Proportional Rate Reduction [RFC6937], can be mechanisms, such as Proportional Rate Reduction [RFC6937], can be
used to reduce the sending rate during loss recovery more gradually. used to reduce the sending rate during loss recovery more gradually.
The parameter β__cubic_ SHOULD be set to 0.7, which is different from The parameter β__cubic_ SHOULD be set to 0.7, which is different from
the multiplicative decrease factor used in [RFC5681] (and [RFC6675]) the multiplicative decrease factor used in [RFC5681] (and [RFC6675])
during fast recovery. during fast recovery.
In Figure 5, _flight_size_ is the amount of outstanding In Figure 5, _flight_size_ is the amount of outstanding
(unacknowledged) data in the network, as defined in [RFC5681]. Note (unacknowledged) data in the network, as defined in [RFC5681]. Note
that a rate-limited application with idle periods or periods when that a rate-limited application with idle periods or periods when
unable to send at the full rate permitted by _cwnd_ could easily unable to send at the full rate permitted by _cwnd_ could easily
encounter notable variations in the volume of data sent from one RTT encounter notable variations in the volume of data sent from one RTT
to another, resulting in _flight_size_ that is significantly less to another, resulting in _flight_size_ that is significantly less
than _cwnd_ when there is a congestion event. The congestion than _cwnd_ when there is a congestion event. The congestion
response would therefore decrease _cwnd_ to a much lower value than response would therefore decrease _cwnd_ to a much lower value than
necessary. To avoid such suboptimal performance, the mechanisms necessary. To avoid such suboptimal performance, the mechanisms
described in [RFC7661] can be used. These describe how to manage and described in [RFC7661] can be used. [RFC7661] describes how to
use _cwnd_ and _ssthresh_ during a rate-limited Interval, and how to manage and use _cwnd_ and _ssthresh_ during a rate-limited interval,
update _cwnd_ and _ssthresh_ after congestion has been detected. The and how to update _cwnd_ and _ssthresh_ after congestion has been
mechanism defined in [RFC7661] is safe to use even when _cwnd_ is detected. The mechanisms defined in [RFC7661] are safe to use even
greater than the receive window, because it validates _cwnd_ based on when _cwnd_ is greater than the receive window, because they validate
the amount of data acknowledged by the network in an RTT, which _cwnd_ based on the amount of data acknowledged by the network in an
implicitly accounts for the allowed receive window. RTT, which implicitly accounts for the allowed receive window.
Some implementations of CUBIC currently use _cwnd_ instead of Some implementations of CUBIC currently use _cwnd_ instead of
_flight_size_ when calculating a new _ssthresh_. Implementations that _flight_size_ when calculating a new _ssthresh_. Implementations
use _cwnd_ MUST use other measures to prevent _cwnd_ from growing that use _cwnd_ MUST use other measures to prevent _cwnd_ from
when the volume of bytes in flight is smaller than _cwnd_. This also growing when the volume of bytes in flight is smaller than
effectively avoids _cwnd_ from growing beyond the receive window. _cwnd_. This also effectively prevents _cwnd_ from growing beyond
Such measures are important to prevent a CUBIC sender from using an the receive window. Such measures are important for preventing a
arbitrarily high cwnd _value_ when calculating new values for CUBIC sender from using an arbitrarily high cwnd _value_ when
_ssthresh_ and _cwnd_ when congestion is detected. This might not be calculating new values for _ssthresh_ and _cwnd_ when congestion is
as robust as the mechanisms described in [RFC7661]. detected. This might not be as robust as the mechanisms described in
[RFC7661].
A QUIC sender that uses _cwnd_ to calculate new values for _cwnd_ and A QUIC sender that uses a _cwnd_ _value_ to calculate new values for
_ssthresh_ after detecting a congestion event is REQUIRED to apply _cwnd_ and _ssthresh_ after detecting a congestion event is REQUIRED
similar mechanisms [RFC9002]. to apply similar mechanisms [RFC9002].
ssthresh = flight_size * β new ssthresh ssthresh = flight_size * β new ssthresh
cubic cubic
cwnd = cwnd save cwnd cwnd = cwnd save cwnd
prior prior
⎧ ⎧max(ssthresh, 2) reduction on loss, cwnd >= 2 SMSS
⎨max(ssthresh, 2) reduction on loss, cwnd is at least 2 MSS cwnd = ⎨max(ssthresh, 1) reduction on ECE, cwnd >= 1 SMSS
cwnd = ⎩max(ssthresh, 1) reduction on ECE, cwnd is at least 1 MSS ⎩
ssthresh = max(ssthresh, 2) ssthresh is at least 2 MSS ssthresh = max(ssthresh, 2) ssthresh >= 2 SMSS
Figure 5 Figure 5
A side effect of setting β__cubic_ to a value bigger than 0.5 is that A side effect of setting β__cubic_ to a value bigger than 0.5 is that
packet loss can happen for more than one round-trip in certain cases, packet loss can happen for more than one RTT in certain cases, but it
but it can work efficiently in other cases, for example, when can work efficiently in other cases -- for example, when HyStart++
HyStart++ is used along with CUBIC or when the sending rate is [RFC9406] is used along with CUBIC or when the sending rate is
limited by the application. While a more adaptive setting of limited by the application. While a more adaptive setting of
β__cubic_ could help limit packet loss to a single round, it would β__cubic_ could help limit packet loss to a single round, it would
require detailed analyses and large-scale evaluations to validate require detailed analyses and large-scale evaluations to validate
such algorithms. such algorithms.
Note that CUBIC MUST continue to reduce _cwnd_ in response to Note that CUBIC MUST continue to reduce _cwnd_ in response to
congestion events due to ECN-Echo ACKs until it reaches a value of 1 congestion events detected by ECN-Echo ACKs until it reaches a value
MSS. If congestion events indicated by ECN-Echo ACKs persist, a of 1 SMSS. If congestion events indicated by ECN-Echo ACKs persist,
sender with a _cwnd_ of 1 MSS MUST reduce its sending rate even a sender with a _cwnd_ of 1 SMSS MUST reduce its sending rate even
further. It can achieve that by using a retransmission timer with further. This can be achieved by using a retransmission timer with
exponential backoff, as described in [RFC3168]. exponential backoff, as described in [RFC3168].
4.7. Fast Convergence 4.7. Fast Convergence
To improve convergence speed, CUBIC uses a heuristic. When a new To improve convergence speed, CUBIC uses a heuristic. When a new
flow joins the network, existing flows need to give up some of their flow joins the network, existing flows need to give up some of their
bandwidth to allow the new flow some room for growth, if the existing bandwidth to allow the new flow some room for growth if the existing
flows have been using all the network bandwidth. To speed up this flows have been using all the network bandwidth. To speed up this
bandwidth release by existing flows, the following "Fast Convergence" bandwidth release by existing flows, the following fast convergence
mechanism SHOULD be implemented. mechanism SHOULD be implemented.
With Fast Convergence, when a congestion event occurs, _W_max_ is With fast convergence, when a congestion event occurs, _W_max_ is
updated as follows, before the window reduction described in updated as follows, before the window reduction described in
Section 4.6. Section 4.6.
⎧ 1 + β ⎧ 1 + β
⎪ cubic ⎪ cubic
⎪cwnd * ────────── if cwnd < W and fast convergence enabled, ⎪cwnd * ────────── if cwnd < W and fast convergence enabled,
W = ⎨ 2 max W = ⎨ 2 max
max ⎪ further reduce W max ⎪ further reduce W
⎪ max ⎪ max
⎩cwnd otherwise, remember cwnd before reduction ⎩cwnd otherwise, remember cwnd before reduction
At a congestion event, if the current _cwnd_ is less than _W_max_, During a congestion event, if the current _cwnd_ is less than
this indicates that the saturation point experienced by this flow is _W_max_, this indicates that the saturation point experienced by this
getting reduced because of a change in available bandwidth. This flow is getting reduced because of a change in available bandwidth.
flow can then release more bandwidth by reducing _W_max_ further. This flow can then release more bandwidth by reducing _W_max_
This action effectively lengthens the time for this flow to increase further. This action effectively lengthens the time for this flow to
its congestion window, because the reduced _W_max_ forces the flow to increase its congestion window, because the reduced _W_max_ forces
plateau earlier. This allows more time for the new flow to catch up the flow to plateau earlier. This allows more time for the new flow
to its congestion window size. to catch up to its congestion window size.
Fast Convergence is designed for network environments with multiple Fast convergence is designed for network environments with multiple
CUBIC flows. In network environments with only a single CUBIC flow CUBIC flows. In network environments with only a single CUBIC flow
and without any other traffic, Fast Convergence SHOULD be disabled. and without any other traffic, fast convergence SHOULD be disabled.
4.8. Timeout 4.8. Timeout
In case of a timeout, CUBIC follows Reno to reduce _cwnd_ [RFC5681], In the case of a timeout, CUBIC follows Reno to reduce _cwnd_
but sets _ssthresh_ using β__cubic_ (same as in Section 4.6) in a way [RFC5681] but sets _ssthresh_ using β__cubic_ (same as in
that is different from Reno TCP [RFC5681]. Section 4.6) in a way that is different from Reno TCP [RFC5681].
During the first congestion avoidance stage after a timeout, CUBIC During the first congestion avoidance stage after a timeout, CUBIC
increases its congestion window size using Figure 1, where _t_ is the increases its congestion window size using Figure 1, where _t_ is the
elapsed time since the beginning of the current congestion avoidance, 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 stage, _K_ is set to 0, and _W_max_ is set to the congestion window
the beginning of the current congestion avoidance stage. In size at the beginning of the current congestion avoidance stage. In
addition, for the Reno-friendly region, _W_est_ SHOULD be set to the addition, for the Reno-friendly region, _W_est_ SHOULD be set to the
congestion window size at the beginning of the current congestion congestion window size at the beginning of the current congestion
avoidance. avoidance stage.
4.9. Spurious Congestion Events 4.9. Spurious Congestion Events
In cases where CUBIC reduces its congestion window in response to In cases where CUBIC reduces its congestion window in response to
having detected packet loss via duplicate ACKs or timeouts, there is having detected packet loss via duplicate ACKs or timeouts, it is
a possibility that the missing ACK would arrive after the congestion possible that the missing ACK could arrive after the congestion
window reduction and a corresponding packet retransmission. For window reduction and a corresponding packet retransmission. For
example, packet reordering could trigger this behavior. A high example, packet reordering could trigger this behavior. A high
degree of packet reordering could cause multiple congestion window degree of packet reordering could cause multiple congestion window
reduction events, where spurious losses are incorrectly interpreted reduction events, where spurious losses are incorrectly interpreted
as congestion signals, thus degrading CUBIC's performance as congestion signals, thus degrading CUBIC's performance
significantly. significantly.
For TCP, there are two types of spurious events - spurious timeouts For TCP, there are two types of spurious events: spurious timeouts
and spurious fast retransmits. In case of QUIC, there are no and spurious fast retransmits. In the case of QUIC, there are no
spurious timeouts as the loss is only detected after receiving an spurious timeouts, as the loss is only detected after receiving an
ACK. ACK.
4.9.1. Spurious timeout 4.9.1. Spurious Timeouts
An implementation MAY detect spurious timeouts based on the An implementation MAY detect spurious timeouts based on the
mechanisms described in Forward RTO-Recovery [RFC5682]. Experimental mechanisms described in Forward RTO-Recovery [RFC5682]. Experimental
alternatives include Eifel [RFC3522]. When a spurious timeout is alternatives include the Eifel detection algorithm [RFC3522]. When a
detected, a TCP implementation MAY follow the response algorithm spurious timeout is detected, a TCP implementation MAY follow the
described in [RFC4015] to restore the congestion control state and response algorithm described in [RFC4015] to restore the congestion
adapt the retransmission timer to avoid further spurious timeouts. control state and adapt the retransmission timer to avoid further
spurious timeouts.
4.9.2. Spurious loss detected by acknowledgments 4.9.2. Spurious Fast Retransmits
Upon receiving an ACK, a TCP implementation MAY detect spurious Upon receiving an ACK, a TCP implementation MAY detect spurious fast
losses either using TCP Timestamps or via D-SACK[RFC2883]. retransmits either using TCP Timestamps or via D-SACK [RFC2883]. As
Experimental alternatives include Eifel detection algorithm [RFC3522] noted above, experimental alternatives include the Eifel detection
which uses TCP Timestamps and DSACK based detection [RFC3708] which algorithm [RFC3522], which uses TCP Timestamps; and DSACK-based
uses DSACK information. A QUIC implementation can easily determine a detection [RFC3708], which uses DSACK information. A QUIC
spurious loss if a QUIC packet is acknowledged after it has been implementation can easily determine a spurious fast retransmit if a
marked as lost and the original data has been retransmitted with a QUIC packet is acknowledged after it has been marked as lost and the
new QUIC packet. original data has been retransmitted with a new QUIC packet.
This section specifies a simple response algorithm when a spurious This section specifies a simple response algorithm when a spurious
loss is detected by acknowledgments. Implementations would need to fast retransmit is detected by acknowledgments. Implementations
carefully evaluate the impact of using this algorithm in different would need to carefully evaluate the impact of using this algorithm
environments that may experience sudden change in available capacity in different environments that may experience a sudden change in
(e.g., due to variable radio capacity, a routing change, or a available capacity (e.g., due to variable radio capacity, a routing
mobility event). change, or a mobility event).
When a packet loss is detected via acknowledgments, a CUBIC When packet loss is detected via acknowledgments, a CUBIC
implementation MAY save the current value of the following variables implementation MAY save the current value of the following variables
before the congestion window is reduced. before the congestion window is reduced.
undo_cwnd = cwnd undo_cwnd = cwnd
undo_cwnd = cwnd undo_cwnd = cwnd
prior prior prior prior
undo_ssthresh = ssthresh undo_ssthresh = ssthresh
undo_W = W undo_W = W
max max max max
undo_K = K undo_K = K
undo_t = t undo_t = t
epoch epoch epoch epoch
undo_W = W undo_W = W
est est est est
Once the previously declared packet loss is confirmed to be spurious, Once the previously declared packet loss is confirmed to be spurious,
CUBIC MAY restore the original values of the above-mentioned CUBIC MAY restore the original values of the above-mentioned
variables as follows if the current _cwnd_ is lower than variables as follows if the current _cwnd_ is lower than
_cwnd_prior_. Restoring the original values ensures that CUBIC's _cwnd_prior_. Restoring the original values ensures that CUBIC's
performance is similar to what it would be without spurious losses. performance is similar to what it would be without spurious losses.
cwnd = undo_cwnd ⎫ cwnd = undo_cwnd ⎫
cwnd = undo_cwnd ⎮ cwnd = undo_cwnd ⎮
prior prior ⎮ prior prior ⎮
ssthresh = undo_ssthresh ⎮ ssthresh = undo_ssthresh ⎮
W = undo_W ⎮ W = undo_W ⎮
max max ⎬if cwnd < cwnd max max ⎬if cwnd < cwnd
K = undo_K ⎮ prior K = undo_K ⎮ prior
t = undo_t ⎮ t = undo_t ⎮
epoch epoch ⎮ epoch epoch ⎮
W = undo_W ⎮ W = undo_W ⎮
est est ⎭ est est ⎭
In rare cases, when the detection happens long after a spurious loss In rare cases, when the detection happens long after a spurious fast
event and the current _cwnd_ is already higher than _cwnd_prior_, retransmit event and the current _cwnd_ is already higher than
CUBIC SHOULD continue to use the current and the most recent values _cwnd_prior_, CUBIC SHOULD continue to use the current and the most
of these variables. recent values of these variables.
4.10. Slow Start 4.10. Slow Start
CUBIC MUST employ a slow-start algorithm, when _cwnd_ is no more than When _cwnd_ is no more than _ssthresh_, CUBIC MUST employ a slow
_ssthresh_. In general, CUBIC SHOULD use the HyStart++ slow start start algorithm. In general, CUBIC SHOULD use the HyStart++ slow
algorithm [I-D.ietf-tcpm-hystartplusplus], or MAY use the Reno TCP start algorithm [RFC9406] or MAY use the Reno TCP slow start
slow start algorithm [RFC5681] in the rare cases when HyStart++ is algorithm [RFC5681] in the rare cases when HyStart++ is not suitable.
not suitable. Experimental alternatives include hybrid slow start Experimental alternatives include hybrid slow start [HR11], a
[HR11], a predecessor to HyStart++ that some CUBIC implementations predecessor to HyStart++ that some CUBIC implementations have used as
have used as the default for the last decade, and limited slow start the default for the last decade, and limited slow start [RFC3742].
[RFC3742]. Whichever start-up algorithm is used, work might be Whichever startup algorithm is used, work might be needed to ensure
needed to ensure that the end of slow start and the first that the end of slow start and the first multiplicative decrease of
multiplicative decrease of congestion avoidance work well together. congestion avoidance work well together.
When CUBIC uses HyStart++ [I-D.ietf-tcpm-hystartplusplus], it may When CUBIC uses HyStart++ [RFC9406], it may exit the first slow start
exit the first slow start without incurring any packet loss and thus without incurring any packet loss and thus _W_max_ is undefined. In
_W_max_ is undefined. In this special case, CUBIC sets _cwnd_prior = this special case, CUBIC sets _cwnd_prior = cwnd_ and switches to
cwnd_ and switches to congestion avoidance. It then increases its congestion avoidance. It then increases its congestion window size
congestion window size using Figure 1, where _t_ is the elapsed time using Figure 1, where _t_ is the elapsed time since the beginning of
since the beginning of the current congestion avoidance, _K_ is set the current congestion avoidance stage, _K_ is set to 0, and _W_max_
to 0, and _W_max_ is set to the congestion window size at the is set to the congestion window size at the beginning of the current
beginning of the current congestion avoidance stage. congestion avoidance stage.
5. Discussion 5. Discussion
This section further discusses the safety features of CUBIC following This section further discusses the safety features of CUBIC,
the guidelines specified in [RFC5033]. following the guidelines specified in [RFC5033].
With a deterministic loss model where the number of packets between With a deterministic loss model where the number of packets between
two successive packet losses is always _1/p_, CUBIC always operates two successive packet losses is always _1/p_, CUBIC always operates
with the concave window profile, which greatly simplifies the with the concave window profile, which greatly simplifies the
performance analysis of CUBIC. The average window size of CUBIC (see performance analysis of CUBIC. The average window size of CUBIC (see
Appendix C) can be obtained by the following function: Appendix B) can be obtained via the following function:
┌────────────────┐ 4 ┌────┐ ┌────────────────┐ 4 ┌────┐
│C * (3 + β ) ╲ │ 3 │C * (3 + β ) ╲ │ 3
4 │ cubic ╲│RTT 4 │ cubic ╲│RTT
AVG_W = ╲ │──────────────── * ──────── AVG_W = ╲ │──────────────── * ────────
cubic ╲ │4 * (1 - β ) 4 ┌──┐ cubic ╲ │4 * (1 - β ) 4 ┌──┐
╲│ cubic ╲ │ 3 ╲│ cubic ╲ │ 3
╲│p ╲│p
Figure 6 Figure 6
With β__cubic_ set to 0.7, the above formula reduces to: With β__cubic_ set to 0.7, the above formula reduces to
4 ┌────┐ 4 ┌────┐
┌───────┐ ╲ │ 3 ┌───────┐ ╲ │ 3
4 │C * 3.7 ╲│RTT 4 │C * 3.7 ╲│RTT
AVG_W = ╲ │─────── * ──────── AVG_W = ╲ │─────── * ────────
cubic ╲│ 1.2 4 ┌──┐ cubic ╲│ 1.2 4 ┌──┐
╲ │ 3 ╲ │ 3
╲│p ╲│p
Figure 7 Figure 7
skipping to change at page 21, line 14 skipping to change at line 901
5.1. Fairness to Reno 5.1. Fairness to Reno
In environments where Reno is able to make reasonable use of the In environments where Reno is able to make reasonable use of the
available bandwidth, CUBIC does not significantly change this state. available bandwidth, CUBIC does not significantly change this state.
Reno performs well in the following two types of networks: Reno performs well in the following two types of networks:
1. networks with a small bandwidth-delay product (BDP) 1. networks with a small bandwidth-delay product (BDP)
2. networks with a short RTTs, but not necessarily a small BDP 2. networks with short RTTs, but not necessarily a small BDP
CUBIC is designed to behave very similarly to Reno in the above two CUBIC is designed to behave very similarly to Reno in the above two
types of networks. The following two tables show the average window types of networks. The following two tables show the average window
sizes of Reno TCP, HSTCP, and CUBIC TCP. The average window sizes of sizes of Reno TCP, HSTCP, and CUBIC TCP. The average window sizes of
Reno TCP and HSTCP are from [RFC3649]. The average window size of Reno TCP and HSTCP are from [RFC3649]. The average window size of
CUBIC is calculated using Figure 7 and the CUBIC Reno-friendly region CUBIC is calculated using Figure 7 and the CUBIC Reno-friendly region
for three different values of _C_. for three different values of _C_.
+=============+=======+========+================+=========+========+ +=============+=======+========+================+=========+========+
| Loss Rate P | Reno | HSTCP | CUBIC (C=0.04) | CUBIC | CUBIC | | Loss Rate P | Reno | HSTCP | CUBIC (C=0.04) | CUBIC | CUBIC |
skipping to change at page 21, line 42 skipping to change at line 929
+-------------+-------+--------+----------------+---------+--------+ +-------------+-------+--------+----------------+---------+--------+
| 1.0e-05 | 379 | 1795 | 593 | 1054 | 1874 | | 1.0e-05 | 379 | 1795 | 593 | 1054 | 1874 |
+-------------+-------+--------+----------------+---------+--------+ +-------------+-------+--------+----------------+---------+--------+
| 1.0e-06 | 1200 | 12280 | 3332 | 5926 | 10538 | | 1.0e-06 | 1200 | 12280 | 3332 | 5926 | 10538 |
+-------------+-------+--------+----------------+---------+--------+ +-------------+-------+--------+----------------+---------+--------+
| 1.0e-07 | 3795 | 83981 | 18740 | 33325 | 59261 | | 1.0e-07 | 3795 | 83981 | 18740 | 33325 | 59261 |
+-------------+-------+--------+----------------+---------+--------+ +-------------+-------+--------+----------------+---------+--------+
| 1.0e-08 | 12000 | 574356 | 105383 | 187400 | 333250 | | 1.0e-08 | 12000 | 574356 | 105383 | 187400 | 333250 |
+-------------+-------+--------+----------------+---------+--------+ +-------------+-------+--------+----------------+---------+--------+
Table 1: Reno TCP, HSTCP, and CUBIC with RTT = 0.1 seconds Table 1: Reno TCP, HSTCP, and CUBIC with RTT = 0.1 Seconds
Table 1 describes the response function of Reno TCP, HSTCP, and CUBIC Table 1 describes the response function of Reno TCP, HSTCP, and CUBIC
in networks with _RTT_ = 0.1 seconds. The average window size is in in networks with _RTT_ = 0.1 seconds. The average window size is in
MSS-sized segments. SMSS-sized segments.
+=============+=======+========+================+=========+=======+ +=============+=======+========+================+=========+=======+
| Loss Rate P | Reno | HSTCP | CUBIC (C=0.04) | CUBIC | CUBIC | | Loss Rate P | Reno | HSTCP | CUBIC (C=0.04) | CUBIC | CUBIC |
| | | | | (C=0.4) | (C=4) | | | | | | (C=0.4) | (C=4) |
+=============+=======+========+================+=========+=======+ +=============+=======+========+================+=========+=======+
| 1.0e-02 | 12 | 12 | 12 | 12 | 12 | | 1.0e-02 | 12 | 12 | 12 | 12 | 12 |
+-------------+-------+--------+----------------+---------+-------+ +-------------+-------+--------+----------------+---------+-------+
| 1.0e-03 | 38 | 38 | 38 | 38 | 38 | | 1.0e-03 | 38 | 38 | 38 | 38 | 38 |
+-------------+-------+--------+----------------+---------+-------+ +-------------+-------+--------+----------------+---------+-------+
| 1.0e-04 | 120 | 263 | 120 | 120 | 120 | | 1.0e-04 | 120 | 263 | 120 | 120 | 120 |
+-------------+-------+--------+----------------+---------+-------+ +-------------+-------+--------+----------------+---------+-------+
| 1.0e-05 | 379 | 1795 | 379 | 379 | 379 | | 1.0e-05 | 379 | 1795 | 379 | 379 | 379 |
+-------------+-------+--------+----------------+---------+-------+ +-------------+-------+--------+----------------+---------+-------+
| 1.0e-06 | 1200 | 12280 | 1200 | 1200 | 1874 | | 1.0e-06 | 1200 | 12280 | 1200 | 1200 | 1874 |
+-------------+-------+--------+----------------+---------+-------+ +-------------+-------+--------+----------------+---------+-------+
| 1.0e-07 | 3795 | 83981 | 3795 | 5926 | 10538 | | 1.0e-07 | 3795 | 83981 | 3795 | 5926 | 10538 |
+-------------+-------+--------+----------------+---------+-------+ +-------------+-------+--------+----------------+---------+-------+
| 1.0e-08 | 12000 | 574356 | 18740 | 33325 | 59261 | | 1.0e-08 | 12000 | 574356 | 18740 | 33325 | 59261 |
+-------------+-------+--------+----------------+---------+-------+ +-------------+-------+--------+----------------+---------+-------+
Table 2: Reno TCP, HSTCP, and CUBIC with RTT = 0.01 seconds Table 2: Reno TCP, HSTCP, and CUBIC with RTT = 0.01 Seconds
Table 2 describes the response function of Reno TCP, HSTCP, and CUBIC Table 2 describes the response function of Reno TCP, HSTCP, and CUBIC
in networks with _RTT_ = 0.01 seconds. The average window size is in in networks with _RTT_ = 0.01 seconds. The average window size is in
MSS-sized segments. SMSS-sized segments.
Both tables show that CUBIC with any of these three _C_ values is Both tables show that CUBIC with any of these three _C_ values is
more friendly to Reno TCP than HSTCP, especially in networks with a more friendly to Reno TCP than HSTCP, especially in networks with a
short _RTT_ where Reno TCP performs reasonably well. For example, in short _RTT_ where Reno TCP performs reasonably well. For example, in
a network with _RTT_ = 0.01 seconds and p=10^-6, Reno TCP has an a network with _RTT_ = 0.01 seconds and p=10^-6, Reno TCP has an
average window of 1200 packets. If the packet size is 1500 bytes, average window of 1200 packets. If the packet size is 1500 bytes,
then Reno TCP can achieve an average rate of 1.44 Gbps. In this then Reno 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 case, CUBIC with _C_=0.04 or _C_=0.4 achieves exactly the same rate
as Reno TCP, whereas HSTCP is about ten times more aggressive than as Reno TCP, whereas HSTCP is about ten times more aggressive than
Reno TCP. Reno TCP.
_C_ determines the aggressiveness of CUBIC in competing with other _C_ determines the aggressiveness of CUBIC in competing with other
congestion control algorithms for bandwidth. CUBIC is more friendly congestion control algorithms for bandwidth. CUBIC is more friendly
to Reno TCP, if the value of _C_ is lower. However, it is NOT to Reno TCP if the value of _C_ is lower. However, it is NOT
RECOMMENDED to set _C_ to a very low value like 0.04, since CUBIC RECOMMENDED to set _C_ to a very low value like 0.04, since CUBIC
with a low _C_ cannot efficiently use the bandwidth in fast and long- with a low _C_ cannot efficiently use the bandwidth in fast and long-
distance networks. Based on these observations and extensive distance networks. Based on these observations and extensive
deployment experience, _C_=0.4 seems to give a good balance between deployment experience, _C_=0.4 seems to provide a good balance
Reno-friendliness and aggressiveness of window increase. Therefore, between Reno-friendliness and aggressiveness of window increase.
_C_ SHOULD be set to 0.4. With _C_ set to 0.4, Figure 7 is reduced Therefore, _C_ SHOULD be set to 0.4. With _C_ set to 0.4, Figure 7
to: is reduced to
4 ┌────┐ 4 ┌────┐
╲ │ 3 ╲ │ 3
╲│RTT ╲│RTT
AVG_W = 1.054 * ──────── AVG_W = 1.054 * ────────
cubic 4 ┌──┐ cubic 4 ┌──┐
╲ │ 3 ╲ │ 3
╲│p ╲│p
Figure 8 Figure 8
Figure 8 is then used in the next subsection to show the scalability Figure 8 is then used in the next subsection to show the scalability
of CUBIC. of CUBIC.
5.2. Using Spare Capacity 5.2. Using Spare Capacity
CUBIC uses a more aggressive window increase function than Reno for CUBIC uses a more aggressive window increase function than Reno for
fast and long-distance networks. fast and long-distance networks.
The following table shows that to achieve the 10 Gbps rate, Reno TCP Table 3 shows that to achieve the 10 Gbps rate, Reno TCP requires a
requires a packet loss rate of 2.0e-10, while CUBIC TCP requires a packet loss rate of 2.0e-10, while CUBIC TCP requires a packet loss
packet loss rate of 2.9e-8. rate of 2.9e-8.
+===================+===========+=========+=========+=========+ +===================+===========+=========+=========+=========+
| Throughput (Mbps) | Average W | Reno P | HSTCP P | CUBIC P | | Throughput (Mbps) | Average W | Reno P | HSTCP P | CUBIC P |
+===================+===========+=========+=========+=========+ +===================+===========+=========+=========+=========+
| 1 | 8.3 | 2.0e-2 | 2.0e-2 | 2.0e-2 | | 1 | 8.3 | 2.0e-2 | 2.0e-2 | 2.0e-2 |
+-------------------+-----------+---------+---------+---------+ +-------------------+-----------+---------+---------+---------+
| 10 | 83.3 | 2.0e-4 | 3.9e-4 | 2.9e-4 | | 10 | 83.3 | 2.0e-4 | 3.9e-4 | 2.9e-4 |
+-------------------+-----------+---------+---------+---------+ +-------------------+-----------+---------+---------+---------+
| 100 | 833.3 | 2.0e-6 | 2.5e-5 | 1.4e-5 | | 100 | 833.3 | 2.0e-6 | 2.5e-5 | 1.4e-5 |
+-------------------+-----------+---------+---------+---------+ +-------------------+-----------+---------+---------+---------+
| 1000 | 8333.3 | 2.0e-8 | 1.5e-6 | 6.3e-7 | | 1000 | 8333.3 | 2.0e-8 | 1.5e-6 | 6.3e-7 |
+-------------------+-----------+---------+---------+---------+ +-------------------+-----------+---------+---------+---------+
| 10000 | 83333.3 | 2.0e-10 | 1.0e-7 | 2.9e-8 | | 10000 | 83333.3 | 2.0e-10 | 1.0e-7 | 2.9e-8 |
+-------------------+-----------+---------+---------+---------+ +-------------------+-----------+---------+---------+---------+
Table 3: Required packet loss rate for Reno TCP, HSTCP, and Table 3: Required Packet Loss Rate for Reno TCP, HSTCP, and
CUBIC to achieve a certain throughput CUBIC to Achieve a Certain Throughput
Table 3 describes the required packet loss rate for Reno TCP, HSTCP, Table 3 describes the required packet loss rate for Reno TCP, HSTCP,
and CUBIC to achieve a certain throughput, with 1500-byte packets and and CUBIC to achieve a certain throughput, with 1500-byte packets and
an _RTT_ of 0.1 seconds. an _RTT_ of 0.1 seconds.
The test results in [HLRX07] indicate that, in typical cases with a The test results provided in [HLRX07] indicate that, in typical cases
degree of background traffic, CUBIC uses the spare bandwidth left with a degree of background traffic, CUBIC uses the spare bandwidth
unused by existing Reno TCP flows in the same bottleneck link without left unused by existing Reno TCP flows in the same bottleneck link
taking away much bandwidth from the existing flows. without taking away much bandwidth from the existing flows.
5.3. Difficult Environments 5.3. Difficult Environments
CUBIC is designed to remedy the poor performance of Reno in fast and CUBIC is designed to remedy the poor performance of Reno in fast and
long-distance networks. long-distance networks.
5.4. Investigating a Range of Environments 5.4. Investigating a Range of Environments
CUBIC has been extensively studied using simulations, testbed CUBIC has been extensively studied using simulations, testbed
emulations, Internet experiments, and Internet measurements, covering emulations, Internet experiments, and Internet measurements, covering
a wide range of network environments a wide range of network environments [HLRX07] [H16] [CEHRX09] [HR11]
[HLRX07][H16][CEHRX09][HR11][BSCLU13][LBEWK16]. They have [BSCLU13] [LBEWK16]. They have convincingly demonstrated that CUBIC
convincingly demonstrated that CUBIC delivers substantial benefits delivers substantial benefits over classical Reno congestion control
over classical Reno congestion control [RFC5681]. [RFC5681].
Same as Reno, CUBIC is a loss-based congestion control algorithm. Same as Reno, CUBIC is a loss-based congestion control algorithm.
Because CUBIC is designed to be more aggressive (due to a faster Because CUBIC is designed to be more aggressive (due to a faster
window increase function and bigger multiplicative decrease factor) window increase function and bigger multiplicative decrease factor)
than Reno in fast and long-distance networks, it can fill large drop- than Reno in fast and long-distance networks, it can fill large drop-
tail buffers more quickly than Reno and increases the risk of a tail buffers more quickly than Reno and increases the risk of a
standing queue [RFC8511]. In this case, proper queue sizing and standing queue [RFC8511]. In this case, proper queue sizing and
management [RFC7567] could be used to mitigate the risk to some management [RFC7567] could be used to mitigate the risk to some
extent and reduce the packet queuing delay. Also, in large-BDP extent and reduce the packet queuing delay. Also, in large-BDP
networks after a congestion event, CUBIC, due its cubic window networks after a congestion event, CUBIC, due to its cubic window
increase function, recovers quickly to the highest link utilization increase function, recovers quickly to the highest link utilization
point. This means that link utilization is less sensitive to an point. This means that link utilization is less sensitive to an
active queue management (AQM) target that is lower than the amplitude active queue management (AQM) target that is lower than the amplitude
of the whole sawtooth. of the whole sawtooth.
Similar to Reno, the performance of CUBIC as a loss-based congestion Similar to Reno, the performance of CUBIC as a loss-based congestion
control algorithm suffers in networks where a packet loss is not a control algorithm suffers in networks where packet loss is not a good
good indication of bandwidth utilization, such as wireless or mobile indication of bandwidth utilization, such as wireless or mobile
networks [LIU16]. networks [LIU16].
5.5. Protection against Congestion Collapse 5.5. Protection against Congestion Collapse
With regard to the potential of causing congestion collapse, CUBIC With regard to the potential of causing congestion collapse, CUBIC
behaves like Reno, since CUBIC modifies only the window adjustment behaves like Reno, since CUBIC modifies only the window adjustment
algorithm of Reno. Thus, it does not modify the ACK clocking and algorithm of Reno. Thus, it does not modify the ACK clocking and
timeout behaviors of Reno. timeout behaviors of Reno.
CUBIC also satisfies the "full backoff" requirement as described in CUBIC also satisfies the "full backoff" requirement as described in
[RFC5033]. After reducing the sending rate to one packet per RTT in [RFC5033]. After reducing the sending rate to one packet per RTT in
response to congestion events due to ECN-Echo ACKs, CUBIC then response to congestion events detected by ECN-Echo ACKs, CUBIC then
exponentially increases the transmission timer for each packet exponentially increases the transmission timer for each packet
retransmission while congestion persists. retransmission while congestion persists.
5.6. Fairness within the Alternative Congestion Control Algorithm 5.6. Fairness within the Alternative Congestion Control Algorithm
CUBIC ensures convergence of competing CUBIC flows with the same RTT CUBIC ensures convergence of competing CUBIC flows with the same RTT
in the same bottleneck links to an equal throughput. When competing in the same bottleneck links to an equal throughput. When competing
flows have different RTT values, their throughput ratio is linearly flows have different RTT values, their throughput ratio is linearly
proportional to the inverse of their RTT ratios. This is true proportional to the inverse of their RTT ratios. This is true and is
independently of the level of statistical multiplexing on the link. independent of the level of statistical multiplexing on the link.
The convergence time depends on the network environments (e.g., The convergence time depends on the network environments (e.g.,
bandwidth, RTT) and the level of statistical multiplexing, as bandwidth, RTT) and the level of statistical multiplexing, as
mentioned in Section 3.4. mentioned in Section 3.4.
5.7. Performance with Misbehaving Nodes and Outside Attackers 5.7. Performance with Misbehaving Nodes and Outside Attackers
CUBIC does not introduce new entities or signals, so its CUBIC does not introduce new entities or signals, so its
vulnerability to misbehaving nodes or attackers is unchanged from vulnerability to misbehaving nodes or attackers is unchanged from
Reno. Reno.
5.8. Behavior for Application-Limited Flows 5.8. Behavior for Application-Limited Flows
A flow is application-limited if it is currently sending less than A flow is application limited if it is currently sending less than
what is allowed by the congestion window. This can happen if the what is allowed by the congestion window. This can happen if the
flow is limited by either the sender application or the receiver flow is limited by either the sender application or the receiver
application (via the receiver advertised window) and thus sends less application (via the receiver's advertised window) and thus sends
data than what is allowed by the sender's congestion window. less data than what is allowed by the sender's congestion window.
CUBIC does not increase its congestion window if a flow is CUBIC does not increase its congestion window if a flow is
application-limited. Section 4.2 requires that _t_ in Figure 1 does application limited. Per Section 4.2, it is required that _t_ in
not include application-limited periods, such as idle periods, Figure 1 not include application-limited periods, such as idle
otherwise W_cubic(_t_) might be very high after restarting from these periods; otherwise, W_cubic(_t_) might be very high after restarting
periods. from these periods.
5.9. Responses to Sudden or Transient Events 5.9. Responses to Sudden or Transient Events
If there is a sudden increase in capacity, e.g., due to variable If there is a sudden increase in capacity, e.g., due to variable
radio capacity, a routing change, or a mobility event, CUBIC is radio capacity, a routing change, or a mobility event, CUBIC is
designed to utilize the newly available capacity faster than Reno. designed to utilize the newly available capacity more quickly than
Reno.
On the other hand, if there is a sudden decrease in capacity, CUBIC On the other hand, if there is a sudden decrease in capacity, CUBIC
reduces more slowly than Reno. This remains true regardless of reduces more slowly than Reno. This remains true regardless of
whether CUBIC is in Reno-friendly mode and regardless of whether fast whether CUBIC is in Reno-friendly mode and regardless of whether fast
convergence is enabled. convergence is enabled.
5.10. Incremental Deployment 5.10. Incremental Deployment
CUBIC requires only changes to the congestion control at the sender, CUBIC requires only changes to congestion control at the sender, and
and it does not require any changes at receivers. That is, a CUBIC it does not require any changes at receivers. That is, a CUBIC
sender works correctly with Reno receivers. In addition, CUBIC does sender works correctly with Reno receivers. In addition, CUBIC does
not require any changes to routers and does not require any not require any changes to routers and does not require any
assistance from routers. assistance from routers.
6. Security Considerations 6. Security Considerations
CUBIC makes no changes to the underlying security of a transport CUBIC makes no changes to the underlying security of a transport
protocol and inherits the general security concerns described in protocol and inherits the general security concerns described in
[RFC5681]. Specifically, changing the window computation on the [RFC5681]. Specifically, changing the window computation on the
sender may allow an attacker, through dropping or injecting ACKs (as sender may allow an attacker, through dropping or injecting ACKs (as
described in [RFC5681]), to either force the CUBIC implementation to described in [RFC5681]), to either force the CUBIC implementation to
reduce its bandwidth, or to convince it that there is no congestion reduce its bandwidth or convince it that there is no congestion when
when congestion does exist, and use the CUBIC implementation as an congestion does exist, and to use the CUBIC implementation as an
attack vector against other hosts. These attacks are not new to attack vector against other hosts. These attacks are not new to
CUBIC and are inherently part of any transport protocol like TCP. CUBIC and are inherently part of any transport protocol like TCP.
7. IANA Considerations 7. IANA Considerations
This document does not require any IANA actions. This document does not require any IANA actions.
8. References 8. References
8.1. Normative References 8.1. Normative References
[I-D.ietf-tcpm-hystartplusplus]
Balasubramanian, P., Huang, Y., and M. Olson, "HyStart++:
Modified Slow Start for TCP", Work in Progress, Internet-
Draft, draft-ietf-tcpm-hystartplusplus-13, 30 January
2023, <https://datatracker.ietf.org/doc/html/draft-ietf-
tcpm-hystartplusplus-13>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997, DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/rfc/rfc2119>. <https://www.rfc-editor.org/info/rfc2119>.
[RFC2883] Floyd, S., Mahdavi, J., Mathis, M., and M. Podolsky, "An [RFC2883] Floyd, S., Mahdavi, J., Mathis, M., and M. Podolsky, "An
Extension to the Selective Acknowledgement (SACK) Option Extension to the Selective Acknowledgement (SACK) Option
for TCP", RFC 2883, DOI 10.17487/RFC2883, July 2000, for TCP", RFC 2883, DOI 10.17487/RFC2883, July 2000,
<https://www.rfc-editor.org/rfc/rfc2883>. <https://www.rfc-editor.org/info/rfc2883>.
[RFC2914] Floyd, S., "Congestion Control Principles", BCP 41, [RFC2914] Floyd, S., "Congestion Control Principles", BCP 41,
RFC 2914, DOI 10.17487/RFC2914, September 2000, RFC 2914, DOI 10.17487/RFC2914, September 2000,
<https://www.rfc-editor.org/rfc/rfc2914>. <https://www.rfc-editor.org/info/rfc2914>.
[RFC3168] Ramakrishnan, K., Floyd, S., and D. Black, "The Addition [RFC3168] Ramakrishnan, K., Floyd, S., and D. Black, "The Addition
of Explicit Congestion Notification (ECN) to IP", of Explicit Congestion Notification (ECN) to IP",
RFC 3168, DOI 10.17487/RFC3168, September 2001, RFC 3168, DOI 10.17487/RFC3168, September 2001,
<https://www.rfc-editor.org/rfc/rfc3168>. <https://www.rfc-editor.org/info/rfc3168>.
[RFC4015] Ludwig, R. and A. Gurtov, "The Eifel Response Algorithm [RFC4015] Ludwig, R. and A. Gurtov, "The Eifel Response Algorithm
for TCP", RFC 4015, DOI 10.17487/RFC4015, February 2005, for TCP", RFC 4015, DOI 10.17487/RFC4015, February 2005,
<https://www.rfc-editor.org/rfc/rfc4015>. <https://www.rfc-editor.org/info/rfc4015>.
[RFC5033] Floyd, S. and M. Allman, "Specifying New Congestion [RFC5033] Floyd, S. and M. Allman, "Specifying New Congestion
Control Algorithms", BCP 133, RFC 5033, Control Algorithms", BCP 133, RFC 5033,
DOI 10.17487/RFC5033, August 2007, DOI 10.17487/RFC5033, August 2007,
<https://www.rfc-editor.org/rfc/rfc5033>. <https://www.rfc-editor.org/info/rfc5033>.
[RFC5348] Floyd, S., Handley, M., Padhye, J., and J. Widmer, "TCP [RFC5348] Floyd, S., Handley, M., Padhye, J., and J. Widmer, "TCP
Friendly Rate Control (TFRC): Protocol Specification", Friendly Rate Control (TFRC): Protocol Specification",
RFC 5348, DOI 10.17487/RFC5348, September 2008, RFC 5348, DOI 10.17487/RFC5348, September 2008,
<https://www.rfc-editor.org/rfc/rfc5348>. <https://www.rfc-editor.org/info/rfc5348>.
[RFC5681] Allman, M., Paxson, V., and E. Blanton, "TCP Congestion [RFC5681] Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
Control", RFC 5681, DOI 10.17487/RFC5681, September 2009, Control", RFC 5681, DOI 10.17487/RFC5681, September 2009,
<https://www.rfc-editor.org/rfc/rfc5681>. <https://www.rfc-editor.org/info/rfc5681>.
[RFC5682] Sarolahti, P., Kojo, M., Yamamoto, K., and M. Hata, [RFC5682] Sarolahti, P., Kojo, M., Yamamoto, K., and M. Hata,
"Forward RTO-Recovery (F-RTO): An Algorithm for Detecting "Forward RTO-Recovery (F-RTO): An Algorithm for Detecting
Spurious Retransmission Timeouts with TCP", RFC 5682, Spurious Retransmission Timeouts with TCP", RFC 5682,
DOI 10.17487/RFC5682, September 2009, DOI 10.17487/RFC5682, September 2009,
<https://www.rfc-editor.org/rfc/rfc5682>. <https://www.rfc-editor.org/info/rfc5682>.
[RFC6298] Paxson, V., Allman, M., Chu, J., and M. Sargent, [RFC6298] Paxson, V., Allman, M., Chu, J., and M. Sargent,
"Computing TCP's Retransmission Timer", RFC 6298, "Computing TCP's Retransmission Timer", RFC 6298,
DOI 10.17487/RFC6298, June 2011, DOI 10.17487/RFC6298, June 2011,
<https://www.rfc-editor.org/rfc/rfc6298>. <https://www.rfc-editor.org/info/rfc6298>.
[RFC6582] Henderson, T., Floyd, S., Gurtov, A., and Y. Nishida, "The [RFC6582] Henderson, T., Floyd, S., Gurtov, A., and Y. Nishida, "The
NewReno Modification to TCP's Fast Recovery Algorithm", NewReno Modification to TCP's Fast Recovery Algorithm",
RFC 6582, DOI 10.17487/RFC6582, April 2012, RFC 6582, DOI 10.17487/RFC6582, April 2012,
<https://www.rfc-editor.org/rfc/rfc6582>. <https://www.rfc-editor.org/info/rfc6582>.
[RFC6675] Blanton, E., Allman, M., Wang, L., Jarvinen, I., Kojo, M., [RFC6675] Blanton, E., Allman, M., Wang, L., Jarvinen, I., Kojo, M.,
and Y. Nishida, "A Conservative Loss Recovery Algorithm and Y. Nishida, "A Conservative Loss Recovery Algorithm
Based on Selective Acknowledgment (SACK) for TCP", Based on Selective Acknowledgment (SACK) for TCP",
RFC 6675, DOI 10.17487/RFC6675, August 2012, RFC 6675, DOI 10.17487/RFC6675, August 2012,
<https://www.rfc-editor.org/rfc/rfc6675>. <https://www.rfc-editor.org/info/rfc6675>.
[RFC7567] Baker, F., Ed. and G. Fairhurst, Ed., "IETF [RFC7567] Baker, F., Ed. and G. Fairhurst, Ed., "IETF
Recommendations Regarding Active Queue Management", Recommendations Regarding Active Queue Management",
BCP 197, RFC 7567, DOI 10.17487/RFC7567, July 2015, BCP 197, RFC 7567, DOI 10.17487/RFC7567, July 2015,
<https://www.rfc-editor.org/rfc/rfc7567>. <https://www.rfc-editor.org/info/rfc7567>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/rfc/rfc8174>. May 2017, <https://www.rfc-editor.org/info/rfc8174>.
[RFC8985] Cheng, Y., Cardwell, N., Dukkipati, N., and P. Jha, "The [RFC8985] Cheng, Y., Cardwell, N., Dukkipati, N., and P. Jha, "The
RACK-TLP Loss Detection Algorithm for TCP", RFC 8985, RACK-TLP Loss Detection Algorithm for TCP", RFC 8985,
DOI 10.17487/RFC8985, February 2021, DOI 10.17487/RFC8985, February 2021,
<https://www.rfc-editor.org/rfc/rfc8985>. <https://www.rfc-editor.org/info/rfc8985>.
[RFC9002] Iyengar, J., Ed. and I. Swett, Ed., "QUIC Loss Detection [RFC9002] Iyengar, J., Ed. and I. Swett, Ed., "QUIC Loss Detection
and Congestion Control", RFC 9002, DOI 10.17487/RFC9002, and Congestion Control", RFC 9002, DOI 10.17487/RFC9002,
May 2021, <https://www.rfc-editor.org/rfc/rfc9002>. May 2021, <https://www.rfc-editor.org/info/rfc9002>.
[RFC9406] Balasubramanian, P., Huang, Y., and M. Olson, "HyStart++:
Modified Slow Start for TCP", RFC 9406,
DOI 10.17487/RFC9406, May 2023,
<https://www.rfc-editor.org/info/rfc9406>.
8.2. Informative References 8.2. Informative References
[AIMD-friendliness] [AIMD-friendliness]
Briscoe, B. and O. Albisser, "Friendliness between AIMD Briscoe, B. and O. Albisser, "Friendliness between AIMD
Algorithms", RFC Editor, please replace this URL with the Algorithms", DOI 10.48550/arXiv.2305.10581, May 2023,
permanent arXiv one , 8 August 2022, <https://arxiv.org/abs/2305.10581>.
<https://raw.githubusercontent.com/bbriscoe/cubic-
reno/main/creno_tr.pdf>.
[BSCLU13] Belhareth, S., Sassatelli, L., Collange, D., Lopez- [BSCLU13] Belhareth, S., Sassatelli, L., Collange, D., Lopez-
Pacheco, D., and G. Urvoy-Keller, "Understanding TCP cubic Pacheco, D., and G. Urvoy-Keller, "Understanding TCP cubic
performance in the cloud: A mean-field approach", 2013 performance in the cloud: A mean-field approach", 2013
IEEE 2nd International Conference on Cloud IEEE 2nd International Conference on Cloud Networking
Networking (CloudNet), DOI 10.1109/cloudnet.2013.6710576, (CloudNet), DOI 10.1109/cloudnet.2013.6710576, November
November 2013, 2013, <https://doi.org/10.1109/cloudnet.2013.6710576>.
<https://doi.org/10.1109/cloudnet.2013.6710576>.
[CEHRX09] Cai, H., Eun, D., Ha, S., Rhee, I., and L. Xu, "Stochastic [CEHRX09] Cai, H., Eun, D., Ha, S., Rhee, I., and L. Xu, "Stochastic
convex ordering for multiplicative decrease internet convex ordering for multiplicative decrease internet
congestion control", Computer Networks vol. 53, no. 3, pp. congestion control", Computer Networks, vol. 53, no. 3,
365-381, DOI 10.1016/j.comnet.2008.10.012, February 2009, pp. 365-381, DOI 10.1016/j.comnet.2008.10.012, February
<https://doi.org/10.1016/j.comnet.2008.10.012>. 2009, <https://doi.org/10.1016/j.comnet.2008.10.012>.
[FHP00] Floyd, S., Handley, M., and J. Padhye, "A Comparison of [FHP00] Floyd, S., Handley, M., and J. Padhye, "A Comparison of
Equation-Based and AIMD Congestion Control", May 2000, Equation-Based and AIMD Congestion Control", May 2000,
<https://www.icir.org/tfrc/aimd.pdf>. <https://www.icir.org/tfrc/aimd.pdf>.
[GV02] Gorinsky, S. and H. Vin, "Extended Analysis of Binary [GV02] Gorinsky, S. and H. Vin, "Extended Analysis of Binary
Adjustment Algorithms", Technical Report TR2002-29, Adjustment Algorithms", Technical Report TR2002-39,
Department of Computer Sciences, The University of Department of Computer Sciences, The University of Texas
Texas at Austin, 11 August 2002, at Austin, August 2002, <https://citeseerx.ist.psu.edu/doc
<https://www.cs.utexas.edu/ftp/techreports/tr02-39.ps.gz>. ument?repid=rep1&type=pdf&doi=1828bdcef118b02d3996b8e00b8a
aa92b50abb0f>.
[H16] Ha, S., "Simulation, Testbed, and Deployment Testing [H16] Ha, S., "Deployment, Testbed, and Simulation Results for
Results of CUBIC", 3 November 2016, CUBIC", Wayback Machine archive, 3 November 2016,
<https://web.archive.org/web/20161118125842/ <https://web.archive.org/web/20161118125842/
http://netsrv.csc.ncsu.edu/wiki/index.php/TCP_Testing>. http://netsrv.csc.ncsu.edu/wiki/index.php/TCP_Testing>.
[HLRX07] Ha, S., Le, L., Rhee, I., and L. Xu, "Impact of background [HLRX07] Ha, S., Le, L., Rhee, I., and L. Xu, "Impact of background
traffic on performance of high-speed TCP variant traffic on performance of high-speed TCP variant
protocols", Computer Networks vol. 51, no. 7, pp. protocols", Computer Networks, vol. 51, no. 7, pp.
1748-1762, DOI 10.1016/j.comnet.2006.11.005, May 2007, 1748-1762, DOI 10.1016/j.comnet.2006.11.005, May 2007,
<https://doi.org/10.1016/j.comnet.2006.11.005>. <https://doi.org/10.1016/j.comnet.2006.11.005>.
[HR11] Ha, S. and I. Rhee, "Taming the elephants: New TCP slow [HR11] Ha, S. and I. Rhee, "Taming the elephants: New TCP slow
start", Computer Networks vol. 55, no. 9, pp. 2092-2110, start", Computer Networks, vol. 55, no. 9, pp. 2092-2110,
DOI 10.1016/j.comnet.2011.01.014, June 2011, DOI 10.1016/j.comnet.2011.01.014, June 2011,
<https://doi.org/10.1016/j.comnet.2011.01.014>. <https://doi.org/10.1016/j.comnet.2011.01.014>.
[HRX08] Ha, S., Rhee, I., and L. Xu, "CUBIC: a new TCP-friendly [HRX08] Ha, S., Rhee, I., and L. Xu, "CUBIC: a new TCP-friendly
high-speed TCP variant", ACM SIGOPS Operating Systems high-speed TCP variant", ACM SIGOPS Operating Systems
Review vol. 42, no. 5, pp. 64-74, Review, vol. 42, no. 5, pp. 64-74,
DOI 10.1145/1400097.1400105, July 2008, DOI 10.1145/1400097.1400105, July 2008,
<https://doi.org/10.1145/1400097.1400105>. <https://doi.org/10.1145/1400097.1400105>.
[K03] Kelly, T., "Scalable TCP: improving performance in [K03] Kelly, T., "Scalable TCP: improving performance in
highspeed wide area networks", ACM SIGCOMM Computer highspeed wide area networks", ACM SIGCOMM Computer
Communication Review vol. 33, no. 2, pp. 83-91, Communication Review, vol. 33, no. 2, pp. 83-91,
DOI 10.1145/956981.956989, April 2003, DOI 10.1145/956981.956989, April 2003,
<https://doi.org/10.1145/956981.956989>. <https://doi.org/10.1145/956981.956989>.
[LBEWK16] Lukaseder, T., Bradatsch, L., Erb, B., Van Der Heijden, [LBEWK16] Lukaseder, T., Bradatsch, L., Erb, B., Van Der Heijden,
R., and F. Kargl, "A Comparison of TCP Congestion Control R., and F. Kargl, "A Comparison of TCP Congestion Control
Algorithms in 10G Networks", 2016 IEEE 41st Conference on Algorithms in 10G Networks", 2016 IEEE 41st Conference on
Local Computer Networks (LCN), DOI 10.1109/lcn.2016.121, Local Computer Networks (LCN), DOI 10.1109/lcn.2016.121,
November 2016, <https://doi.org/10.1109/lcn.2016.121>. November 2016, <https://doi.org/10.1109/lcn.2016.121>.
[LIU16] Liu, K. and J. Lee, "On Improving TCP Performance over [LIU16] Liu, K. and J. Lee, "On Improving TCP Performance over
Mobile Data Networks", IEEE Transactions on Mobile Mobile Data Networks", IEEE Transactions on Mobile
Computing vol. 15, no. 10, pp. 2522-2536, Computing, vol. 15, no. 10, pp. 2522-2536,
DOI 10.1109/tmc.2015.2500227, October 2016, DOI 10.1109/tmc.2015.2500227, October 2016,
<https://doi.org/10.1109/tmc.2015.2500227>. <https://doi.org/10.1109/tmc.2015.2500227>.
[RFC3522] Ludwig, R. and M. Meyer, "The Eifel Detection Algorithm [RFC3522] Ludwig, R. and M. Meyer, "The Eifel Detection Algorithm
for TCP", RFC 3522, DOI 10.17487/RFC3522, April 2003, for TCP", RFC 3522, DOI 10.17487/RFC3522, April 2003,
<https://www.rfc-editor.org/rfc/rfc3522>. <https://www.rfc-editor.org/info/rfc3522>.
[RFC3649] Floyd, S., "HighSpeed TCP for Large Congestion Windows", [RFC3649] Floyd, S., "HighSpeed TCP for Large Congestion Windows",
RFC 3649, DOI 10.17487/RFC3649, December 2003, RFC 3649, DOI 10.17487/RFC3649, December 2003,
<https://www.rfc-editor.org/rfc/rfc3649>. <https://www.rfc-editor.org/info/rfc3649>.
[RFC3708] Blanton, E. and M. Allman, "Using TCP Duplicate Selective [RFC3708] Blanton, E. and M. Allman, "Using TCP Duplicate Selective
Acknowledgement (DSACKs) and Stream Control Transmission Acknowledgement (DSACKs) and Stream Control Transmission
Protocol (SCTP) Duplicate Transmission Sequence Numbers Protocol (SCTP) Duplicate Transmission Sequence Numbers
(TSNs) to Detect Spurious Retransmissions", RFC 3708, (TSNs) to Detect Spurious Retransmissions", RFC 3708,
DOI 10.17487/RFC3708, February 2004, DOI 10.17487/RFC3708, February 2004,
<https://www.rfc-editor.org/rfc/rfc3708>. <https://www.rfc-editor.org/info/rfc3708>.
[RFC3742] Floyd, S., "Limited Slow-Start for TCP with Large [RFC3742] Floyd, S., "Limited Slow-Start for TCP with Large
Congestion Windows", RFC 3742, DOI 10.17487/RFC3742, March Congestion Windows", RFC 3742, DOI 10.17487/RFC3742, March
2004, <https://www.rfc-editor.org/rfc/rfc3742>. 2004, <https://www.rfc-editor.org/info/rfc3742>.
[RFC6937] Mathis, M., Dukkipati, N., and Y. Cheng, "Proportional [RFC6937] Mathis, M., Dukkipati, N., and Y. Cheng, "Proportional
Rate Reduction for TCP", RFC 6937, DOI 10.17487/RFC6937, Rate Reduction for TCP", RFC 6937, DOI 10.17487/RFC6937,
May 2013, <https://www.rfc-editor.org/rfc/rfc6937>. May 2013, <https://www.rfc-editor.org/info/rfc6937>.
[RFC7661] Fairhurst, G., Sathiaseelan, A., and R. Secchi, "Updating [RFC7661] Fairhurst, G., Sathiaseelan, A., and R. Secchi, "Updating
TCP to Support Rate-Limited Traffic", RFC 7661, TCP to Support Rate-Limited Traffic", RFC 7661,
DOI 10.17487/RFC7661, October 2015, DOI 10.17487/RFC7661, October 2015,
<https://www.rfc-editor.org/rfc/rfc7661>. <https://www.rfc-editor.org/info/rfc7661>.
[RFC8312] Rhee, I., Xu, L., Ha, S., Zimmermann, A., Eggert, L., and [RFC8312] Rhee, I., Xu, L., Ha, S., Zimmermann, A., Eggert, L., and
R. Scheffenegger, "CUBIC for Fast Long-Distance Networks", R. Scheffenegger, "CUBIC for Fast Long-Distance Networks",
RFC 8312, DOI 10.17487/RFC8312, February 2018, RFC 8312, DOI 10.17487/RFC8312, February 2018,
<https://www.rfc-editor.org/rfc/rfc8312>. <https://www.rfc-editor.org/info/rfc8312>.
[RFC8511] Khademi, N., Welzl, M., Armitage, G., and G. Fairhurst, [RFC8511] Khademi, N., Welzl, M., Armitage, G., and G. Fairhurst,
"TCP Alternative Backoff with ECN (ABE)", RFC 8511, "TCP Alternative Backoff with ECN (ABE)", RFC 8511,
DOI 10.17487/RFC8511, December 2018, DOI 10.17487/RFC8511, December 2018,
<https://www.rfc-editor.org/rfc/rfc8511>. <https://www.rfc-editor.org/info/rfc8511>.
[RFC9000] Iyengar, J., Ed. and M. Thomson, Ed., "QUIC: A UDP-Based [RFC9000] Iyengar, J., Ed. and M. Thomson, Ed., "QUIC: A UDP-Based
Multiplexed and Secure Transport", RFC 9000, Multiplexed and Secure Transport", RFC 9000,
DOI 10.17487/RFC9000, May 2021, DOI 10.17487/RFC9000, May 2021,
<https://www.rfc-editor.org/rfc/rfc9000>. <https://www.rfc-editor.org/info/rfc9000>.
[RFC9260] Stewart, R., Tüxen, M., and K. Nielsen, "Stream Control [RFC9260] Stewart, R., Tüxen, M., and K. Nielsen, "Stream Control
Transmission Protocol", RFC 9260, DOI 10.17487/RFC9260, Transmission Protocol", RFC 9260, DOI 10.17487/RFC9260,
June 2022, <https://www.rfc-editor.org/rfc/rfc9260>. June 2022, <https://www.rfc-editor.org/info/rfc9260>.
[SXEZ19] Sun, W., Xu, L., Elbaum, S., and D. Zhao, "Model-Agnostic [SXEZ19] Sun, W., Xu, L., Elbaum, S., and D. Zhao, "Model-Agnostic
and Efficient Exploration of Numerical Congestion Control and Efficient Exploration of Numerical Congestion Control
State Space of Real-World TCP Implementations", IEEE/ACM State Space of Real-World TCP Implementations", IEEE/ACM
Transactions on Networking vol. 29, no. 5, pp. 1990-2004, Transactions on Networking, vol. 29, no. 5, pp. 1990-2004,
DOI 10.1109/tnet.2021.3078161, October 2021, DOI 10.1109/tnet.2021.3078161, October 2021,
<https://doi.org/10.1109/tnet.2021.3078161>. <https://doi.org/10.1109/tnet.2021.3078161>.
[XHR04] Xu, L., Harfoush, K., and I. Rhee, "Binary increase [XHR04] Xu, L., Harfoush, K., and I. Rhee, "Binary increase
congestion control (BIC) for fast long-distance networks", congestion control (BIC) for fast long-distance networks",
IEEE INFOCOM 2004, DOI 10.1109/infcom.2004.1354672, IEEE INFOCOM 2004, DOI 10.1109/infcom.2004.1354672, March
February 2005, 2004, <https://doi.org/10.1109/infcom.2004.1354672>.
<https://doi.org/10.1109/infcom.2004.1354672>.
Appendix A. Acknowledgments
Richard Scheffenegger and Alexander Zimmermann originally co-authored
[RFC8312].
These individuals suggested improvements to this document:
* Bob Briscoe
* Christian Huitema
* Gorry Fairhurst
* Jonathan Morton
* Juhamatti Kuusisaari
* Junho Choi
* Markku Kojo
* Martin Duke
* Martin Thomson
* Matt Mathis
* Matt Olson
* Michael Welzl
* Mirja Kühlewind
* Mohit P. Tahiliani
* Neal Cardwell
* Praveen Balasubramanian
* Randall Stewart
* Richard Scheffenegger
* Rod Grimes
* Spencer Dawkins
* Tom Henderson
* Tom Petch
* Wesley Rosenblum
* Yoav Nir
* Yoshifumi Nishida
* Yuchung Cheng
Appendix B. Evolution of CUBIC
B.1. Since draft-ietf-tcpm-rfc8312bis-14
* Specify how security considerations of TCP applies to CUBIC.
* Elaborate differences between RFC 5681 and Cubic.
* Tweak math for better plaintext rendering. (#164
(https://github.com/NTAP/rfc8312bis/pull/164))
B.2. Since draft-ietf-tcpm-rfc8312bis-13
* Add contents of https://cse.unl.edu/~xu/avg_cubic_cwnd.pdf to
Appendix C.
* Multiple comments from Martin, define synchronized/asynchronized
loss model, clean up 3465 reference, clarficiation for when Cubic
is not in Reno-friendly region, referring to proof of avg Cubic
window, better text for misbehaving nodes and fix typo in
_cwnd_epoch_. (#158 (https://github.com/NTAP/rfc8312bis/pull/158))
B.3. Since draft-ietf-tcpm-rfc8312bis-12
* Fix plaintext version of Figure 5.
B.4. Since draft-ietf-tcpm-rfc8312bis-11
* Fix various nits. (#157 (https://github.com/NTAP/rfc8312bis/
pull/157))
B.5. Since draft-ietf-tcpm-rfc8312bis-10
* Improve text related to [RFC7661]. (#149
(https://github.com/NTAP/rfc8312bis/issues/149))
* Made variable naming a bit more consistent. (#156
(https://github.com/NTAP/rfc8312bis/pull/156))
B.6. Since draft-ietf-tcpm-rfc8312bis-09
* Improve text for Reno friendliness, multiplicative decrease and
reference to HLRX07. (#152 (https://github.com/NTAP/rfc8312bis/
pull/152))
B.7. Since draft-ietf-tcpm-rfc8312bis-08
* Fix the text specifying when alpha_cubic SHOULD be set to 1 to
indicate this should happen when cwnd >= cwnd_prior rather than
cwnd >= W_max, since these are different in the fast convergence
case (#146 (https://github.com/NTAP/rfc8312bis/pull/146))
* Restrict use of _cwnd_ directly on a congestion event (#148
(https://github.com/NTAP/rfc8312bis/pull/148))
B.8. Since draft-ietf-tcpm-rfc8312bis-07
* Document the WG discussion and decision around [RFC5033] and
[RFC2914] (#145 (https://github.com/NTAP/rfc8312bis/pull/145))
B.9. Since draft-ietf-tcpm-rfc8312bis-06
* RFC7661 is safe even when cwnd grows beyond rwnd (#143
(https://github.com/NTAP/rfc8312bis/issues/143))
B.10. Since draft-ietf-tcpm-rfc8312bis-05
* Clarify meaning of "application-limited" in Section 5.8 (#137
(https://github.com/NTAP/rfc8312bis/issues/137))
* Create new subsections for spurious timeouts and spurious loss via
ACK (#90 (https://github.com/NTAP/rfc8312bis/issues/90))
* Brief discussion of convergence in Section 5.6 (#96
(https://github.com/NTAP/rfc8312bis/issues/96))
* Add more test results to Section 5 and update some references (#91
(https://github.com/NTAP/rfc8312bis/issues/91))
* Change wording around setting ssthresh (#131
(https://github.com/NTAP/rfc8312bis/issues/131))
B.11. Since draft-ietf-tcpm-rfc8312bis-04
* Fix incorrect math (#106 (https://github.com/NTAP/rfc8312bis/
issues/106))
* Update RFC5681 (#99 (https://github.com/NTAP/rfc8312bis/
issues/99))
* Rephrase text around algorithmic alternatives, add HyStart++ (#85
(https://github.com/NTAP/rfc8312bis/issues/85), #86
(https://github.com/NTAP/rfc8312bis/issues/86), #90
(https://github.com/NTAP/rfc8312bis/issues/90))
* Clarify what we mean by "new ACK" and use it in the text in more
places. (#101 (https://github.com/NTAP/rfc8312bis/issues/101))
* Rewrite the Responses to Sudden or Transient Events section (#98
(https://github.com/NTAP/rfc8312bis/issues/98))
* Remove confusing text about _cwnd_epoch_ in Section 4.2 (#100
(https://github.com/NTAP/rfc8312bis/issues/100))
* Change terminology from "AIMD" to "Reno" (#108
(https://github.com/NTAP/rfc8312bis/issues/108))
* Moved MUST NOT from app-limited section to main cubic AI section
(#97 (https://github.com/NTAP/rfc8312bis/issues/97))
* Clarify cwnd decrease during multiplicative decrease (#102
(https://github.com/NTAP/rfc8312bis/issues/102))
* Clarify text around queuing and slow adaptation of CUBIC in
wireless environments (#94 (https://github.com/NTAP/rfc8312bis/
issues/94))
* Set lower bound of cwnd to 1 MSS and use retransmit timer
thereafter (#83 (https://github.com/NTAP/rfc8312bis/issues/83))
* Use FlightSize instead of cwnd to update ssthresh (#114
(https://github.com/NTAP/rfc8312bis/issues/114))
B.12. Since draft-ietf-tcpm-rfc8312bis-03
* Remove reference from abstract (#82
(https://github.com/NTAP/rfc8312bis/pull/82))
B.13. Since draft-ietf-tcpm-rfc8312bis-02
* Description of packet loss rate _p_ (#65
(https://github.com/NTAP/rfc8312bis/issues/65))
* Clarification of TCP Friendly Equation for ABC and Delayed ACK
(#66 (https://github.com/NTAP/rfc8312bis/issues/66))
* add applicability to QUIC and SCTP (#61
(https://github.com/NTAP/rfc8312bis/issues/61))
* clarity on setting alpha__aimd_ to 1 (#68
(https://github.com/NTAP/rfc8312bis/issues/68))
* introduce alpha__cubic_ (#64 (https://github.com/NTAP/rfc8312bis/
issues/64))
* clarify _cwnd_ growth in convex region (#69
(https://github.com/NTAP/rfc8312bis/issues/69))
* add guidance for using bytes and mention that segments count is
decimal (#67 (https://github.com/NTAP/rfc8312bis/issues/67))
* add loss events detected by RACK and QUIC loss detection (#62
(https://github.com/NTAP/rfc8312bis/issues/62))
B.14. Since draft-ietf-tcpm-rfc8312bis-01
* address Michael Scharf's editorial suggestions. (#59
(https://github.com/NTAP/rfc8312bis/issues/59))
* add "Note to the RFC Editor" about removing underscores
B.15. Since draft-ietf-tcpm-rfc8312bis-00
* use updated xml2rfc with better text rendering of subscripts
B.16. Since draft-eggert-tcpm-rfc8312bis-03
* fix spelling nits
* rename to draft-ietf
* define _W_max_ more clearly
B.17. Since draft-eggert-tcpm-rfc8312bis-02
* add definition for segments_acked and alpha__aimd_. (#47
(https://github.com/NTAP/rfc8312bis/issues/47))
* fix a mistake in _W_max_ calculation in the fast convergence
section. (#51 (https://github.com/NTAP/rfc8312bis/issues/51))
* clarity on setting _ssthresh_ and _cwnd_epoch_ during
multiplicative decrease. (#53 (https://github.com/NTAP/rfc8312bis/
issues/53))
B.18. Since draft-eggert-tcpm-rfc8312bis-01
* rename TCP-Friendly to AIMD-Friendly and rename Standard TCP to
AIMD TCP to avoid confusion as CUBIC has been widely used on the
Internet. (#38 (https://github.com/NTAP/rfc8312bis/issues/38))
* change introductory text to reflect the significant broader
deployment of CUBIC on the Internet. (#39
(https://github.com/NTAP/rfc8312bis/issues/39))
* rephrase introduction to avoid referring to variables that have
not been defined yet.
B.19. Since draft-eggert-tcpm-rfc8312bis-00
* acknowledge former co-authors (#15
(https://github.com/NTAP/rfc8312bis/issues/15))
* prevent _cwnd_ from becoming less than two (#7
(https://github.com/NTAP/rfc8312bis/issues/7))
* add list of variables and constants (#5
(https://github.com/NTAP/rfc8312bis/issues/5), #6
(https://github.com/NTAP/rfc8312bis/issues/6))
* update _K_'s definition and add bounds for CUBIC _target_ _cwnd_
[SXEZ19] (#1 (https://github.com/NTAP/rfc8312bis/issues/1), #14
(https://github.com/NTAP/rfc8312bis/issues/14))
* update _W_est_ to use AIMD approach (#20
(https://github.com/NTAP/rfc8312bis/issues/20))
* set alpha__aimd_ to 1 once _W_est_ reaches _W_max_ (#2
(https://github.com/NTAP/rfc8312bis/issues/2))
* add Vidhi as co-author (#17 (https://github.com/NTAP/rfc8312bis/
issues/17))
* note for Fast Recovery during _cwnd_ decrease due to congestion
event (#11 (https://github.com/NTAP/rfc8312bis/issues/11))
* add section for spurious congestion events (#23
(https://github.com/NTAP/rfc8312bis/issues/23))
* initialize _W_est_ after timeout and remove variable
_W_(last_max)_ (#28 (https://github.com/NTAP/rfc8312bis/
issues/28))
B.20. Since RFC8312
* converted to Markdown and xml2rfc v3
* updated references (as part of the conversion)
* updated author information
* various formatting changes
* move to Standards Track
B.21. Since the Original Paper Appendix A. Evolution of CUBIC since the Original Paper
CUBIC has gone through a few changes since the initial release CUBIC has gone through a few changes since the initial release
[HRX08] of its algorithm and implementation. This section highlights [HRX08] of its algorithm and implementation. This appendix
the differences between the original paper and [RFC8312]. highlights the differences between the original paper and [RFC8312].
* The original paper [HRX08] includes the pseudocode of CUBIC * The original paper [HRX08] includes the pseudocode of CUBIC
implementation using Linux's pluggable congestion control implementation using Linux's pluggable congestion control
framework, which excludes system-specific optimizations. The framework, which excludes system-specific optimizations. The
simplified pseudocode might be a good source to start with and simplified pseudocode might be a good starting point for learning
understand CUBIC. about CUBIC.
* [HRX08] also includes experimental results showing its performance * [HRX08] also includes experimental results showing its performance
and fairness. and fairness.
* The definition of beta__cubic_ constant was changed in [RFC8312]. * The definition of the β__cubic_ constant was changed in [RFC8312].
For example, beta__cubic_ in the original paper was the window For example, β__cubic_ in the original paper was referred to as
decrease constant while [RFC8312] changed it to CUBIC the window decrease constant, while [RFC8312] changed it to "CUBIC
multiplication decrease factor. With this change, the current multiplicative decrease factor". With this change, the current
congestion window size after a congestion event in [RFC8312] was congestion window size after a congestion event as listed in
beta__cubic_ * _W_max_ while it was (1-beta__cubic_) * _W_max_ in [RFC8312] was β__cubic_ * _W_max_, while it was (1-β__cubic_) *
the original paper. _W_max_ in the original paper.
* Its pseudocode used _W_(last_max)_ while [RFC8312] used _W_max_. * Its pseudocode used _W_(last_max)_, while [RFC8312] used _W_max_.
* Its AIMD-friendly window was _W_tcp_ while [RFC8312] used _W_est_. * Its AIMD-friendly window was _W_tcp_, while [RFC8312] used
_W_est_.
Appendix C. Proof of the Average CUBIC Window Size Appendix B. Proof of the Average CUBIC Window Size
This appendix contains a proof for the average CUBIC window size This appendix contains a proof for the average CUBIC window size
_AVG_W_cubic_ in Figure 6. _AVG_W_cubic_ in Figure 6.
We find _AVG_W_cubic_ under a deterministic loss model, where the We find _AVG_W_cubic_ under a deterministic loss model, where the
number of packets between two successive packet losses is 1/_p_. With number of packets between two successive packet losses is
this model, CUBIC always operates with the concave window profile and 1/_p_. With this model, CUBIC always operates with the concave
the time period between two successive packet losses is _K_. window profile and the time period between two successive packet
losses is _K_.
The average window size _AVG_W_cubic_ is defined as follows, where The average window size _AVG_W_cubic_ is defined as follows, where
the numerator 1/_p_ is the total number of packets between two the numerator 1/_p_ is the total number of packets between two
successive packet losses, and the denominator _K_/_RTT_ is the total successive packet losses and the denominator _K_/_RTT_ is the total
number of RTTs between two successive packet losses. number of RTTs between two successive packet losses.
1 1
─ ─
p p
AVG_W = ─── AVG_W = ───
cubic K cubic K
─── ───
RTT RTT
Figure 9 Figure 9
Below, we find _K_ as a function of CUBIC parameters β__cubic_ and Below, we find _K_ as a function of CUBIC parameters β__cubic_ and
_C_, and network parameters _p_ and _RTT_. According to the _C_, and network parameters _p_ and _RTT_. According to the
definition of _K_ in Figure 2, we have definition of _K_ in Figure 2, we have
┌────────────────────┐ ┌────────────────────┐
3 │W - W * β 3 │W - W * β
╲ │ max max cubic ╲ │ max max cubic
K = ╲ │──────────────────── K = ╲ │────────────────────
╲│ C ╲│ C
Figure 10 Figure 10
The total number of packets between two successive packet losses can The total number of packets between two successive packet losses can
also be obtained as follows using the window increase function in also be obtained as follows, using the window increase function in
Figure 1. Specifically, the window size in the first RTT (i.e., Figure 1. Specifically, the window size in the first RTT (i.e.,
_n_=1 or equivalently _t_=0) is _C_(-_K_)^3+_W_max_ and the window _n_=1, or equivalently, _t_=0) is _C_(-_K_)^3+_W_max_ and the window
size in the last RTT (i.e., _n_=_K_/_RTT_ or equivalently _t_=_K_- size in the last RTT (i.e., _n_=_K_/_RTT_, or equivalently, _t_=_K_-
_RTT_) is _C_(-_RTT_)^3+_W_max_. _RTT_) is _C_(-_RTT_)^3+_W_max_.
K K
─── ───
RTT RTT
⎯⎯ ⎯⎯
1 ╲ ⎛ 3 ⎞ 1 ╲ ⎛ 3 ⎞
─ = ╱ ⎜C((n-1) * RTT-K) + W ⎟ ─ = ╱ ⎜C((n-1) * RTT-K) + W ⎟
p ⎺⎺ ⎝ max⎠ p ⎺⎺ ⎝ max⎠
n=1 n=1
skipping to change at page 39, line 40 skipping to change at line 1466
3 1 ⎛ K ⎞ K 3 1 ⎛ K ⎞ K
≈ -C * RTT * ─ *⎜───⎟ + W * ─── ≈ -C * RTT * ─ *⎜───⎟ + W * ───
4 ⎝RTT⎠ max RTT 4 ⎝RTT⎠ max RTT
4 4
1 K K 1 K K
= -C * ─ * ─── + W * ─── = -C * ─ * ─── + W * ───
4 RTT max RTT 4 RTT max RTT
Figure 11 Figure 11
After solving Figure 10 and Figure 11 for _K_ and _W_max_, we have After solving the equations in Figures 10 and 11 for _K_ and _W_max_,
we have
┌──────────────────────┐ ┌──────────────────────┐
│ 4 * ⎛1-β ⎞ │ 4 * ⎛1-β ⎞
4 │ ⎝ cubic⎠ RTT 4 │ ⎝ cubic⎠ RTT
K = ╲ │──────────────── * ─── K = ╲ │──────────────── * ───
╲ │C * ⎛3 + β ⎞ p ╲ │C * ⎛3 + β ⎞ p
╲│ ⎝ cubic⎠ ╲│ ⎝ cubic⎠
Figure 12 Figure 12
The average CUBIC window size _AVG_W_cubic_ can be obtained by The average CUBIC window size _AVG_W_cubic_ can be obtained by
substituting _K_ with Figure 12 in Figure 9 substituting _K_ from Figure 12 in Figure 9.
1 ┌───────────────────────┐ 1 ┌───────────────────────┐
─ │C * ⎛3 + β ⎞ 3 ─ │C * ⎛3 + β ⎞ 3
p 4 │ ⎝ cubic⎠ RTT p 4 │ ⎝ cubic⎠ RTT
AVG_W = ─── = ╲ │──────────────── * ──── AVG_W = ─── = ╲ │──────────────── * ────
cubic K ╲ │ 4 * ⎛1-β ⎞ 3 cubic K ╲ │ 4 * ⎛1-β ⎞ 3
─── ╲│ ⎝ cubic⎠ p ─── ╲│ ⎝ cubic⎠ p
RTT RTT
Acknowledgments
Richard Scheffenegger and Alexander Zimmermann originally coauthored
[RFC8312].
These individuals suggested improvements to this document:
* Bob Briscoe
* Christian Huitema
* Gorry Fairhurst
* Jonathan Morton
* Juhamatti Kuusisaari
* Junho Choi
* Markku Kojo
* Martin Duke
* Martin Thomson
* Matt Mathis
* Matt Olson
* Michael Welzl
* Mirja Kühlewind
* Mohit P. Tahiliani
* Neal Cardwell
* Praveen Balasubramanian
* Randall Stewart
* Richard Scheffenegger
* Rod Grimes
* Spencer Dawkins
* Tom Henderson
* Tom Petch
* Wesley Rosenblum
* Yoav Nir
* Yoshifumi Nishida
* Yuchung Cheng
Authors' Addresses Authors' Addresses
Lisong Xu Lisong Xu
University of Nebraska-Lincoln University of Nebraska-Lincoln
Department of Computer Science and Engineering Department of Computer Science and Engineering
Lincoln, NE 68588-0115 Lincoln, NE 68588-0115
United States of America United States of America
Email: xu@unl.edu Email: xu@unl.edu
URI: https://cse.unl.edu/~xu/ URI: https://cse.unl.edu/~xu/
Sangtae Ha Sangtae Ha
University of Colorado at Boulder University of Colorado at Boulder
Department of Computer Science Department of Computer Science
Boulder, CO 80309-0430 Boulder, CO 80309-0430
United States of America United States of America
Email: sangtae.ha@colorado.edu Email: sangtae.ha@colorado.edu
URI: https://netstech.org/sangtaeha/ URI: https://netstech.org/sangtaeha/
Injong Rhee Injong Rhee
Bowery Farming Bowery Farming
151 W 26TH Street, 12TH Floor 151 W 26th Street, 12th Floor
New York, NY 10001 New York, NY 10001
United States of America United States of America
Email: injongrhee@gmail.com Email: injongrhee@gmail.com
Vidhi Goel Vidhi Goel
Apple Inc. Apple Inc.
One Apple Park Way One Apple Park Way
Cupertino, California 95014 Cupertino, CA 95014
United States of America United States of America
Email: vidhi_goel@apple.com Email: vidhi_goel@apple.com
Lars Eggert (editor) Lars Eggert (editor)
NetApp NetApp
Stenbergintie 12 B Stenbergintie 12 B
FI-02700 Kauniainen FI-02700 Kauniainen
Finland Finland
Email: lars@eggert.org Email: lars@eggert.org
URI: https://eggert.org/ URI: https://eggert.org/
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