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<front> <front>
<title abbrev="TCP CUBIC">CUBIC for Fast and Long-Distance Networks</title> <title abbrev="TCP CUBIC">CUBIC for Fast and Long-Distance Networks</title>
<seriesInfo name="Internet-Draft" value="draft-ietf-tcpm-rfc8312bis-15"/> <seriesInfo name="RFC" value="9438"/>
<author initials="L." surname="Xu" fullname="Lisong Xu"> <author initials="L." surname="Xu" fullname="Lisong Xu">
<organization abbrev="UNL">University of Nebraska-Lincoln</organization> <organization abbrev="UNL">University of Nebraska-Lincoln</organization>
<address> <address>
<postal> <postal>
<street>Department of Computer Science and Engineering</street> <street>Department of Computer Science and Engineering</street>
<city>Lincoln</city> <city>Lincoln</city>
<region>NE</region> <region>NE</region>
<code>68588-0115</code> <code>68588-0115</code>
<country>USA</country> <country>United States of America</country>
</postal> </postal>
<email>xu@unl.edu</email> <email>xu@unl.edu</email>
<uri>https://cse.unl.edu/~xu/</uri> <uri>https://cse.unl.edu/~xu/</uri>
</address> </address>
</author> </author>
<author initials="S." surname="Ha" fullname="Sangtae Ha"> <author initials="S." surname="Ha" fullname="Sangtae Ha">
<organization abbrev="Colorado">University of Colorado at Boulder</organiz ation> <organization abbrev="Colorado">University of Colorado at Boulder</organiz ation>
<address> <address>
<postal> <postal>
<street>Department of Computer Science</street> <street>Department of Computer Science</street>
<city>Boulder</city> <city>Boulder</city>
<region>CO</region> <region>CO</region>
<code>80309-0430</code> <code>80309-0430</code>
<country>USA</country> <country>United States of America</country>
</postal> </postal>
<email>sangtae.ha@colorado.edu</email> <email>sangtae.ha@colorado.edu</email>
<uri>https://netstech.org/sangtaeha/</uri> <uri>https://netstech.org/sangtaeha/</uri>
</address> </address>
</author> </author>
<author initials="I." surname="Rhee" fullname="Injong Rhee"> <author initials="I." surname="Rhee" fullname="Injong Rhee">
<organization abbrev="Bowery">Bowery Farming</organization> <organization abbrev="Bowery">Bowery Farming</organization>
<address> <address>
<postal> <postal>
<street>151 W 26TH Street, 12TH Floor</street> <street>151 W 26th Street, 12th Floor</street>
<city>New York</city> <city>New York</city>
<region>NY</region> <region>NY</region>
<code>10001</code> <code>10001</code>
<country>USA</country> <country>United States of America</country>
</postal> </postal>
<email>injongrhee@gmail.com</email> <email>injongrhee@gmail.com</email>
</address> </address>
</author> </author>
<author initials="V." surname="Goel" fullname="Vidhi Goel"> <author initials="V." surname="Goel" fullname="Vidhi Goel">
<organization>Apple Inc.</organization> <organization>Apple Inc.</organization>
<address> <address>
<postal> <postal>
<street>One Apple Park Way</street> <street>One Apple Park Way</street>
<city>Cupertino</city> <city>Cupertino</city>
<region>California</region> <region>CA</region>
<code>95014</code> <code>95014</code>
<country>USA</country> <country>United States of America</country>
</postal> </postal>
<email>vidhi_goel@apple.com</email> <email>vidhi_goel@apple.com</email>
</address> </address>
</author> </author>
<author initials="L." surname="Eggert" fullname="Lars Eggert" role="editor"> <author initials="L." surname="Eggert" fullname="Lars Eggert" role="editor">
<organization>NetApp</organization> <organization>NetApp</organization>
<address> <address>
<postal> <postal>
<street>Stenbergintie 12 B</street> <street>Stenbergintie 12 B</street>
<city>Kauniainen</city> <city>Kauniainen</city>
<code>02700</code> <code>02700</code>
<country>FI</country> <country>Finland</country>
</postal> </postal>
<email>lars@eggert.org</email> <email>lars@eggert.org</email>
<uri>https://eggert.org/</uri> <uri>https://eggert.org/</uri>
</address> </address>
</author> </author>
<date/> <date year="2023" month="August"/>
<area>Transport</area> <area>tsv</area>
<workgroup>TCPM</workgroup> <workgroup>tcpm</workgroup>
<keyword>Congestion control</keyword>
<keyword>large BDP</keyword>
<keyword>window scalability</keyword>
<keyword>RTT fairness</keyword>
<abstract> <abstract>
<t>CUBIC is a standard TCP congestion control algorithm that uses a cubic <t>CUBIC is a standard TCP congestion control algorithm that uses a cubic
function instead of a linear congestion window increase function function instead of a linear congestion window increase function
to improve scalability and stability over fast and long-distance to improve scalability and stability over fast and long-distance
networks. CUBIC has been adopted as the default TCP congestion control networks. CUBIC has been adopted as the default TCP congestion control
algorithm by the Linux, Windows, and Apple stacks.</t> algorithm by the Linux, Windows, and Apple stacks.</t>
<t>This document updates the specification of CUBIC to include <t>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 Track and obs
obsoleting RFC 8312. This also requires updating RFC 5681, to allow oletes RFC 8312. This document also updates RFC 5681, to allow
for CUBIC's occasionally more aggressive sending behavior.</t> for CUBIC's occasionally more aggressive sending behavior.</t>
</abstract> </abstract>
<note removeInRFC="true">
<name>About This Document</name>
<t>
Status information for this document may be found at <eref target="https
://datatracker.ietf.org/doc/draft-ietf-tcpm-rfc8312bis/"/>.
</t>
<t>
Discussion of this document takes place on the
TCPM Working Group mailing list (<eref target="mailto:tcpm@ietf.org"/>),
which is archived at <eref target="https://mailarchive.ietf.org/arch/bro
wse/tcpm/"/>.
Subscribe at <eref target="https://www.ietf.org/mailman/listinfo/tcpm/"/
>.
</t>
<t>Source for this draft and an issue tracker can be found at
<eref target="https://github.com/NTAP/rfc8312bis"/>.</t>
</note>
<note>
<name>Note to the RFC Editor</name>
<t>xml2rfc currently renders <tt>&lt;em&gt;&lt;/em&gt;</tt> in the XML by
surrounding the
corresponding text with underscores. This is highly distracting;
please manually remove the underscores when doing the final edits to
the text version of this document.</t>
<t>(There is an issue open against xml2rfc to stop doing this in the
future: https://github.com/ietf-tools/xml2rfc/issues/596)</t>
<t>Also, please manually change "Figure" to "Equation" for all artwork
with anchors beginning with "eq" - xml2rfc doesn't seem to be able to
do this.</t>
</note>
</front> </front>
<middle> <middle>
<section anchor="introduction"> <section anchor="introduction">
<name>Introduction</name> <name>Introduction</name>
<t>CUBIC has been adopted as the default TCP congestion control algorithm <t>CUBIC has been adopted as the default TCP congestion control algorithm
in the Linux, Windows, and Apple stacks, and has been used and in the Linux, Windows, and Apple stacks, and has been used and
deployed globally. Extensive, decade-long deployment experience in deployed globally. Extensive, decade-long deployment experience in
vastly different Internet scenarios has convincingly demonstrated 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 <xref target="RFC568 1"/>. It is substantial benefits over classical Reno congestion control <xref target="RFC568 1"/>. It is
therefore to be regarded as the currently most widely deployed therefore to be regarded as the currently most widely deployed
standard for TCP congestion control. CUBIC can also be used for other standard for TCP congestion control. CUBIC can also be used for other
transport protocols such as QUIC <xref target="RFC9000"/> and SCTP <xref target= "RFC9260"/> transport protocols such as QUIC <xref target="RFC9000"/> and the Stream Control Transmission Protocol (SCTP) <xref target="RFC9260"/>
as a default congestion controller.</t> as a default congestion controller.</t>
<t>The design of CUBIC was motivated by the well-documented problem <t>The design of CUBIC was motivated by the well-documented problem
classical Reno TCP has with low utilization over fast and long-distance classical Reno TCP has with low utilization over fast and long-distance
networks <xref target="K03"/><xref target="RFC3649"/>. This problem arises from networks <xref target="K03"/> <xref target="RFC3649"/>. This problem arises from
a slow increase a slow increase
of the congestion window following a congestion event in a network with of the congestion window (cwnd) following a congestion event in a network with
a large bandwidth-delay product (BDP). <xref target="HLRX07"/> indicates that th is a large bandwidth-delay product (BDP). <xref target="HLRX07"/> indicates that th is
problem is frequently observed even in the range of congestion window problem is frequently observed even in the range of congestion window
sizes over several hundreds of packets. This problem is equally sizes over several hundreds of packets. This problem is equally
applicable to all Reno-style standards and their variants, including applicable to all Reno-style standards and their variants, including
TCP-Reno <xref target="RFC5681"/>, TCP-NewReno <xref target="RFC6582"/><xref tar TCP-Reno <xref target="RFC5681"/>, TCP-NewReno <xref target="RFC6582"/> <xref ta
get="RFC6675"/>, SCTP rget="RFC6675"/>, SCTP
<xref target="RFC9260"/>, TFRC <xref target="RFC5348"/>, and QUIC congestion con <xref target="RFC9260"/>, TCP Friendly Rate Control (TFRC) <xref target="RFC5348
trol "/>, and QUIC congestion control
<xref target="RFC9002"/>, which use the same linear increase function for window <xref target="RFC9002"/>, which use the same linear increase function for window
growth. All Reno-style standards and their variants are growth. All Reno-style standards and their variants are
collectively referred to as "Reno" in this document.</t> collectively referred to as "Reno" in this document.</t>
<t>CUBIC, originally proposed in <xref target="HRX08"/>, is a modification to the <t>CUBIC, originally proposed in <xref target="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 linear problem. Specifically, CUBIC uses a cubic function instead of the linear
window increase function of Reno to improve scalability and window increase function of Reno to improve scalability and
stability under fast and long-distance networks.</t> stability under fast and long-distance networks.</t>
<t>This document updates the specification of CUBIC to include algorithmic <t>This document updates the specification of CUBIC to include algorithmic
improvements based on the Linux, Windows, and Apple implementations and improvements based on the Linux, Windows, and Apple implementations and
recent academic work. Based on the extensive deployment experience with recent academic work. Based on the extensive deployment experience with
CUBIC, it also moves the specification to the Standards Track, CUBIC, it also moves the specification to the Standards Track,
obsoleting <xref target="RFC8312"/>. This requires an update to <xref section="3 " sectionFormat="of" target="RFC5681"/>, which obsoleting <xref target="RFC8312"/>. This requires an update to <xref section="3 " sectionFormat="of" target="RFC5681"/>, which
limits the aggressiveness of Reno TCP implementations. limits the aggressiveness of Reno TCP implementations.
Since CUBIC is occasionally more aggressive than the <xref target="RFC5681"/> Since CUBIC is occasionally more aggressive than the algorithms defined in <xref
algorithms, this document updates the first paragraph of <xref section="3" secti target="RFC5681"/>,
onFormat="of" target="RFC5681"/>, replacing it with a normative reference to gui this document updates the first paragraph of <xref section="3" sectionFormat="of
deline (1) " target="RFC5681"/>, replacing it with a normative reference to guideline (1)
in <xref section="3" sectionFormat="of" target="RFC5033"/>, which allows for CUB IC's behavior as defined in <xref section="3" sectionFormat="of" target="RFC5033"/>, which allows for CUB IC's behavior as defined
in this document.</t> in this document.</t>
<t>Specifically, CUBIC may increase the congestion window more aggressivel y than <t>Specifically, CUBIC may increase the congestion window more aggressivel y than
Reno during the congestion avoidance phase. According to <xref target="RFC5681"/ >, Reno during the congestion avoidance phase. According to <xref target="RFC5681"/ >,
during congestion avoidance, the sender must not increment cwnd by more than during congestion avoidance, the sender must not increment cwnd by more than
SMSS bytes once per RTT, whereas CUBIC may increase cwnd much more Sender Maximum Segment Size (SMSS) bytes once per round-trip time (RTT), whereas CUBIC may increase cwnd much more
aggressively. Additionally, CUBIC recommends the HyStart++ aggressively. Additionally, CUBIC recommends the HyStart++
algorithm <xref target="I-D.ietf-tcpm-hystartplusplus"/> for slow start, which a llows for algorithm <xref target="RFC9406"/> for slow start, which allows for
cwnd increases of more than SMSS bytes for incoming acknowledgments during cwnd increases of more than SMSS bytes for incoming acknowledgments during
slow start, while this behavior is not allowed as part of <xref target="RFC5681" slow start, while this behavior is not allowed as part of
/> the standard behavior prescribed by <xref target="RFC5681"/>.</t>
standard.</t>
<t>Binary Increase Congestion Control (BIC-TCP) <xref target="XHR04"/>, a predecessor <t>Binary Increase Congestion Control (BIC-TCP) <xref target="XHR04"/>, a predecessor
of CUBIC, was selected as the default TCP congestion control algorithm of CUBIC, was selected as the default TCP congestion control algorithm
by Linux in the year 2005 and had been used for several years by the by Linux in the year 2005 and had been used for several years by the
Internet community at large.</t> Internet community at large.</t>
<t>CUBIC uses a similar window increase function as BIC-TCP and is <t>CUBIC uses a window increase function similar to BIC-TCP and is
designed to be less aggressive and fairer to Reno in bandwidth designed to be less aggressive and fairer to Reno in bandwidth
usage than BIC-TCP while maintaining the strengths of BIC-TCP such as usage than BIC-TCP while maintaining the strengths of BIC-TCP such as
stability, window scalability, and round-trip time (RTT) fairness.</t> stability, window scalability, and RTT-fairness.</t>
<t><xref target="RFC5033"/> documents the IETF's best current practices fo r <t><xref target="RFC5033"/> documents the IETF's best current practices fo r
specifying new congestion control algorithms, specifically, ones that specifying new congestion control algorithms, specifically those that
differ from the general congestion control principles outlined in differ from the general congestion control principles outlined in
<xref target="RFC2914"/>. It describes what type of evaluation is expected by th e <xref target="RFC2914"/>. It describes what type of evaluation is expected by th e
IETF to understand the suitability of a new congestion control IETF to understand the suitability of a new congestion control
algorithm and the process to enable a specification to be approved algorithm and the process of enabling a specification to be approved
for widespread deployment in the global Internet.</t> for widespread deployment in the global Internet.</t>
<t>There are areas in which CUBIC differs from the congestion control <t>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 <xref target="RFC2914"/>, so the process in principles outlined in <xref target="RFC2914"/>, so the process documented in
<xref target="RFC5033"/> may not apply.</t> <xref target="RFC5033"/> may not apply.</t>
<t>Also, the wide deployment of CUBIC on the Internet was driven by <t>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 <xref target="RFC5033"/>. However, due to the follow the practices documented in <xref target="RFC5033"/>. However, due to the
resulting Internet-scale deployment experience over a long resulting Internet-scale deployment experience over a long
period of time, the IETF has determined that CUBIC may be published period of time, the IETF determined that CUBIC could be published
as a standards-track specification. This decision by the IETF does as a Standards Track specification. This decision by the IETF does
not alter the general guidance in <xref target="RFC2914"/>.</t> not alter the general guidance provided in <xref target="RFC2914"/>.</t>
<t>The following sections first briefly explain the design <t>The following sections</t>
principles of CUBIC, provide the exact specification of CUBIC, <ol>
and finally discuss the safety features of CUBIC following the <li>briefly explain the design principles of CUBIC,</li>
guidelines specified in <xref target="RFC5033"/>.</t> <li>provide the exact specification of CUBIC, and</li>
<li>discuss the safety features of CUBIC, following the
guidelines specified in <xref target="RFC5033"/>.</li>
</ol>
</section> </section>
<section anchor="conventions"> <section anchor="conventions">
<name>Conventions</name> <name>Conventions</name>
<t>The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp14 <t>The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>",
>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>",
NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECO "<bcp14>SHALL NOT</bcp14>", "<bcp14>SHOULD</bcp14>",
MMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", "<bcp14>SHOULD NOT</bcp14>",
"<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to be i "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
nterpreted as "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document
described in BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and are to be interpreted as described in BCP&nbsp;14
only when, they <xref target="RFC2119"/> <xref target="RFC8174"/> when, and only
appear in all capitals, as shown here.</t> when, they appear in all capitals, as shown here.</t>
</section> </section>
<section anchor="design-principles-of-cubic"> <section anchor="design-principles-of-cubic">
<name>Design Principles of CUBIC</name> <name>Design Principles of CUBIC</name>
<t>CUBIC is designed according to the following design principles:</t> <t>CUBIC is designed according to the following design principles:</t>
<dl> <dl>
<dt>Principle 1:</dt> <dt>Principle 1:</dt>
<dd> <dd>
<t>For better network utilization and stability, CUBIC <t>For better network utilization and stability, CUBIC
uses both the concave and convex profiles of a cubic function to uses both the concave and convex profiles of a cubic function to
increase the congestion window size, instead of using just a increase the congestion window size, instead of using just a
skipping to change at line 242 skipping to change at line 232
performs well.</t> performs well.</t>
</dd> </dd>
<dt>Principle 3:</dt> <dt>Principle 3:</dt>
<dd> <dd>
<t>For RTT-fairness, CUBIC is designed to achieve linear bandwidth <t>For RTT-fairness, CUBIC is designed to achieve linear bandwidth
sharing among flows with different RTTs.</t> sharing among flows with different RTTs.</t>
</dd> </dd>
<dt>Principle 4:</dt> <dt>Principle 4:</dt>
<dd> <dd>
<t>CUBIC appropriately sets its multiplicative window decrease factor <t>CUBIC appropriately sets its multiplicative window decrease factor
in order to balance between the scalability and convergence speed.</t> in order to achieve a balance between scalability and convergence speed.</t>
</dd> </dd>
</dl> </dl>
<section anchor="cubic-inc"> <section anchor="cubic-inc">
<name>Principle 1 for the CUBIC Increase Function</name> <name>Principle 1 for the CUBIC Increase Function</name>
<t>For better network utilization and stability, CUBIC <xref target="HRX 08"/> uses a <t>For better network utilization and stability, CUBIC <xref target="HRX 08"/> 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 to Reno increase the congestion window using convex algorithms that provide alternatives to Reno increase the congestion window usin
g convex
functions, CUBIC uses both the concave and convex profiles of a cubic functions, CUBIC uses both the concave and convex profiles of a cubic
function for window growth.</t> function for window growth.</t>
<t>After a window reduction in response to a congestion event detected b y <t>After a window reduction in response to a congestion event detected b y
duplicate ACKs, Explicit Congestion Notification-Echo (ECN-Echo, ECE) duplicate acknowledgments (ACKs), Explicit Congestion Notification-Echo (ECN-Ech
ACKs <xref target="RFC3168"/>, TCP RACK <xref target="RFC8985"/> or QUIC loss de o (ECE))
tection ACKs <xref target="RFC3168"/>, RACK-TLP for TCP <xref target="RFC8985"/>, or QUI
C loss detection
<xref target="RFC9002"/>, CUBIC remembers the congestion window size at which it <xref target="RFC9002"/>, CUBIC remembers the congestion window size at which it
received the congestion event and performs a multiplicative decrease of received the congestion event and performs a multiplicative decrease of
the congestion window. When CUBIC enters into congestion avoidance, it the congestion window. When CUBIC enters into congestion avoidance, it
starts to increase the congestion window using the concave profile of starts to increase the congestion window using the concave profile of
the cubic function. The cubic function is set to have its plateau at the cubic function. The cubic function is set to have its plateau at
the remembered congestion window size, so that the concave window the remembered congestion window size, so that the concave window
increase continues until then. After that, the cubic function turns increase continues until then. After that, the cubic function turns
into a convex profile and the convex window increase begins.</t> into a convex profile and the convex window increase begins.</t>
<t>This style of window adjustment (concave and then convex) improves th e <t>This style of window adjustment (concave and then convex) improves
algorithm stability while maintaining high network utilization algorithm stability while maintaining high network utilization
<xref target="CEHRX09"/>. This is because the window size remains almost constan t, <xref target="CEHRX09"/>. This is because the window size remains almost constan t,
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.</t> utilization and stability.</t>
<t>Note that congestion control algorithms that only use convex function s <t>Note that congestion control algorithms that only use convex function s
to increase the congestion window size have their maximum increments to increase the congestion window size have their maximum increments
around the remembered congestion window size of the last congestion around the remembered congestion window size of the last congestion
event, and thus introduce many packet bursts around the 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.</t> synchronizations.</t>
</section> </section>
<section anchor="principle-2-for-reno-friendliness"> <section anchor="principle-2-for-reno-friendliness">
<name>Principle 2 for Reno-Friendliness</name> <name>Principle 2 for Reno-Friendliness</name>
<t>CUBIC promotes per-flow fairness to Reno. Note that Reno <t>CUBIC promotes per-flow fairness to Reno. Note that Reno
performs well over paths with small bandwidth-delay products, and only performs well over paths with small BDPs and only
experiences problems when attempting to increase bandwidth utilization experiences problems when attempting to increase bandwidth utilization
on paths with large bandwidth-delay products.</t> on paths with large BDPs.</t>
<t>A congestion control algorithm designed to be friendly to Reno on <t>A congestion control algorithm designed to be friendly to Reno on
a per-flow basis must increase its congestion window less aggressively a per-flow basis must increase its congestion window less aggressively
in small-BDP networks than in large-BDP networks.</t> in small-BDP networks than in large-BDP networks.</t>
<t>The aggressiveness of CUBIC mainly depends on the maximum window size <t>The aggressiveness of CUBIC mainly depends on the maximum window size
before a window reduction, which is smaller in small-BDP networks than before a window reduction, which is smaller in small-BDP networks than
in large-BDP networks. Thus, CUBIC increases its congestion window in large-BDP networks. Thus, CUBIC increases its congestion window
less aggressively in small-BDP networks than in large-BDP networks.</t> less aggressively in small-BDP networks than in large-BDP networks.</t>
<t>Furthermore, in cases when the cubic function of CUBIC would increase <t>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 where CUBIC behaves like Reno is called the "Reno-friendly
region".</t> region".</t>
</section> </section>
<section anchor="principle-3-for-rtt-fairness"> <section anchor="principle-3-for-rtt-fairness">
<name>Principle 3 for RTT Fairness</name> <name>Principle 3 for RTT-Fairness</name>
<t>Two CUBIC flows with different RTTs have a throughput ratio that is <t>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.</t> window divided by its RTT.</t>
<t>Specifically, CUBIC maintains a window increase rate independent of <t>Specifically, CUBIC maintains a window increase rate that is independ
RTTs outside the Reno-friendly region, and thus flows with ent of RTTs outside the Reno-friendly region, and thus flows with
different RTTs have similar congestion window sizes under steady state different RTTs have similar congestion window sizes under steady state
when they operate outside the Reno-friendly region.</t> when they operate outside the Reno-friendly region.</t>
<t>This notion of a linear throughput ratio is similar to that of Reno <t>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 different have the same packet loss rate but experience loss events at different
times. However, under a synchronous loss model, where flows with different times. However, under a synchronous loss model, where flows with different
RTTs experience loss events at the same time but have different packet loss RTTs experience loss events at the same time but have different packet loss
rates, the throughput ratio of Reno flows with different RTTs is quadratically rates, the throughput ratio of Reno flows with different RTTs is quadratically
proportional to the inverse of their RTT ratio <xref target="XHR04"/>.</t> proportional to the inverse of their RTT ratio <xref target="XHR04"/>.</t>
<t>CUBIC always ensures a linear throughput ratio independent of the <t>CUBIC always ensures a linear throughput ratio that is independent of
loss environment. This is an improvement over Reno. the loss environment. This is an improvement over Reno.
While there is no consensus on the optimal throughput ratio for While there is no consensus on the optimal throughput ratio for
different RTT flows, over wired Internet paths, use of different RTT flows, over wired Internet paths, use of
a linear throughput ratio seems more reasonable than equal throughputs a linear throughput ratio seems more reasonable than equal throughputs
(i.e., the same throughput for flows with different RTTs) or a (i.e., the same throughput for flows with different RTTs) or a
higher-order throughput ratio (e.g., a quadratical throughput ratio of higher-order throughput ratio (e.g., a quadratic throughput ratio of
Reno in synchronous loss environments).</t> Reno in synchronous loss environments).</t>
</section> </section>
<section anchor="prin-beta"> <section anchor="prin-beta">
<name>Principle 4 for the CUBIC Decrease Factor</name> <name>Principle 4 for the CUBIC Decrease Factor</name>
<t>To balance between scalability and convergence speed, CUBIC sets the <t>To achieve a balance between scalability and convergence speed, CUBIC sets the
multiplicative window decrease factor to 0.7, whereas Reno uses multiplicative window decrease factor to 0.7, whereas Reno uses
0.5.</t> 0.5.</t>
<t>While this improves the scalability of CUBIC, a side effect of this <t>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) <xref target="RFC3649"/> and other approaches (e.g., HighSpeed TCP (HSTCP) <xref target="RFC3649"/> and other approaches (e.g.,
<xref target="GV02"/>) made: the current Internet becomes more asynchronous with <xref target="GV02"/>) made: the current Internet becomes more asynchronous with
less frequent loss synchronizations under high statistical less frequent loss synchronizations under high statistical
multiplexing.</t> multiplexing.</t>
<t>In such environments, even strict Multiplicative-Increase <t>In such environments, even strict Multiplicative-Increase
Multiplicative-Decrease (MIMD) can converge. CUBIC flows with the same Multiplicative-Decrease (MIMD) can converge. CUBIC flows with the same
RTT always converge to the same throughput independent of statistical RTT always converge to the same throughput independently of statistical
multiplexing, thus achieving intra-algorithm fairness. 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.</t> convergence speed of CUBIC is reasonable.</t>
</section> </section>
</section> </section>
<section anchor="cubic-congestion-control"> <section anchor="cubic-congestion-control">
<name>CUBIC Congestion Control</name> <name>CUBIC Congestion Control</name>
<t>This section discusses how the congestion window is updated <t>This section discusses how the congestion window is updated
during the different stages of the CUBIC congestion controller.</t> during the different stages of the CUBIC congestion controller.</t>
<section anchor="definitions"> <section anchor="definitions">
<name>Definitions</name> <name>Definitions</name>
<t>The unit of all window sizes in this document is segments of the <t>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 bytes to express window sizes, which would Implementations can use bytes to express window sizes, which would
require factoring in the maximum segment size wherever necessary require factoring in the SMSS wherever necessary
and replacing <em>segments_acked</em> with the number of bytes and replacing <em>segments_acked</em> (<xref target="eq4"/>) with the number of
acknowledged in <xref target="eq4"/>.</t> acknowledged bytes.</t>
<section anchor="constants-of-interest"> <section anchor="constants-of-interest">
<name>Constants of Interest</name> <name>Constants of Interest</name>
<t><contact fullname="β" asciiFullname=""/><em><sub>cubic</sub></em>: <ul>
CUBIC multiplicative decrease factor as described in <xref target="mult-dec"/>.< <li><t>β<em><sub>cubic</sub></em>:
/t> CUBIC multiplicative decrease factor as described in <xref target="mult-dec"/>.<
<t><contact fullname="α" asciiFullname=""/><em><sub>cubic</sub></em>: /t></li>
CUBIC additive increase factor used in Reno-friendly region <li><t>α<em><sub>cubic</sub></em>:
as described in <xref target="Reno-friendly"/>.</t> CUBIC additive increase factor used in the Reno-friendly region
<t><em>C</em>: as described in <xref target="Reno-friendly"/>.</t></li>
constant that determines the aggressiveness of CUBIC in competing with <li><t><em>C</em>:
Constant that determines the aggressiveness of CUBIC in competing with
other congestion control algorithms in high-BDP networks. Please see other congestion control algorithms in high-BDP networks. Please see
<xref target="discussion"/> for more explanation on how it is set. The unit for <em>C</em> <xref target="discussion"/> for more explanation on how it is set. The unit for <em>C</em>
is</t> is</t></li>
</ul>
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<section anchor="variables-of-interest"> <section anchor="variables-of-interest">
<name>Variables of Interest</name> <name>Variables of Interest</name>
<t>This section defines the variables required to implement CUBIC:</t> <t>This section defines the variables required to implement CUBIC:</t>
<t><em>RTT</em>: <ul>
<li><em>RTT</em>:
Smoothed round-trip time in seconds, calculated as described in Smoothed round-trip time in seconds, calculated as described in
<xref target="RFC6298"/>.</t> <xref target="RFC6298"/>.</li>
<t><em>cwnd</em>: <li><em>cwnd</em>:
Current congestion window in segments.</t> Current congestion window in segments.</li>
<t><em>ssthresh</em>: <li><em>ssthresh</em>:
Current slow start threshold in segments.</t> Current slow start threshold in segments.</li>
<t><em>cwnd<sub>prior</sub></em>: <li><em>cwnd<sub>prior</sub></em>:
Size of <em>cwnd</em> in segments at the time of setting <em>ssthresh</em> Size of <em>cwnd</em> in segments at the time of setting <em>ssthresh</em>
most recently, either upon exiting the first slow start, or most recently, either upon exiting the first slow start or
just before <em>cwnd</em> was reduced in the last congestion event.</t> just before <em>cwnd</em> was reduced in the last congestion event.</li>
<t><em>W<sub>max</sub></em>: <li><em>W<sub>max</sub></em>:
Size of <em>cwnd</em> in segments just before <em>cwnd</em> was reduced in the l ast Size of <em>cwnd</em> in segments just before <em>cwnd</em> was reduced in the l ast
congestion event when fast convergence is disabled (same as congestion event when fast convergence is disabled (same as
<em>cwnd<sub>prior</sub></em> on a congestion event). However, if fast <em>cwnd<sub>prior</sub></em> on a congestion event). However, if fast
convergence is enabled, <em>W<sub>max</sub></em> may be further reduced convergence is enabled, <em>W<sub>max</sub></em> may be further reduced
based on the current saturation point.</t> based on the current saturation point.</li>
<t><em>K</em>: <li><em>K</em>:
The time period in seconds it takes to increase the congestion window The time period in seconds it takes to increase the congestion window
size at the beginning of the current congestion avoidance stage to size at the beginning of the current congestion avoidance stage to
<em>W<sub>max</sub></em>.</t> <em>W<sub>max</sub></em>.</li>
<t><em>t<sub>current</sub></em>: <li><em>t<sub>current</sub></em>:
Current time of the system in seconds.</t> Current time of the system in seconds.</li>
<t><em>t<sub>epoch</sub></em>: <li><em>t<sub>epoch</sub></em>:
The time in seconds at which the current congestion avoidance stage The time in seconds at which the current congestion avoidance stage
started.</t> started.</li>
<t><em>cwnd<sub>epoch</sub></em>: <li><em>cwnd<sub>epoch</sub></em>:
The <em>cwnd</em> at the beginning of the current congestion avoidance stage, The <em>cwnd</em> at the beginning of the current congestion avoidance stage,
i.e., at time <em>t<sub>epoch</sub></em>.</t> i.e., at time <em>t<sub>epoch</sub></em>.</li>
<t>W<sub>cubic</sub>(<em>t</em>): <li>W<sub>cubic</sub>(<em>t</em>):
The congestion window in segments at time <em>t</em> in seconds The congestion window in segments at time <em>t</em> in seconds
based on the cubic increase function, as described in <xref target="win-inc"/>.< based on the cubic increase function, as described in <xref target="win-inc"/>.<
/t> /li>
<t><em>target</em>: <li><em>target</em>:
Target value of congestion window in segments after the next RTT, Target value of the congestion window in segments after the next RTT --
that is, W<sub>cubic</sub>(<em>t</em> + <em>RTT</em>), as described in <xref tar that is, W<sub>cubic</sub>(<em>t</em> + <em>RTT</em>), as described in <xref tar
get="win-inc"/>.</t> get="win-inc"/>.</li>
<t><em>W<sub>est</sub></em>: <li><em>W<sub>est</sub></em>:
An estimate for the congestion window in segments in the Reno-friendly An estimate for the congestion window in segments in the Reno-friendly
region, that is, an estimate for the congestion window of Reno.</t> region -- that is, an estimate for the congestion window of Reno.</li>
<t><em>segments_acked</em>: <li><em>segments_acked</em>:
Number of MSS-sized segments acked when a "new ACK" is received, i.e., an Number of SMSS-sized segments acked when a "new ACK" is received, i.e., an
ACK that cumulatively acknowledges the delivery of new data. This ACK that cumulatively acknowledges the delivery of previously unacknowledged dat
a. This
number will be a decimal value when a new ACK acknowledges an amount of number will be a decimal value when a new ACK acknowledges an amount of
data that is not MSS-sized. Specifically, it can be less than 1 when a data that is not SMSS-sized. Specifically, it can be less than 1 when a
new ACK acknowledges a segment smaller than the MSS.</t> new ACK acknowledges a segment smaller than the SMSS.</li>
</ul>
</section> </section>
</section> </section>
<section anchor="win-inc"> <section anchor="win-inc">
<name>Window Increase Function</name> <name>Window Increase Function</name>
<t>CUBIC maintains the acknowledgment (ACK) clocking of Reno by <t>CUBIC maintains the ACK clocking of Reno by
increasing the congestion window only at the reception of a new ACK. It increasing the congestion window only at the reception of a new ACK. It
does not make any changes to the TCP Fast Recovery and Fast Retransmit does not make any changes to the TCP Fast Recovery and Fast Retransmit
algorithms <xref target="RFC6582"/><xref target="RFC6675"/>.</t> algorithms <xref target="RFC6582"/> <xref target="RFC6675"/>.</t>
<t>During congestion avoidance, after a congestion event is detected <t>During congestion avoidance, after a congestion event is detected
by mechanisms described in <xref target="cubic-inc"/>, CUBIC uses a window as described in <xref target="cubic-inc"/>, CUBIC uses a window
increase function different from Reno.</t> increase function different from Reno.</t>
<t>CUBIC uses the following window increase function:</t> <t>CUBIC uses the following window increase function:</t>
<figure anchor="eq1"> <figure anchor="eq1">
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<artwork type="ascii-art" align="center"><![CDATA[ 3 <artwork type="ascii-art" align="center"><![CDATA[ 3
W (t) = C * (t - K) + W W (t) = C * (t - K) + W
cubic max cubic max
]]></artwork> ]]></artwork>
</artset> </artset>
</figure> </figure>
<t>where <em>t</em> is the elapsed time in seconds from the beginning of the <t>where <em>t</em> is the elapsed time in seconds from the beginning of the
current congestion avoidance stage, that is,</t> current congestion avoidance stage -- that is,</t>
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<artwork type="ascii-art" align="center"><![CDATA[t = t - t <artwork type="ascii-art" align="center"><![CDATA[t = t - t
current epoch current epoch
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</artset> </artset>
<t>and where <em>t<sub>epoch</sub></em> is the time at which the current <t>and where <em>t<sub>epoch</sub></em> is the time at which the current
congestion avoidance stage starts. <em>K</em> is the time period that the congestion avoidance stage starts.  &lt;em>K</em> is the time period that the
above function takes to increase the congestion window size at the above function takes to increase the congestion window size at the
beginning of the current congestion avoidance stage to beginning of the current congestion avoidance stage to
<em>W<sub>max</sub></em> if there are no further congestion events and is <em>W<sub>max</sub></em> if there are no further congestion events. &nbsp;<em>K< /em> is
calculated using the following equation:</t> calculated using the following equation:</t>
<figure anchor="eq2"> <figure anchor="eq2">
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<artwork type="ascii-art" align="center"><![CDATA[ ┌────────── ──────┐ <artwork type="ascii-art" align="center"><![CDATA[ ┌────────── ──────┐
3 │W - cwnd 3 │W - cwnd
╲ │ max epoch ╲ │ max epoch
K = ╲ │──────────────── K = ╲ │────────────────
skipping to change at line 677 skipping to change at line 668
<t>where <em>cwnd<sub>epoch</sub></em> is the congestion window at the b eginning <t>where <em>cwnd<sub>epoch</sub></em> is the congestion window at the b eginning
of the current congestion avoidance stage.</t> of the current congestion avoidance stage.</t>
<t>Upon receiving a new ACK during congestion avoidance, CUBIC computes the <t>Upon receiving a new ACK during congestion avoidance, CUBIC computes the
<em>target</em> congestion window size after the next <em>RTT</em> using <xref t arget="eq1"/> as <em>target</em> congestion window size after the next <em>RTT</em> using <xref t arget="eq1"/> as
follows, where <em>RTT</em> is the smoothed round-trip time. The lower and follows, where <em>RTT</em> is the smoothed round-trip time. The lower and
upper bounds below ensure that CUBIC's congestion window increase rate upper bounds below ensure that CUBIC's congestion window increase rate
is non-decreasing and is less than the increase rate of slow start <xref target= "SXEZ19"/>.</t> is non-decreasing and is less than the increase rate of slow start <xref target= "SXEZ19"/>.</t>
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<artwork type="ascii-art" align="center"><![CDATA[ ⎧ <artwork type="ascii-art" align="center"><![CDATA[ ⎧
⎪cwnd if W (t + RTT) < cwnd ⎪cwnd if W (t + RTT) < cwnd
⎪ cubic ⎪ cubic
skipping to change at line 877 skipping to change at line 868
<li>The convex region, if CUBIC is not in the Reno-friendly region and <li>The convex region, if CUBIC is not in the Reno-friendly region and
<em>cwnd</em> is greater than <em>W<sub>max</sub></em>.</li> <em>cwnd</em> is greater than <em>W<sub>max</sub></em>.</li>
</ol> </ol>
<t>To summarize, CUBIC computes both W<sub>cubic</sub>(<em>t</em>) and <t>To summarize, CUBIC computes both W<sub>cubic</sub>(<em>t</em>) and
<em>W<sub>est</sub></em> (see <xref target="Reno-friendly"/>) on receiving a new ACK <em>W<sub>est</sub></em> (see <xref target="Reno-friendly"/>) on receiving a new ACK
in congestion avoidance and chooses the larger of the two values.</t> in congestion avoidance and chooses the larger of the two values.</t>
<t>The next sections describe the exact actions taken by CUBIC in each r egion.</t> <t>The next sections describe the exact actions taken by CUBIC in each r egion.</t>
</section> </section>
<section anchor="Reno-friendly"> <section anchor="Reno-friendly">
<name>Reno-Friendly Region</name> <name>Reno-Friendly Region</name>
<t>Reno performs well in certain types of networks, for example, <t>Reno performs well in certain types of networks -- for example,
under short RTTs and small bandwidths (or small BDPs). In these under short RTTs and small bandwidths (or small BDPs). In these
networks, CUBIC remains in the Reno-friendly region to achieve at networks, CUBIC remains in the Reno-friendly region to achieve at
least the same throughput as Reno.</t> least the same throughput as Reno.</t>
<t>The Reno-friendly region is designed according to the analysis in <t>The Reno-friendly region is designed according to the analysis discus sed in
<xref target="FHP00"/>, which studies the performance of an AIMD algorithm with an <xref target="FHP00"/>, which studies the performance of an AIMD algorithm with an
additive factor of <contact fullname="α" asciiFullname=""/> (segments per <em>RT additive factor of α (segments per <em>RTT</em>) and
T</em>) and a multiplicative factor of β, denoted by
a multiplicative factor of <contact fullname="β" asciiFullname=""/>, denoted by AIMD(α, β). &nbsp;<em>p</em> is the packet loss rate.
AIMD(<contact fullname="α" asciiFullname=""/>, <contact fullname="β" asciiFullna
me=""/>). <em>p</em> is the packet loss rate.
Specifically, the average congestion window size of Specifically, the average congestion window size of
AIMD(<contact fullname="α" asciiFullname=""/>, <contact fullname="β" asciiFullna me=""/>) can be AIMD(α, β) can be
calculated using <xref target="eq3"/>.</t> calculated using <xref target="eq3"/>.</t>
<figure anchor="eq3"> <figure anchor="eq3">
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<artwork type="ascii-art" align="center"><![CDATA[ ┌───────────────┐ <artwork type="ascii-art" align="center"><![CDATA[ ┌───────────────┐
│ α * (1 + β) │ α * (1 + β)
AVG_AIMD(α, β) = ╲ │─────────────── AVG_AIMD(α, β) = ╲ │───────────────
╲│2 * (1 - β) * p ╲│2 * (1 - β) * p
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</figure> </figure>
<t>By the same analysis, to achieve a similar average window size as Ren <t>By the same analysis, to achieve an average window size similar to Re
o no
that uses AIMD(1, 0.5), <contact fullname="α" asciiFullname=""/> must be equal t that uses AIMD(1, 0.5), α must be equal to</t>
o,</t>
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<artwork type="ascii-art" align="center"><![CDATA[ 1 - β <artwork type="ascii-art" align="center"><![CDATA[ 1 - β
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<t>Thus, CUBIC uses <xref target="eq4"/> to estimate the window <t>Thus, CUBIC uses <xref target="eq4"/> to estimate the window
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<artwork type="ascii-art" align="center"><![CDATA[ 1 - β <artwork type="ascii-art" align="center"><![CDATA[ 1 - β
cubic cubic
α = 3 * ────────── α = 3 * ──────────
cubic 1 + β cubic 1 + β
cubic cubic
]]></artwork> ]]></artwork>
</artset> </artset>
<t>which achieves approximately the same average window size as Reno in <t>which achieves approximately the same average window size as Reno in
many cases. The model used to calculate <contact fullname="α" asciiFullname=""/> many cases. The model used to calculate α<em><sub>cubic</sub></em> is not
<em><sub>cubic</sub></em> is not absolutely precise, but analysis and simulation as discussed in <xref target="AI
absolutely precise, but analysis and simulation in <xref target="AIMD-friendline MD-friendliness"/>,
ss"/>,
as well as over a decade of experience with CUBIC in the public as well as over a decade of experience with CUBIC in the public
Internet, show that this approach produces acceptable levels of Internet, show that this approach produces acceptable levels of
rate fairness between CUBIC and Reno flows. Also, no significant rate fairness between CUBIC and Reno flows. Also, no significant
drawbacks of the model have been reported. However, it would be drawbacks of the model have been reported. However, continued detailed
beneficial to see continued detailed analysis on it. When analysis of this approach would be beneficial. When
receiving a new ACK in congestion avoidance (where <em>cwnd</em> could be receiving a new ACK in congestion avoidance (where <em>cwnd</em> could be
greater than or less than <em>W<sub>max</sub></em>), CUBIC checks whether greater than or less than <em>W<sub>max</sub></em>), CUBIC checks whether
W<sub>cubic</sub>(<em>t</em>) is less than <em>W<sub>est</sub></em>. If so, CUBI C is W<sub>cubic</sub>(<em>t</em>) is less than <em>W<sub>est</sub></em>. &nbsp;If so , CUBIC is
in the Reno-friendly region and <em>cwnd</em> <bcp14>SHOULD</bcp14> be set to in the Reno-friendly region and <em>cwnd</em> <bcp14>SHOULD</bcp14> be set to
<em>W<sub>est</sub></em> at each reception of a new ACK.</t> <em>W<sub>est</sub></em> at each reception of a new ACK.</t>
<t><em>W<sub>est</sub></em> is set equal to <em>cwnd<sub>epoch</sub></em > at the start <t><em>W<sub>est</sub></em> is set equal to <em>cwnd<sub>epoch</sub></em > at the start
of the congestion avoidance stage. After that, on every new ACK, of the congestion avoidance stage. After that, on every new ACK,
<em>W<sub>est</sub></em> is updated using <xref target="eq4"/>. Note that this e quation <em>W<sub>est</sub></em> is updated using <xref target="eq4"/>. Note that this e quation
uses <em>segments_acked</em> and <em>cwnd</em> is measured in segments. An imple mentation uses <em>segments_acked</em> and <em>cwnd</em> is measured in segments. An imple mentation
that measures <em>cwnd</em> in bytes should adjust the equation accordingly usin g that measures <em>cwnd</em> in bytes should adjust the equation accordingly usin g
number of acknowledged bytes and MSS. Also note that this equation works for the number of acknowledged bytes and the SMSS. Also note that this equation work
connections with enabled or disabled Delayed ACKs <xref target="RFC5681"/>, as s for
connections with enabled or disabled delayed ACKs <xref target="RFC5681"/>, as
<em>segments_acked</em> will be different based on the segments actually <em>segments_acked</em> will be different based on the segments actually
acknowledged by a new ACK.</t> acknowledged by a new ACK.</t>
<figure anchor="eq4"> <figure anchor="eq4">
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<artwork type="ascii-art" align="center"><![CDATA[ segments_acked <artwork type="ascii-art" align="center"><![CDATA[ segments_acked
W = W + α * ────────────── W = W + α * ──────────────
est est cubic cwnd est est cubic cwnd
]]></artwork> ]]></artwork>
</artset> </artset>
</figure> </figure>
<t>Once <em>W<sub>est</sub></em> has grown to reach the <em>cwnd</em> at the time of <t>Once <em>W<sub>est</sub></em> has grown to reach the <em>cwnd</em> at the time of
most recently setting <em>ssthresh</em>, that is, <em>W<sub>est</sub></em> &gt;= most recently setting <em>ssthresh</em> -- that is, <em>W<sub>est</sub></em> &gt
<em>cwnd<sub>prior</sub></em>, ;= <em>cwnd<sub>prior</sub></em> --
the sender <bcp14>SHOULD</bcp14> set <contact fullname="α" asciiFullname=""/><em the sender <bcp14>SHOULD</bcp14> set α<em><sub>cubic</sub></em> to 1 to ensure t
><sub>cubic</sub></em> to 1 to ensure that hat
it can achieve the same congestion window increment rate as Reno, it can achieve the same congestion window increment rate as Reno,
which uses AIMD(1, 0.5).</t> which uses AIMD(1, 0.5).</t>
<t>The next two sections assume that CUBIC is not in the Reno-friendly r egion and <t>The next two sections assume that CUBIC is not in the Reno-friendly r egion and
uses the window increase function described in <xref target="win-inc"/>. Althoug h uses the window increase function described in <xref target="win-inc"/>. Althoug h
<em>cwnd</em> is incremented in the same way for both concave and convex regions , <em>cwnd</em> is incremented in the same way for both concave and convex regions ,
they are discussed separately to analyze and understand the difference they are discussed separately to analyze and understand the difference
between the two regions.</t> between the two regions.</t>
</section> </section>
<section anchor="concave-region"> <section anchor="concave-region">
<name>Concave Region</name> <name>Concave Region</name>
<t>When receiving a new ACK in congestion avoidance, if CUBIC is not in the <t>When receiving a new ACK in congestion avoidance, if CUBIC is not in the
Reno-friendly region and <em>cwnd</em> is less than <em>W<sub>max</sub></em>, th en Reno-friendly region and <em>cwnd</em> is less than <em>W<sub>max</sub></em>, th en
CUBIC is in the concave region. In this region, <em>cwnd</em> <bcp14>MUST</bcp14 > be CUBIC is in the concave region. In this region, <em>cwnd</em> <bcp14>MUST</bcp14 > be
incremented by</t> incremented by</t>
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skipping to change at line 1265 skipping to change at line 1256
<section anchor="convex-region"> <section anchor="convex-region">
<name>Convex Region</name> <name>Convex Region</name>
<t>When receiving a new ACK in congestion avoidance, if CUBIC is not in the <t>When receiving a new ACK in congestion avoidance, if CUBIC is not in the
Reno-friendly region and <em>cwnd</em> is larger than or equal to Reno-friendly region and <em>cwnd</em> is larger than or equal to
<em>W<sub>max</sub></em>, then CUBIC is in the convex region.</t> <em>W<sub>max</sub></em>, then CUBIC is in the convex region.</t>
<t>The convex region indicates that the network conditions might have <t>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 is available bandwidth after some flow departures. Since the Internet is
highly asynchronous, some amount of perturbation is always possible highly asynchronous, some amount of perturbation is always possible
without causing a major change in available bandwidth.</t> without causing a major change in available bandwidth.</t>
<t>Unless it is overridden by the AIMD window increase, CUBIC is very <t>Unless the cwnd is overridden by the AIMD window increase,
careful in this region. The convex profile aims to CUBIC will behave cautiously when operating in this region. The convex profile a
ims to
increase the window very slowly at the beginning when <em>cwnd</em> is increase the window very slowly at the beginning when <em>cwnd</em> is
around <em>W<sub>max</sub></em> and then gradually increases its rate of increas e. around <em>W<sub>max</sub></em> and then gradually increases its rate of increas e.
This region is also called the "maximum probing phase", since CUBIC is This region is also called the "maximum probing phase", since CUBIC is
searching for a new <em>W<sub>max</sub></em>. In this region, <em>cwnd</em> <bcp 14>MUST</bcp14> be searching for a new <em>W<sub>max</sub></em>. &nbsp;In this region, <em>cwnd</em > <bcp14>MUST</bcp14> be
incremented by</t> incremented by</t>
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<artwork type="ascii-art" align="center"><![CDATA[target - cwnd <artwork type="ascii-art" align="center"><![CDATA[target - cwnd
───────────── ─────────────
cwnd cwnd
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<t>for each received new ACK, where <em>target</em> is calculated as des cribed in <t>for each received new ACK, where <em>target</em> is calculated as des cribed in
<xref target="win-inc"/>.</t> <xref target="win-inc"/>.</t>
</section> </section>
<section anchor="mult-dec"> <section anchor="mult-dec">
<name>Multiplicative Decrease</name> <name>Multiplicative Decrease</name>
<t>When a congestion event is detected by mechanisms described in <t>When a congestion event is detected by the mechanisms described in
<xref target="cubic-inc"/>, CUBIC updates <em>W<sub>max</sub></em> and reduces < em>cwnd</em> <xref target="cubic-inc"/>, CUBIC updates <em>W<sub>max</sub></em> and reduces < em>cwnd</em>
and <em>ssthresh</em> immediately as described below. and <em>ssthresh</em> immediately, as described below.
In case of packet loss, the sender <bcp14>MUST</bcp14> reduce <em>cwnd</em> In the case of packet loss, the sender <bcp14>MUST</bcp14> reduce <em>cwnd</em>
and <em>ssthresh</em> immediately upon entering loss recovery, similar to and <em>ssthresh</em> immediately upon entering loss recovery, similar to
<xref target="RFC5681"/> (and <xref target="RFC6675"/>). Note that other mechani sms, <xref target="RFC5681"/> (and <xref target="RFC6675"/>). Note that other mechani sms,
such as Proportional Rate Reduction <xref target="RFC6937"/>, can be used such as Proportional Rate Reduction <xref target="RFC6937"/>, can be used
to reduce the sending rate during loss recovery more gradually. to reduce the sending rate during loss recovery more gradually.
The parameter <contact fullname="β" asciiFullname=""/><em><sub>cubic</sub></em> <bcp14>SHOULD</bcp14> be set to 0.7, which The parameter β<em><sub>cubic</sub></em> <bcp14>SHOULD</bcp14> be set to 0.7, wh ich
is different from the multiplicative decrease factor used in <xref target="RFC56 81"/> is different from the multiplicative decrease factor used in <xref target="RFC56 81"/>
(and <xref target="RFC6675"/>) during fast recovery.</t> (and <xref target="RFC6675"/>) during fast recovery.</t>
<t>In <xref target="eqssthresh"/>, <em>flight_size</em> is the amount of outstanding <t>In <xref target="eqssthresh"/>, <em>flight_size</em> is the amount of outstanding
(unacknowledged) data in the network, as defined in (unacknowledged) data in the network, as defined in
<xref target="RFC5681"/>. Note that a rate-limited application with idle periods <xref target="RFC5681"/>. Note that a rate-limited application with idle periods
or periods when unable to send at the full rate permitted by <em>cwnd</em> or periods when unable to send at the full rate permitted by <em>cwnd</em>
could easily encounter notable variations in the volume of data sent could easily encounter notable variations in the volume of data sent
from one RTT to another, resulting in <em>flight_size</em> that is from one RTT to another, resulting in <em>flight_size</em> that is
significantly less than <em>cwnd</em> when there is a congestion event. The significantly less than <em>cwnd</em> when there is a congestion event. The
congestion response would therefore decrease <em>cwnd</em> to a much lower congestion response would therefore decrease <em>cwnd</em> to a much lower
value than necessary. To avoid such suboptimal performance, the value than necessary. To avoid such suboptimal performance, the
mechanisms described in <xref target="RFC7661"/> can be used. These describe how mechanisms described in <xref target="RFC7661"/> can be used. <xref target="RFC7
to manage and use <em>cwnd</em> and <em>ssthresh</em> during a rate-limited Inte 661"/> describes how to manage and use <em>cwnd</em> and <em>ssthresh</em> durin
rval, g a rate-limited interval,
and how to update <em>cwnd</em> and <em>ssthresh</em> after congestion has been detected. The and how to update <em>cwnd</em> and <em>ssthresh</em> after congestion has been detected. The
mechanism defined in <xref target="RFC7661"/> is safe to use even when <em>cwnd< mechanisms defined in <xref target="RFC7661"/> are safe to use even when <em>cwn
/em> is d</em> is
greater than the receive window, because it validates <em>cwnd</em> based on greater than the receive window, because they validate <em>cwnd</em> based on
the amount of data acknowledged by the network in an RTT, which the amount of data acknowledged by the network in an RTT, which
implicitly accounts for the allowed receive window.</t> implicitly accounts for the allowed receive window.</t>
<t>Some implementations of CUBIC currently use <em>cwnd</em> instead of <t>Some implementations of CUBIC currently use <em>cwnd</em> instead of
<em>flight_size</em> when calculating a new <em>ssthresh</em>. Implementations t hat <em>flight_size</em> when calculating a new <em>ssthresh</em>. &nbsp;Implementat ions that
use <em>cwnd</em> <bcp14>MUST</bcp14> use other measures to prevent <em>cwnd</em > from growing when use <em>cwnd</em> <bcp14>MUST</bcp14> use other measures to prevent <em>cwnd</em > from growing when
the volume of bytes in flight is smaller than <em>cwnd</em>. This also the volume of bytes in flight is smaller than <em>cwnd</em>. &nbsp;This also
effectively avoids <em>cwnd</em> from growing beyond the receive window. Such effectively prevents <em>cwnd</em> from growing beyond the receive window. Such
measures are important to prevent a CUBIC sender from using an measures are important for preventing a CUBIC sender from using an
arbitrarily high cwnd <em>value</em> when calculating new values for arbitrarily high cwnd <em>value</em> when calculating new values for
<em>ssthresh</em> and <em>cwnd</em> when congestion is detected. This might not be as <em>ssthresh</em> and <em>cwnd</em> when congestion is detected. This might not be as
robust as the mechanisms described in <xref target="RFC7661"/>.</t> robust as the mechanisms described in <xref target="RFC7661"/>.</t>
<t>A QUIC sender that uses <em>cwnd</em> to calculate new values for <em >cwnd</em> and <t>A QUIC sender that uses a <em>cwnd</em> <em>value</em> to calculate n ew values for <em>cwnd</em> and
<em>ssthresh</em> after detecting a congestion event is <bcp14>REQUIRED</bcp14> to apply <em>ssthresh</em> after detecting a congestion event is <bcp14>REQUIRED</bcp14> to apply
similar mechanisms <xref target="RFC9002"/>.</t> similar mechanisms <xref target="RFC9002"/>.</t>
<figure anchor="eqssthresh"> <figure anchor="eqssthresh">
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<artwork type="ascii-art" align="center"><![CDATA[ssthresh = flight _size * β new ssthresh <artwork type="ascii-art" align="center"><![CDATA[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
]]></artwork> ]]></artwork>
</artset> </artset>
</figure> </figure>
<t>A side effect of setting <contact fullname="β" asciiFullname=""/><em> <t>A side effect of setting β<em><sub>cubic</sub></em> to a value bigger
<sub>cubic</sub></em> to a value bigger than 0.5 is that packet loss can happen for more than one RTT in certain
than 0.5 is that packet loss can happen for more than one round-trip in certain cases, but it can work efficiently in other cases -- for example, when HyStart++
cases, but it can work efficiently in other cases, for example, when HyStart++ <xref target="RFC9406"/>
is used along with CUBIC or when the sending rate is limited by the application. is used along with CUBIC or when the sending rate is limited by the application.
While a more adaptive setting of <contact fullname="β" asciiFullname=""/><em><su b>cubic</sub></em> While a more adaptive setting of β<em><sub>cubic</sub></em>
could help limit packet loss to a single round, it would require detailed could help limit packet loss to a single round, it would require detailed
analyses and large-scale evaluations to validate such algorithms.</t> analyses and large-scale evaluations to validate such algorithms.</t>
<t>Note that CUBIC <bcp14>MUST</bcp14> continue to reduce <em>cwnd</em> in response to congestion <t>Note that CUBIC <bcp14>MUST</bcp14> continue to reduce <em>cwnd</em> in response to congestion
events due to ECN-Echo ACKs until it reaches a value of 1 MSS. events detected by ECN-Echo ACKs until it reaches a value of 1 SMSS.
If congestion events indicated by ECN-Echo ACKs persist, a sender with a If congestion events indicated by ECN-Echo ACKs persist, a sender with a
<em>cwnd</em> of 1 MSS <bcp14>MUST</bcp14> reduce its sending rate even further. <em>cwnd</em> of 1 SMSS <bcp14>MUST</bcp14> reduce its sending rate even further
It can achieve . This can be achieved
that by using a retransmission timer with exponential backoff, as by using a retransmission timer with exponential backoff, as
described in <xref target="RFC3168"/>.</t> described in <xref target="RFC3168"/>.</t>
</section> </section>
<section anchor="fast-convergence"> <section anchor="fast-convergence">
<name>Fast Convergence</name> <name>Fast Convergence</name>
<t>To improve convergence speed, CUBIC uses a heuristic. When a new flow <t>To improve convergence speed, CUBIC uses a heuristic. When a new flow
joins the network, existing flows need to give up some of their 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 <bcp14>SHOULD</bcp14> be implemented.</t> mechanism <bcp14>SHOULD</bcp14> be implemented.</t>
<t>With Fast Convergence, when a congestion event occurs, <em>W<sub>max< /sub></em> <t>With fast convergence, when a congestion event occurs, <em>W<sub>max< /sub></em>
is updated as follows, before the window reduction described is updated as follows, before the window reduction described
in <xref target="mult-dec"/>.</t> in <xref target="mult-dec"/>.</t>
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<artwork type="ascii-art" align="center"><![CDATA[ ⎧ 1 + β <artwork type="ascii-art" align="center"><![CDATA[ ⎧ 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
]]></artwork> ]]></artwork>
</artset> </artset>
<t>At a congestion event, if the current <em>cwnd</em> is less than <t>During a congestion event, if the current <em>cwnd</em> is less than
<em>W<sub>max</sub></em>, this indicates that the saturation point <em>W<sub>max</sub></em>, this indicates that the saturation point
experienced by this flow is getting reduced because of a change in experienced by this flow is getting reduced because of a change in
available bandwidth. This flow can then release more bandwidth available bandwidth. This flow can then release more bandwidth
by reducing <em>W<sub>max</sub></em> further. This action effectively by reducing <em>W<sub>max</sub></em> further. This action effectively
lengthens the time for this flow to increase its congestion window, lengthens the time for this flow to increase its congestion window,
because the reduced <em>W<sub>max</sub></em> forces the flow to plateau because the reduced <em>W<sub>max</sub></em> forces the flow to plateau
earlier. This allows more time for the new flow to catch up to its earlier. This allows more time for the new flow to catch up to its
congestion window size.</t> congestion window size.</t>
<t>Fast Convergence is designed for network environments with multiple <t>Fast convergence is designed for network environments with multiple
CUBIC flows. In network environments with only a single CUBIC flow and CUBIC flows. In network environments with only a single CUBIC flow and
without any other traffic, Fast Convergence <bcp14>SHOULD</bcp14> be disabled.</ t> without any other traffic, fast convergence <bcp14>SHOULD</bcp14> be disabled.</ t>
</section> </section>
<section anchor="timeout"> <section anchor="timeout">
<name>Timeout</name> <name>Timeout</name>
<t>In case of a timeout, CUBIC follows Reno to reduce <em>cwnd</em> <t>In the case of a timeout, CUBIC follows Reno to reduce <em>cwnd</em>
<xref target="RFC5681"/>, but sets <em>ssthresh</em> using <contact fu <xref target="RFC5681"/> but sets <em>ssthresh</em> using β<em><sub>cu
llname="β" asciiFullname=""/><em><sub>cubic</sub></em> bic</sub></em>
(same as in <xref target="mult-dec"/>) in a way that is different from Reno TCP (same as in <xref target="mult-dec"/>) in a way that is different from Reno TCP
<xref target="RFC5681"/>.</t> <xref target="RFC5681"/>.</t>
<t>During the first congestion avoidance stage after a timeout, CUBIC <t>During the first congestion avoidance stage after a timeout, CUBIC
increases its congestion window size using <xref target="eq1"/>, where <em>t</em > is the increases its congestion window size using <xref target="eq1"/>, where <em>t</em > is the
elapsed time since the beginning of the current congestion avoidance, elapsed time since the beginning of the current congestion avoidance stage,
<em>K</em> is set to 0, and <em>W<sub>max</sub></em> is set to the congestion wi ndow <em>K</em> is set to 0, and <em>W<sub>max</sub></em> is set to the congestion wi ndow
size at 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, <em>W<sub>est</sub></em> <bcp14>SHOULD</ bcp14> be addition, for the Reno-friendly region, <em>W<sub>est</sub></em> <bcp14>SHOULD</ bcp14> be
set to the congestion window size at the beginning of the current set to the congestion window size at the beginning of the current
congestion avoidance.</t> congestion avoidance stage.</t>
</section> </section>
<section anchor="spurious-congestion-events"> <section anchor="spurious-congestion-events">
<name>Spurious Congestion Events</name> <name>Spurious Congestion Events</name>
<t>In cases where CUBIC reduces its congestion window in response to <t>In cases where CUBIC reduces its congestion window in response to
having detected packet loss via duplicate ACKs or timeouts, there is a having detected packet loss via duplicate ACKs or timeouts, it is
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 degree example, packet reordering could trigger this behavior. A high degree
of packet reordering could cause multiple congestion window reduction of packet reordering could cause multiple congestion window reduction
events, where spurious losses are incorrectly interpreted as events, where spurious losses are incorrectly interpreted as
congestion signals, thus degrading CUBIC's performance significantly.</t> congestion signals, thus degrading CUBIC's performance significantly.</t>
<t>For TCP, there are two types of spurious events - spurious timeouts <t>For TCP, there are two types of spurious events: spurious timeouts
and spurious fast retransmits. In case of QUIC, there are no spurious and spurious fast retransmits. In the case of QUIC, there are no spurious
timeouts as the loss is only detected after receiving an ACK.</t> timeouts, as the loss is only detected after receiving an ACK.</t>
<section anchor="spurious-timeout"> <section anchor="spurious-timeout">
<name>Spurious timeout</name> <name>Spurious Timeouts</name>
<t>An implementation <bcp14>MAY</bcp14> detect spurious timeouts based on the mechanisms <t>An implementation <bcp14>MAY</bcp14> detect spurious timeouts based on the mechanisms
described in Forward RTO-Recovery <xref target="RFC5682"/>. Experimental alterna tives described in Forward RTO-Recovery <xref target="RFC5682"/>. Experimental alterna tives
include Eifel <xref target="RFC3522"/>. When a spurious timeout is detected, include the Eifel detection algorithm <xref target="RFC3522"/>. When a spurious timeout is detected,
a TCP implementation <bcp14>MAY</bcp14> follow the response algorithm described in a TCP implementation <bcp14>MAY</bcp14> follow the response algorithm described in
<xref target="RFC4015"/> to restore the congestion control state and adapt <xref target="RFC4015"/> to restore the congestion control state and adapt
the retransmission timer to avoid further spurious timeouts.</t> the retransmission timer to avoid further spurious timeouts.</t>
</section> </section>
<section anchor="spurious-loss-detected-by-acknowledgments"> <section anchor="spurious-loss-detected-by-acknowledgments">
<name>Spurious loss detected by acknowledgments</name> <name>Spurious Fast Retransmits</name>
<t>Upon receiving an ACK, a TCP implementation <bcp14>MAY</bcp14> dete <t>Upon receiving an ACK, a TCP implementation <bcp14>MAY</bcp14> dete
ct spurious losses ct spurious fast retransmits
either using TCP Timestamps or via D-SACK<xref target="RFC2883"/>. Experimental either using TCP Timestamps or via D-SACK <xref target="RFC2883"/>. As noted abo
alternatives include Eifel detection algorithm <xref target="RFC3522"/> which us ve, experimental
es alternatives include the Eifel detection algorithm <xref target="RFC3522"/>, whi
TCP Timestamps and DSACK based detection <xref target="RFC3708"/> which uses ch uses
TCP Timestamps; and DSACK-based detection <xref target="RFC3708"/>, which uses
DSACK information. A QUIC implementation can easily determine a DSACK information. A QUIC implementation can easily determine a
spurious loss if a QUIC packet is acknowledged after it has been spurious fast retransmit if a QUIC packet is acknowledged after it has been
marked as lost and the original data has been retransmitted with marked as lost and the original data has been retransmitted with
a new QUIC packet.</t> a new QUIC packet.</t>
<t>This section specifies a simple response algorithm when a spurious <t>This section specifies a simple response algorithm when a spurious
loss is detected by acknowledgments. Implementations would need to carefully fast retransmit is detected by acknowledgments. Implementations would need to ca refully
evaluate the impact of using this algorithm in different environments evaluate the impact of using this algorithm in different environments
that may experience sudden change in available capacity (e.g., due to variable that may experience a sudden change in available capacity (e.g., due to variable
radio capacity, a routing change, or a mobility event).</t> radio capacity, a routing change, or a mobility event).</t>
<t>When a packet loss is detected via acknowledgments, a CUBIC <t>When packet loss is detected via acknowledgments, a CUBIC
implementation <bcp14>MAY</bcp14> save the current value of the following implementation <bcp14>MAY</bcp14> save the current value of the following
variables before the congestion window is reduced.</t> variables before the congestion window is reduced.</t>
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<t>Once the previously declared packet loss is confirmed to be spuriou s, <t>Once the previously declared packet loss is confirmed to be spuriou s,
CUBIC <bcp14>MAY</bcp14> restore the original values of the above-mentioned vari ables CUBIC <bcp14>MAY</bcp14> restore the original values of the above-mentioned vari ables
as follows if the current <em>cwnd</em> is lower than <em>cwnd<sub>prior</sub></ as follows if the current <em>cwnd</em> is lower than <em>cwnd<sub>prior</sub></
em>. em>. &nbsp;Restoring the original values ensures that CUBIC's
Restoring the original values ensures that CUBIC's
performance is similar to what it would be without spurious losses.</t> performance is similar to what it would be without spurious losses.</t>
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<artwork type="ascii-art" align="center"><![CDATA[cwnd = undo_c wnd ⎫ <artwork type="ascii-art" align="center"><![CDATA[cwnd = undo_c wnd ⎫
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 ⎭
]]></artwork> ]]></artwork>
</artset> </artset>
<t>In rare cases, when the detection happens long after a spurious los <t>In rare cases, when the detection happens long after a spurious fas
s t retransmit event and the current <em>cwnd</em> is already higher than <em>cwnd
event and the current <em>cwnd</em> is already higher than <em>cwnd<sub>prior</s <sub>prior</sub></em>,
ub></em>,
CUBIC <bcp14>SHOULD</bcp14> continue to use the current and the most recent valu es of CUBIC <bcp14>SHOULD</bcp14> continue to use the current and the most recent valu es of
these variables.</t> these variables.</t>
</section> </section>
</section> </section>
<section anchor="slow-start"> <section anchor="slow-start">
<name>Slow Start</name> <name>Slow Start</name>
<t>CUBIC <bcp14>MUST</bcp14> employ a slow-start algorithm, when <em>cwn <t>When <em>cwnd</em> is no more than <em>ssthresh</em>, CUBIC <bcp14>MU
d</em> is no more than ST</bcp14> employ a slow start algorithm. In general, CUBIC <bcp14>SHOULD</bcp14
<em>ssthresh</em>. In general, CUBIC <bcp14>SHOULD</bcp14> use the HyStart++ slo > use the HyStart++ slow start
w start algorithm <xref target="RFC9406"/> or <bcp14>MAY</bcp14> use the Reno TCP
algorithm <xref target="I-D.ietf-tcpm-hystartplusplus"/>, or <bcp14>MAY</bcp14>
use the Reno TCP
slow start algorithm <xref target="RFC5681"/> in the rare cases when slow start algorithm <xref target="RFC5681"/> in the rare cases when
HyStart++ is not suitable. Experimental alternatives include HyStart++ is not suitable. Experimental alternatives include
hybrid slow start <xref target="HR11"/>, a predecessor to HyStart++ that some CU BIC hybrid slow start <xref target="HR11"/>, a predecessor to HyStart++ that some CU BIC
implementations have used as the default for the last decade, and implementations have used as the default for the last decade, and
limited slow start <xref target="RFC3742"/>. Whichever start-up algorithm is use d, limited slow start <xref target="RFC3742"/>. Whichever startup algorithm is used ,
work might be needed to ensure that the end of slow start and the first work might be needed to ensure that the end of slow start and the first
multiplicative decrease of congestion avoidance work well together.</t> multiplicative decrease of congestion avoidance work well together.</t>
<t>When CUBIC uses HyStart++ <xref target="I-D.ietf-tcpm-hystartplusplus "/>, it may <t>When CUBIC uses HyStart++ <xref target="RFC9406"/>, it may
exit the first slow start without incurring any packet loss and exit the first slow start without incurring any packet loss and
thus <em>W<sub>max</sub></em> is undefined. In this special case, CUBIC thus <em>W<sub>max</sub></em> is undefined. In this special case, CUBIC
sets <em>cwnd<sub>prior</sub> = cwnd</em> and switches to congestion avoidance. sets <em>cwnd<sub>prior</sub> = cwnd</em> and switches to congestion avoidance.
It then increases its congestion window It then increases its congestion window
size using <xref target="eq1"/>, where <em>t</em> is the elapsed time since the beginning size using <xref target="eq1"/>, where <em>t</em> is the elapsed time since the beginning
of the current congestion avoidance, <em>K</em> is set to 0, of the current congestion avoidance stage, <em>K</em> is set to 0,
and <em>W<sub>max</sub></em> is set to the congestion window size at the and <em>W<sub>max</sub></em> is set to the congestion window size at the
beginning of the current congestion avoidance stage.</t> beginning of the current congestion avoidance stage.</t>
</section> </section>
</section> </section>
<section anchor="discussion"> <section anchor="discussion">
<name>Discussion</name> <name>Discussion</name>
<t>This section further discusses the safety features of CUBIC <t>This section further discusses the safety features of CUBIC,
following the guidelines specified in <xref target="RFC5033"/>.</t> following the guidelines specified in <xref target="RFC5033"/>.</t>
<t>With a deterministic loss model where the number of packets between <t>With a deterministic loss model where the number of packets between
two successive packet losses is always <em>1/p</em>, CUBIC always operates two successive packet losses is always <em>1/p</em>, 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 <xref targe t="proof-avg-window"/>) performance analysis of CUBIC. The average window size of CUBIC (see <xref targe t="proof-avg-window"/>)
can be obtained by the following function:</t> can be obtained via the following function:</t>
<figure anchor="eq5"> <figure anchor="eq5">
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<artwork type="ascii-art" align="center"><![CDATA[ ┌─── ─────────────┐ 4 ┌────┐ <artwork type="ascii-art" align="center"><![CDATA[ ┌─── ─────────────┐ 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
]]></artwork> ]]></artwork>
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</figure> </figure>
<t>With <contact fullname="β" asciiFullname=""/><em><sub>cubic</sub></em> <t>With β<em><sub>cubic</sub></em> set to 0.7, the above formula reduces
set to 0.7, the above formula reduces to</t>
to:</t>
<figure anchor="eq6"> <figure anchor="eq6">
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<artwork type="ascii-art" align="center"><![CDATA[ 4 ┌────┐ <artwork type="ascii-art" align="center"><![CDATA[ 4 ┌────┐
┌───────┐ ╲ │ 3 ┌───────┐ ╲ │ 3
4 │C * 3.7 ╲│RTT 4 │C * 3.7 ╲│RTT
skipping to change at line 2781 skipping to change at line 2751
]]></artwork> ]]></artwork>
</artset> </artset>
</figure> </figure>
<t>The following subsection will determine the value of <em>C</em> using < xref target="eq6"/>.</t> <t>The following subsection will determine the value of <em>C</em> using < xref target="eq6"/>.</t>
<section anchor="fairness-to-reno"> <section anchor="fairness-to-reno">
<name>Fairness to Reno</name> <name>Fairness to Reno</name>
<t>In environments where Reno is able to make reasonable use of the <t>In environments where Reno is able to make reasonable use of the
available bandwidth, CUBIC does not significantly change this state.</t> available bandwidth, CUBIC does not significantly change this state.</t>
<t>Reno performs well in the following two types of networks:</t> <t>Reno performs well in the following two types of networks:</t>
<ol spacing="normal" type="1"><li>networks with a small bandwidth-delay product (BDP)</li> <ol spacing="normal" type="1"><li>networks with a small bandwidth-delay product (BDP)</li>
<li>networks with a short RTTs, but not necessarily a small BDP</li> <li>networks with short RTTs, but not necessarily a small BDP</li>
</ol> </ol>
<t>CUBIC is designed to behave very similarly to Reno in the above <t>CUBIC is designed to behave very similarly to Reno in the above
two types of networks. The following two tables show the average two types of networks. The following two tables show the average
window sizes of Reno TCP, HSTCP, and CUBIC TCP. The average window sizes window sizes of Reno TCP, HSTCP, and CUBIC TCP. The average window sizes
of Reno TCP and HSTCP are from <xref target="RFC3649"/>. The average window size of Reno TCP and HSTCP are from <xref target="RFC3649"/>. The average window size
of CUBIC is calculated using <xref target="eq6"/> and the CUBIC Reno-friendly of CUBIC is calculated using <xref target="eq6"/> and the CUBIC Reno-friendly
region for three different values of <em>C</em>.</t> region for three different values of <em>C</em>.</t>
<table anchor="tab1"> <table anchor="tab1">
<name>Reno TCP, HSTCP, and CUBIC with RTT = 0.1 seconds</name> <name>Reno TCP, HSTCP, and CUBIC with RTT = 0.1 Seconds</name>
<thead> <thead>
<tr> <tr>
<th align="right">Loss Rate P</th> <th align="right">Loss Rate P</th>
<th align="right">Reno</th> <th align="right">Reno</th>
<th align="right">HSTCP</th> <th align="right">HSTCP</th>
<th align="right">CUBIC (C=0.04)</th> <th align="right">CUBIC (C=0.04)</th>
<th align="right">CUBIC (C=0.4)</th> <th align="right">CUBIC (C=0.4)</th>
<th align="right">CUBIC (C=4)</th> <th align="right">CUBIC (C=4)</th>
</tr> </tr>
</thead> </thead>
skipping to change at line 2862 skipping to change at line 2832
<td align="right">12000</td> <td align="right">12000</td>
<td align="right">574356</td> <td align="right">574356</td>
<td align="right">105383</td> <td align="right">105383</td>
<td align="right">187400</td> <td align="right">187400</td>
<td align="right">333250</td> <td align="right">333250</td>
</tr> </tr>
</tbody> </tbody>
</table> </table>
<t><xref target="tab1"/> describes the response function of Reno TCP, HS TCP, and CUBIC <t><xref target="tab1"/> describes the response function of Reno TCP, HS TCP, and CUBIC
in networks with <em>RTT</em> = 0.1 seconds. The average window size is in in networks with <em>RTT</em> = 0.1 seconds. The average window size is in
MSS-sized segments.</t> SMSS-sized segments.</t>
<table anchor="tab2"> <table anchor="tab2">
<name>Reno TCP, HSTCP, and CUBIC with RTT = 0.01 seconds</name> <name>Reno TCP, HSTCP, and CUBIC with RTT = 0.01 Seconds</name>
<thead> <thead>
<tr> <tr>
<th align="right">Loss Rate P</th> <th align="right">Loss Rate P</th>
<th align="right">Reno</th> <th align="right">Reno</th>
<th align="right">HSTCP</th> <th align="right">HSTCP</th>
<th align="right">CUBIC (C=0.04)</th> <th align="right">CUBIC (C=0.04)</th>
<th align="right">CUBIC (C=0.4)</th> <th align="right">CUBIC (C=0.4)</th>
<th align="right">CUBIC (C=4)</th> <th align="right">CUBIC (C=4)</th>
</tr> </tr>
</thead> </thead>
skipping to change at line 2936 skipping to change at line 2906
<td align="right">12000</td> <td align="right">12000</td>
<td align="right">574356</td> <td align="right">574356</td>
<td align="right">18740</td> <td align="right">18740</td>
<td align="right">33325</td> <td align="right">33325</td>
<td align="right">59261</td> <td align="right">59261</td>
</tr> </tr>
</tbody> </tbody>
</table> </table>
<t><xref target="tab2"/> describes the response function of Reno TCP, HS TCP, and CUBIC <t><xref target="tab2"/> describes the response function of Reno TCP, HS TCP, and CUBIC
in networks with <em>RTT</em> = 0.01 seconds. The average window size is in in networks with <em>RTT</em> = 0.01 seconds. The average window size is in
MSS-sized segments.</t> SMSS-sized segments.</t>
<t>Both tables show that CUBIC with any of these three <em>C</em> values is more <t>Both tables show that CUBIC with any of these three <em>C</em> values is more
friendly to Reno TCP than HSTCP, especially in networks with a short friendly to Reno TCP than HSTCP, especially in networks with a short
<em>RTT</em> where Reno TCP performs reasonably well. For example, in a <em>RTT</em> where Reno TCP performs reasonably well. For example, in a
network with <em>RTT</em> = 0.01 seconds and p=10^-6, Reno TCP has an average network with <em>RTT</em> = 0.01 seconds and p=10<sup>-6</sup>, Reno TCP has an average
window of 1200 packets. If the packet size is 1500 bytes, then Reno 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 case, CUBIC with TCP can achieve an average rate of 1.44 Gbps. In this case, CUBIC with
<em>C</em>=0.04 or <em>C</em>=0.4 achieves exactly the same rate as Reno TCP, <em>C</em>=0.04 or <em>C</em>=0.4 achieves exactly the same rate as Reno TCP,
whereas HSTCP is about ten times more aggressive than Reno TCP.</t> whereas HSTCP is about ten times more aggressive than Reno TCP.</t>
<t><em>C</em> determines the aggressiveness of CUBIC in <t><em>C</em> determines the aggressiveness of CUBIC in
competing with other congestion control algorithms for bandwidth. competing with other congestion control algorithms for bandwidth.
CUBIC is more friendly to Reno TCP, if the value of <em>C</em> is lower. CUBIC is more friendly to Reno TCP if the value of <em>C</em> is lower.
However, it is <bcp14>NOT RECOMMENDED</bcp14> to set <em>C</em> to a very low va lue like However, it is <bcp14>NOT RECOMMENDED</bcp14> to set <em>C</em> to a very low va lue like
0.04, since CUBIC with a low <em>C</em> cannot efficiently use the bandwidth 0.04, since CUBIC with a low <em>C</em> cannot efficiently use the bandwidth
in fast and long-distance networks. Based on these observations and in fast and long-distance networks. Based on these observations and
extensive deployment experience, <em>C</em>=0.4 seems to give a good balance extensive deployment experience, <em>C</em>=0.4 seems to provide a good balance
between Reno-friendliness and aggressiveness of window increase. between Reno-friendliness and aggressiveness of window increase.
Therefore, <em>C</em> <bcp14>SHOULD</bcp14> be set to 0.4. With <em>C</em> set t o 0.4, <xref target="eq6"/> is Therefore, <em>C</em> <bcp14>SHOULD</bcp14> be set to 0.4. With <em>C</em> set t o 0.4, <xref target="eq6"/> is
reduced to:</t> reduced to</t>
<figure anchor="eq7"> <figure anchor="eq7">
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<use xlink:href="#E1-STIXWEBMAIN-221A" x="0" y="-60"/> <use xlink:href="#E1-STIXWEBMAIN-221A-gensym018" x="0" y
="-60"/>
<rect height="60" width="943" x="928" y="854"/> <rect height="60" width="943" x="928" y="854"/>
<g transform="translate(928,0)"> <g transform="translate(928,0)">
<use xlink:href="#E1-STIXWEBNORMALI-1D45D" x="0" y="0" <use xlink:href="#E1-STIXWEBNORMALI-1D45D-gensym018" x
/> ="0" y="0"/>
<use xlink:href="#E1-STIXWEBMAIN-33" transform="scale( <use xlink:href="#E1-STIXWEBMAIN-33-gensym018" transfo
0.707)" x="692" y="408"/> rm="scale(0.707)" x="692" y="408"/>
</g> </g>
</g> </g>
</g> </g>
</g> </g>
</g> </g>
</svg> </svg>
</artwork> </artwork>
<artwork type="ascii-art" align="center"><![CDATA[ 4 ┌────┐ <artwork type="ascii-art" align="center"><![CDATA[ 4 ┌────┐
╲ │ 3 ╲ │ 3
╲│RTT ╲│RTT
skipping to change at line 3052 skipping to change at line 3022
]]></artwork> ]]></artwork>
</artset> </artset>
</figure> </figure>
<t><xref target="eq7"/> is then used in the next subsection to show the scalability of <t><xref target="eq7"/> is then used in the next subsection to show the scalability of
CUBIC.</t> CUBIC.</t>
</section> </section>
<section anchor="using-spare-capacity"> <section anchor="using-spare-capacity">
<name>Using Spare Capacity</name> <name>Using Spare Capacity</name>
<t>CUBIC uses a more aggressive window increase function than Reno <t>CUBIC uses a more aggressive window increase function than Reno
for fast and long-distance networks.</t> for fast and long-distance networks.</t>
<t>The following table shows that to achieve the 10 Gbps rate, Reno TCP <t><xref target="tab3"/> shows that to achieve the 10 Gbps rate, Reno TC P
requires a packet loss rate of 2.0e-10, while CUBIC TCP requires a packet requires a packet loss rate of 2.0e-10, while CUBIC TCP requires a packet
loss rate of 2.9e-8.</t> loss rate of 2.9e-8.</t>
<table anchor="tab3"> <table anchor="tab3">
<name>Required packet loss rate for Reno TCP, HSTCP, and CUBIC to achi eve a certain throughput</name> <name>Required Packet Loss Rate for Reno TCP, HSTCP, and CUBIC to Achi eve a Certain Throughput</name>
<thead> <thead>
<tr> <tr>
<th align="right">Throughput (Mbps)</th> <th align="right">Throughput (Mbps)</th>
<th align="right">Average W</th> <th align="right">Average W</th>
<th align="right">Reno P</th> <th align="right">Reno P</th>
<th align="right">HSTCP P</th> <th align="right">HSTCP P</th>
<th align="right">CUBIC P</th> <th align="right">CUBIC P</th>
</tr> </tr>
</thead> </thead>
<tbody> <tbody>
skipping to change at line 3107 skipping to change at line 3077
<td align="right">83333.3</td> <td align="right">83333.3</td>
<td align="right">2.0e-10</td> <td align="right">2.0e-10</td>
<td align="right">1.0e-7</td> <td align="right">1.0e-7</td>
<td align="right">2.9e-8</td> <td align="right">2.9e-8</td>
</tr> </tr>
</tbody> </tbody>
</table> </table>
<t><xref target="tab3"/> describes the required packet loss rate for Ren o TCP, HSTCP, <t><xref target="tab3"/> describes the required packet loss rate for Ren o TCP, HSTCP,
and CUBIC to achieve a certain throughput, with 1500-byte packets and CUBIC to achieve a certain throughput, with 1500-byte packets
and an <em>RTT</em> of 0.1 seconds.</t> and an <em>RTT</em> of 0.1 seconds.</t>
<t>The test results in <xref target="HLRX07"/> indicate that, in typical cases with a <t>The test results provided in <xref target="HLRX07"/> indicate that, i n typical cases with a
degree of background traffic, CUBIC uses the spare degree of background traffic, CUBIC uses the spare
bandwidth left unused by existing Reno TCP flows in the same bandwidth left unused by existing Reno TCP flows in the same
bottleneck link without taking away much bandwidth from the existing bottleneck link without taking away much bandwidth from the existing
flows.</t> flows.</t>
</section> </section>
<section anchor="difficult-environments"> <section anchor="difficult-environments">
<name>Difficult Environments</name> <name>Difficult Environments</name>
<t>CUBIC is designed to remedy the poor performance of Reno in fast <t>CUBIC is designed to remedy the poor performance of Reno in fast
and long-distance networks.</t> and long-distance networks.</t>
</section> </section>
<section anchor="investigating-a-range-of-environments"> <section anchor="investigating-a-range-of-environments">
<name>Investigating a Range of Environments</name> <name>Investigating a Range of Environments</name>
<t>CUBIC has been extensively studied using simulations, <t>CUBIC has been extensively studied using simulations,
testbed emulations, Internet experiments, and Internet testbed emulations, Internet experiments, and Internet
measurements, covering a wide range of network environments measurements, covering a wide range of network environments
<xref target="HLRX07"/><xref target="H16"/><xref target="CEHRX09"/><xref target= "HR11"/><xref target="BSCLU13"/><xref target="LBEWK16"/>. <xref target="HLRX07"/> <xref target="H16"/> <xref target="CEHRX09"/> <xref targ et="HR11"/> <xref target="BSCLU13"/> <xref target="LBEWK16"/>.
They have convincingly demonstrated They have convincingly demonstrated
that CUBIC delivers substantial benefits over that CUBIC delivers substantial benefits over
classical Reno congestion control <xref target="RFC5681"/>.</t> classical Reno congestion control <xref target="RFC5681"/>.</t>
<t>Same as Reno, CUBIC is a loss-based congestion control algorithm. <t>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 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 drop-tail buffers more quickly than Reno and increases the risk of a
standing queue <xref target="RFC8511"/>. In this case, proper queue sizing and standing queue <xref target="RFC8511"/>. In this case, proper queue sizing and
management <xref target="RFC7567"/> could be used to mitigate the risk to some management <xref target="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 active point. This means that link utilization is less sensitive to an active
queue management (AQM) target that is lower than the amplitude of the queue management (AQM) target that is lower than the amplitude of the
whole sawtooth.</t> whole sawtooth.</t>
<t>Similar to Reno, the performance of CUBIC as a loss-based congestion <t>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 indication of bandwidth utilization, such as wireless or mobile good indication of bandwidth utilization, such as wireless or mobile
networks <xref target="LIU16"/>.</t> networks <xref target="LIU16"/>.</t>
</section> </section>
<section anchor="protection-against-congestion-collapse"> <section anchor="protection-against-congestion-collapse">
<name>Protection against Congestion Collapse</name> <name>Protection against Congestion Collapse</name>
<t>With regard to the potential of causing congestion collapse, CUBIC <t>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.</t> timeout behaviors of Reno.</t>
<t>CUBIC also satisfies the "full backoff" requirement as described in <t>CUBIC also satisfies the "full backoff" requirement as described in
<xref target="RFC5033"/>. After reducing the sending rate to one packet per <xref target="RFC5033"/>. After reducing the sending rate to one packet per
RTT in response to congestion events due to ECN-Echo ACKs, CUBIC RTT in response to congestion events detected by ECN-Echo ACKs, CUBIC
then exponentially increases the transmission then exponentially increases the transmission
timer for each packet retransmission while congestion persists.</t> timer for each packet retransmission while congestion persists.</t>
</section> </section>
<section anchor="fairness-within-the-alternative-congestion-control-algori thm"> <section anchor="fairness-within-the-alternative-congestion-control-algori thm">
<name>Fairness within the Alternative Congestion Control Algorithm</name > <name>Fairness within the Alternative Congestion Control Algorithm</name >
<t>CUBIC ensures convergence of competing CUBIC flows with the same RTT <t>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 The convergence time depends on the network environments
(e.g., bandwidth, RTT) and the level of statistical multiplexing, (e.g., bandwidth, RTT) and the level of statistical multiplexing,
as mentioned in <xref target="prin-beta"/>.</t> as mentioned in <xref target="prin-beta"/>.</t>
</section> </section>
<section anchor="performance-with-misbehaving-nodes-and-outside-attackers" > <section anchor="performance-with-misbehaving-nodes-and-outside-attackers" >
<name>Performance with Misbehaving Nodes and Outside Attackers</name> <name>Performance with Misbehaving Nodes and Outside Attackers</name>
<t>CUBIC does not introduce new entities or signals, so its vulnerabilit y to <t>CUBIC does not introduce new entities or signals, so its vulnerabilit y to
misbehaving nodes or attackers is unchanged from Reno.</t> misbehaving nodes or attackers is unchanged from Reno.</t>
</section> </section>
<section anchor="app-limited"> <section anchor="app-limited">
<name>Behavior for Application-Limited Flows</name> <name>Behavior for Application-Limited Flows</name>
<t>A flow is application-limited if it is currently sending <t>A flow is application limited if it is currently sending
less than what is allowed by the congestion window. less than what is allowed by the congestion window.
This can happen if the flow is limited by either the This can happen if the flow is limited by either the
sender application or the receiver application (via the receiver sender application or the receiver application (via the receiver's
advertised window) and thus sends less data than what is allowed by advertised window) and thus sends less data than what is allowed by
the sender's congestion window.</t> the sender's congestion window.</t>
<t>CUBIC does not increase its congestion window if a flow is applicatio <t>CUBIC does not increase its congestion window if a flow is applicatio
n-limited. n limited.
<xref target="win-inc"/> requires that <em>t</em> in <xref target="eq1"/> does n Per <xref target="win-inc"/>, it is required that <em>t</em> in <xref target="eq
ot include 1"/> not include
application-limited periods, such as idle periods, otherwise application-limited periods, such as idle periods; otherwise,
W<sub>cubic</sub>(<em>t</em>) might be very high after restarting from these W<sub>cubic</sub>(<em>t</em>) might be very high after restarting from these
periods.</t> periods.</t>
</section> </section>
<section anchor="responses-to-sudden-or-transient-events"> <section anchor="responses-to-sudden-or-transient-events">
<name>Responses to Sudden or Transient Events</name> <name>Responses to Sudden or Transient Events</name>
<t>If there is a sudden increase in capacity, e.g., due to variable radi o <t>If there is a sudden increase in capacity, e.g., due to variable radi o
capacity, a routing change, or a mobility event, CUBIC is designed to capacity, a routing change, or a mobility event, CUBIC is designed to
utilize the newly available capacity faster than Reno.</t> utilize the newly available capacity more quickly than Reno.</t>
<t>On the other hand, if there is a sudden decrease in capacity, CUBIC <t>On the other hand, if there is a sudden decrease in capacity, CUBIC
reduces more slowly than Reno. This remains true regardless of whether CUBIC reduces more slowly than Reno. This remains true regardless of whether CUBIC
is in Reno-friendly mode and regardless of whether fast convergence is is in Reno-friendly mode and regardless of whether fast convergence is
enabled.</t> enabled.</t>
</section> </section>
<section anchor="incremental-deployment"> <section anchor="incremental-deployment">
<name>Incremental Deployment</name> <name>Incremental Deployment</name>
<t>CUBIC requires only changes to the congestion control at the sender, and it does <t>CUBIC requires only changes to congestion control at the sender, and it does
not require any changes at receivers. That is, a CUBIC sender works correctly not require any changes at receivers. That is, a CUBIC sender works correctly
with Reno receivers. In addition, CUBIC does not require any with Reno receivers. In addition, CUBIC does not require any
changes to routers and does not require any assistance from routers.</t> changes to routers and does not require any assistance from routers.</t>
</section> </section>
</section> </section>
<section anchor="security-considerations"> <section anchor="security-considerations">
<name>Security Considerations</name> <name>Security Considerations</name>
<t>CUBIC makes no changes to the underlying security of a transport protoc ol <t>CUBIC makes no changes to the underlying security of a transport protoc ol
and inherits the general security concerns described in <xref target="RFC5681"/> . and inherits the general security concerns described in <xref target="RFC5681"/> .
Specifically, changing the window computation on the sender may Specifically, changing the window computation on the sender may
allow an attacker, through dropping or injecting ACKs (as described in allow an attacker, through dropping or injecting ACKs (as described in
<xref target="RFC5681"/>), to either force the CUBIC implementation to reduce it <xref target="RFC5681"/>), to either force the CUBIC implementation to reduce it
s bandwidth, s bandwidth
or to convince it that there is no congestion when congestion does exist, and us or convince it that there is no congestion when congestion does exist, and to us
e e
the CUBIC implementation as an attack vector against other hosts. These attacks the CUBIC implementation as an attack vector against other hosts. These attacks
are not new to CUBIC and are inherently part of any transport protocol like TCP. </t> are not new to CUBIC and are inherently part of any transport protocol like TCP. </t>
</section> </section>
<section anchor="iana-considerations"> <section anchor="iana-considerations">
<name>IANA Considerations</name> <name>IANA Considerations</name>
<t>This document does not require any IANA actions.</t> <t>This document does not require any IANA actions.</t>
</section> </section>
</middle> </middle>
<back> <back>
<references> <references>
<name>References</name> <name>References</name>
<references> <references>
<name>Normative References</name> <name>Normative References</name>
<reference anchor="RFC5681">
<front>
<title>TCP Congestion Control</title>
<author fullname="M. Allman" initials="M." surname="Allman">
<organization/>
</author>
<author fullname="V. Paxson" initials="V." surname="Paxson">
<organization/>
</author>
<author fullname="E. Blanton" initials="E." surname="Blanton">
<organization/>
</author>
<date month="September" year="2009"/>
<abstract>
<t>This document defines TCP's four intertwined congestion control
algorithms: slow start, congestion avoidance, fast retransmit, and fast recover
y. In addition, the document specifies how TCP should begin transmission after
a relatively long idle period, as well as discussing various acknowledgment gene
ration methods. This document obsoletes RFC 2581. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5681"/>
<seriesInfo name="DOI" value="10.17487/RFC5681"/>
</reference>
<reference anchor="RFC6582">
<front>
<title>The NewReno Modification to TCP's Fast Recovery Algorithm</ti
tle>
<author fullname="T. Henderson" initials="T." surname="Henderson">
<organization/>
</author>
<author fullname="S. Floyd" initials="S." surname="Floyd">
<organization/>
</author>
<author fullname="A. Gurtov" initials="A." surname="Gurtov">
<organization/>
</author>
<author fullname="Y. Nishida" initials="Y." surname="Nishida">
<organization/>
</author>
<date month="April" year="2012"/>
<abstract>
<t>RFC 5681 documents the following four intertwined TCP congestio
n control algorithms: slow start, congestion avoidance, fast retransmit, and fas
t recovery. RFC 5681 explicitly allows certain modifications of these algorithm
s, including modifications that use the TCP Selective Acknowledgment (SACK) opti
on (RFC 2883), and modifications that respond to "partial acknowledgments" (ACKs
that cover new data, but not all the data outstanding when loss was detected) i
n the absence of SACK. This document describes a specific algorithm for respond
ing to partial acknowledgments, referred to as "NewReno". This response to part
ial acknowledgments was first proposed by Janey Hoe. This document obsoletes RF
C 3782. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="6582"/>
<seriesInfo name="DOI" value="10.17487/RFC6582"/>
</reference>
<reference anchor="RFC6675">
<front>
<title>A Conservative Loss Recovery Algorithm Based on Selective Ack
nowledgment (SACK) for TCP</title>
<author fullname="E. Blanton" initials="E." surname="Blanton">
<organization/>
</author>
<author fullname="M. Allman" initials="M." surname="Allman">
<organization/>
</author>
<author fullname="L. Wang" initials="L." surname="Wang">
<organization/>
</author>
<author fullname="I. Jarvinen" initials="I." surname="Jarvinen">
<organization/>
</author>
<author fullname="M. Kojo" initials="M." surname="Kojo">
<organization/>
</author>
<author fullname="Y. Nishida" initials="Y." surname="Nishida">
<organization/>
</author>
<date month="August" year="2012"/>
<abstract>
<t>This document presents a conservative loss recovery algorithm f
or TCP that is based on the use of the selective acknowledgment (SACK) TCP optio
n. The algorithm presented in this document conforms to the spirit of the curre
nt congestion control specification (RFC 5681), but allows TCP senders to recove
r more effectively when multiple segments are lost from a single flight of data.
This document obsoletes RFC 3517 and describes changes from it. [STANDARDS-TR
ACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="6675"/>
<seriesInfo name="DOI" value="10.17487/RFC6675"/>
</reference>
<reference anchor="RFC5348">
<front>
<title>TCP Friendly Rate Control (TFRC): Protocol Specification</tit
le>
<author fullname="S. Floyd" initials="S." surname="Floyd">
<organization/>
</author>
<author fullname="M. Handley" initials="M." surname="Handley">
<organization/>
</author>
<author fullname="J. Padhye" initials="J." surname="Padhye">
<organization/>
</author>
<author fullname="J. Widmer" initials="J." surname="Widmer">
<organization/>
</author>
<date month="September" year="2008"/>
<abstract>
<t>This document specifies TCP Friendly Rate Control (TFRC). TFRC
is a congestion control mechanism for unicast flows operating in a best-effort
Internet environment. It is reasonably fair when competing for bandwidth with T
CP flows, but has a much lower variation of throughput over time compared with T
CP, making it more suitable for applications such as streaming media where a rel
atively smooth sending rate is of importance.</t>
<t>This document obsoletes RFC 3448 and updates RFC 4342. [STANDA
RDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5348"/>
<seriesInfo name="DOI" value="10.17487/RFC5348"/>
</reference>
<reference anchor="RFC9002">
<front>
<title>QUIC Loss Detection and Congestion Control</title>
<author fullname="J. Iyengar" initials="J." role="editor" surname="I
yengar">
<organization/>
</author>
<author fullname="I. Swett" initials="I." role="editor" surname="Swe
tt">
<organization/>
</author>
<date month="May" year="2021"/>
<abstract>
<t>This document describes loss detection and congestion control m
echanisms for QUIC.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="9002"/>
<seriesInfo name="DOI" value="10.17487/RFC9002"/>
</reference>
<reference anchor="RFC5033">
<front>
<title>Specifying New Congestion Control Algorithms</title>
<author fullname="S. Floyd" initials="S." surname="Floyd">
<organization/>
</author>
<author fullname="M. Allman" initials="M." surname="Allman">
<organization/>
</author>
<date month="August" year="2007"/>
<abstract>
<t>The IETF's standard congestion control schemes have been widely
shown to be inadequate for various environments (e.g., high-speed networks). R
ecent research has yielded many alternate congestion control schemes that signif
icantly differ from the IETF's congestion control principles. Using these new c
ongestion control schemes in the global Internet has possible ramifications to b
oth the traffic using the new congestion control and to traffic using the curren
tly standardized congestion control. Therefore, the IETF must proceed with caut
ion when dealing with alternate congestion control proposals. The goal of this
document is to provide guidance for considering alternate congestion control alg
orithms within the IETF. This document specifies an Internet Best Current Pract
ices for the Internet Community, and requests discussion and suggestions for imp
rovements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="133"/>
<seriesInfo name="RFC" value="5033"/>
<seriesInfo name="DOI" value="10.17487/RFC5033"/>
</reference>
<reference anchor="I-D.ietf-tcpm-hystartplusplus">
<front>
<title>HyStart++: Modified Slow Start for TCP</title>
<author fullname="Praveen Balasubramanian" initials="P." surname="Ba
lasubramanian">
<organization>Confluent</organization>
</author>
<author fullname="Yi Huang" initials="Y." surname="Huang">
<organization>Microsoft</organization>
</author>
<author fullname="Matt Olson" initials="M." surname="Olson">
<organization>Microsoft</organization>
</author>
<date day="30" month="January" year="2023"/>
<abstract>
<t> This document describes HyStart++, a simple modification to
the slow
start phase of congestion control algorithms. Traditional slow start
can overshoot the ideal send rate in many cases, causing high packet
loss and poor performance. HyStart++ uses a delay increase heuristic
to find an exit point before possible overshoot. It also adds a
mitigation to prevent jitter from causing premature slow start exit.
</t> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5681.xml"
</abstract> />
</front> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.6582.xml"
<seriesInfo name="Internet-Draft" value="draft-ietf-tcpm-hystartpluspl />
us-13"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.6675.xml"
</reference> />
<reference anchor="RFC2914"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5348.xml"
<front> />
<title>Congestion Control Principles</title> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.9002.xml"
<author fullname="S. Floyd" initials="S." surname="Floyd"> />
<organization/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5033.xml"
</author> />
<date month="September" year="2000"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.9406.xml"
<abstract> />
<t>The goal of this document is to explain the need for congestion <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2914.xml"
control in the Internet, and to discuss what constitutes correct congestion con />
trol. This document specifies an Internet Best Current Practices for the Intern <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2119.xml"
et Community, and requests discussion and suggestions for improvements.</t> />
</abstract> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8174.xml"
</front> />
<seriesInfo name="BCP" value="41"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3168.xml"
<seriesInfo name="RFC" value="2914"/> />
<seriesInfo name="DOI" value="10.17487/RFC2914"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8985.xml"
</reference> />
<reference anchor="RFC2119"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.6298.xml"
<front> />
<title>Key words for use in RFCs to Indicate Requirement Levels</tit <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5682.xml"
le> />
<author fullname="S. Bradner" initials="S." surname="Bradner"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.4015.xml"
<organization/> />
</author> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2883.xml"
<date month="March" year="1997"/> />
<abstract> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.7567.xml"
<t>In many standards track documents several words are used to sig />
nify the requirements in the specification. These words are often capitalized.
This document defines these words as they should be interpreted in IETF document
s. This document specifies an Internet Best Current Practices for the Internet
Community, and requests discussion and suggestions for improvements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="2119"/>
<seriesInfo name="DOI" value="10.17487/RFC2119"/>
</reference>
<reference anchor="RFC8174">
<front>
<title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</ti
tle>
<author fullname="B. Leiba" initials="B." surname="Leiba">
<organization/>
</author>
<date month="May" year="2017"/>
<abstract>
<t>RFC 2119 specifies common key words that may be used in protoco
l specifications. This document aims to reduce the ambiguity by clarifying tha
t only UPPERCASE usage of the key words have the defined special meanings.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="8174"/>
<seriesInfo name="DOI" value="10.17487/RFC8174"/>
</reference>
<reference anchor="RFC3168">
<front>
<title>The Addition of Explicit Congestion Notification (ECN) to IP<
/title>
<author fullname="K. Ramakrishnan" initials="K." surname="Ramakrishn
an">
<organization/>
</author>
<author fullname="S. Floyd" initials="S." surname="Floyd">
<organization/>
</author>
<author fullname="D. Black" initials="D." surname="Black">
<organization/>
</author>
<date month="September" year="2001"/>
<abstract>
<t>This memo specifies the incorporation of ECN (Explicit Congesti
on Notification) to TCP and IP, including ECN's use of two bits in the IP header
. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="3168"/>
<seriesInfo name="DOI" value="10.17487/RFC3168"/>
</reference>
<reference anchor="RFC8985">
<front>
<title>The RACK-TLP Loss Detection Algorithm for TCP</title>
<author fullname="Y. Cheng" initials="Y." surname="Cheng">
<organization/>
</author>
<author fullname="N. Cardwell" initials="N." surname="Cardwell">
<organization/>
</author>
<author fullname="N. Dukkipati" initials="N." surname="Dukkipati">
<organization/>
</author>
<author fullname="P. Jha" initials="P." surname="Jha">
<organization/>
</author>
<date month="February" year="2021"/>
<abstract>
<t>This document presents the RACK-TLP loss detection algorithm fo
r TCP. RACK-TLP uses per-segment transmit timestamps and selective acknowledgmen
ts (SACKs) and has two parts. Recent Acknowledgment (RACK) starts fast recovery
quickly using time-based inferences derived from acknowledgment (ACK) feedback,
and Tail Loss Probe (TLP) leverages RACK and sends a probe packet to trigger ACK
feedback to avoid retransmission timeout (RTO) events. Compared to the widely u
sed duplicate acknowledgment (DupAck) threshold approach, RACK-TLP detects losse
s more efficiently when there are application-limited flights of data, lost retr
ansmissions, or data packet reordering events. It is intended to be an alternati
ve to the DupAck threshold approach.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="8985"/>
<seriesInfo name="DOI" value="10.17487/RFC8985"/>
</reference>
<reference anchor="RFC6298">
<front>
<title>Computing TCP's Retransmission Timer</title>
<author fullname="V. Paxson" initials="V." surname="Paxson">
<organization/>
</author>
<author fullname="M. Allman" initials="M." surname="Allman">
<organization/>
</author>
<author fullname="J. Chu" initials="J." surname="Chu">
<organization/>
</author>
<author fullname="M. Sargent" initials="M." surname="Sargent">
<organization/>
</author>
<date month="June" year="2011"/>
<abstract>
<t>This document defines the standard algorithm that Transmission
Control Protocol (TCP) senders are required to use to compute and manage their r
etransmission timer. It expands on the discussion in Section 4.2.3.1 of RFC 112
2 and upgrades the requirement of supporting the algorithm from a SHOULD to a MU
ST. This document obsoletes RFC 2988. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="6298"/>
<seriesInfo name="DOI" value="10.17487/RFC6298"/>
</reference>
<reference anchor="RFC5682">
<front>
<title>Forward RTO-Recovery (F-RTO): An Algorithm for Detecting Spur
ious Retransmission Timeouts with TCP</title>
<author fullname="P. Sarolahti" initials="P." surname="Sarolahti">
<organization/>
</author>
<author fullname="M. Kojo" initials="M." surname="Kojo">
<organization/>
</author>
<author fullname="K. Yamamoto" initials="K." surname="Yamamoto">
<organization/>
</author>
<author fullname="M. Hata" initials="M." surname="Hata">
<organization/>
</author>
<date month="September" year="2009"/>
<abstract>
<t>The purpose of this document is to move the F-RTO (Forward RTO-
Recovery) functionality for TCP in RFC 4138 from Experimental to Standards Track
status. The F-RTO support for Stream Control Transmission Protocol (SCTP) in R
FC 4138 remains with Experimental status. See Appendix B for the differences be
tween this document and RFC 4138.</t>
<t>Spurious retransmission timeouts cause suboptimal TCP performan
ce because they often result in unnecessary retransmission of the last window of
data. This document describes the F-RTO detection algorithm for detecting spur
ious TCP retransmission timeouts. F-RTO is a TCP sender-only algorithm that doe
s not require any TCP options to operate. After retransmitting the first unackn
owledged segment triggered by a timeout, the F-RTO algorithm of the TCP sender m
onitors the incoming acknowledgments to determine whether the timeout was spurio
us. It then decides whether to send new segments or retransmit unacknowledged s
egments. The algorithm effectively helps to avoid additional unnecessary retran
smissions and thereby improves TCP performance in the case of a spurious timeout
. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5682"/>
<seriesInfo name="DOI" value="10.17487/RFC5682"/>
</reference>
<reference anchor="RFC4015">
<front>
<title>The Eifel Response Algorithm for TCP</title>
<author fullname="R. Ludwig" initials="R." surname="Ludwig">
<organization/>
</author>
<author fullname="A. Gurtov" initials="A." surname="Gurtov">
<organization/>
</author>
<date month="February" year="2005"/>
<abstract>
<t>Based on an appropriate detection algorithm, the Eifel response
algorithm provides a way for a TCP sender to respond to a detected spurious tim
eout. It adapts the retransmission timer to avoid further spurious timeouts and
(depending on the detection algorithm) can avoid the often unnecessary go-back-
N retransmits that would otherwise be sent. In addition, the Eifel response alg
orithm restores the congestion control state in such a way that packet bursts ar
e avoided. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="4015"/>
<seriesInfo name="DOI" value="10.17487/RFC4015"/>
</reference>
<reference anchor="RFC2883">
<front>
<title>An Extension to the Selective Acknowledgement (SACK) Option f
or TCP</title>
<author fullname="S. Floyd" initials="S." surname="Floyd">
<organization/>
</author>
<author fullname="J. Mahdavi" initials="J." surname="Mahdavi">
<organization/>
</author>
<author fullname="M. Mathis" initials="M." surname="Mathis">
<organization/>
</author>
<author fullname="M. Podolsky" initials="M." surname="Podolsky">
<organization/>
</author>
<date month="July" year="2000"/>
<abstract>
<t>This note defines an extension of the Selective Acknowledgement
(SACK) Option for TCP. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="2883"/>
<seriesInfo name="DOI" value="10.17487/RFC2883"/>
</reference>
<reference anchor="RFC7567">
<front>
<title>IETF Recommendations Regarding Active Queue Management</title
>
<author fullname="F. Baker" initials="F." role="editor" surname="Bak
er">
<organization/>
</author>
<author fullname="G. Fairhurst" initials="G." role="editor" surname=
"Fairhurst">
<organization/>
</author>
<date month="July" year="2015"/>
<abstract>
<t>This memo presents recommendations to the Internet community co
ncerning measures to improve and preserve Internet performance. It presents a s
trong recommendation for testing, standardization, and widespread deployment of
active queue management (AQM) in network devices to improve the performance of t
oday's Internet. It also urges a concerted effort of research, measurement, and
ultimate deployment of AQM mechanisms to protect the Internet from flows that a
re not sufficiently responsive to congestion notification.</t>
<t>Based on 15 years of experience and new research, this document
replaces the recommendations of RFC 2309.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="197"/>
<seriesInfo name="RFC" value="7567"/>
<seriesInfo name="DOI" value="10.17487/RFC7567"/>
</reference>
</references> </references>
<references> <references>
<name>Informative References</name> <name>Informative References</name>
<reference anchor="FHP00" target="https://www.icir.org/tfrc/aimd.pdf"> <reference anchor="FHP00" target="https://www.icir.org/tfrc/aimd.pdf">
<front> <front>
<title>A Comparison of Equation-Based and AIMD Congestion Control</t itle> <title>A Comparison of Equation-Based and AIMD Congestion Control</t itle>
<author initials="S." surname="Floyd"> <author initials="S." surname="Floyd">
<organization/> <organization/>
</author> </author>
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<organization/> <organization/>
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</author> </author>
<date year="2000" month="May"/> <date year="2000" month="May"/>
</front> </front>
</reference> </reference>
<reference anchor="GV02" target="https://www.cs.utexas.edu/ftp/techrepor
ts/tr02-39.ps.gz"> <reference anchor="GV02" target="https://citeseerx.ist.psu.edu/document?
repid=rep1&amp;type=pdf&amp;doi=1828bdcef118b02d3996b8e00b8aaa92b50abb0f">
<front> <front>
<title>Extended Analysis of Binary Adjustment Algorithms</title> <title>Extended Analysis of Binary Adjustment Algorithms</title>
<author initials="S." surname="Gorinsky"> <author initials="S." surname="Gorinsky">
<organization/> <organization/>
</author> </author>
<author initials="H." surname="Vin"> <author initials="H." surname="Vin">
<organization/> <organization/>
</author> </author>
<date year="2002" month="August" day="11"/> <date year="2002" month="August"/>
</front> </front>
<seriesInfo name="Technical Report" value="TR2002-29"/> <refcontent>Technical Report TR2002-39, Department of Computer Science
<seriesInfo name="Department of" value="Computer Sciences"/> s, The University of Texas at Austin</refcontent>
<seriesInfo name="The University of Texas" value="at Austin"/>
</reference> </reference>
<reference anchor="H16" target="https://web.archive.org/web/201611181258 42/http://netsrv.csc.ncsu.edu/wiki/index.php/TCP_Testing"> <reference anchor="H16" target="https://web.archive.org/web/201611181258 42/http://netsrv.csc.ncsu.edu/wiki/index.php/TCP_Testing">
<front> <front>
<title>Simulation, Testbed, and Deployment Testing Results of CUBIC< /title> <title>Deployment, Testbed, and Simulation Results for CUBIC</title>
<author initials="S." surname="Ha"> <author initials="S." surname="Ha">
<organization/> <organization/>
</author> </author>
<date year="2016" month="November" day="03"/> <date year="2016" month="November" day="3"/>
</front> </front>
<refcontent>Wayback Machine archive</refcontent>
</reference> </reference>
<reference anchor="AIMD-friendliness" target="https://raw.githubusercont
ent.com/bbriscoe/cubic-reno/main/creno_tr.pdf"> <reference anchor="AIMD-friendliness" target="https://arxiv.org/abs/2305
.10581">
<front> <front>
<title>Friendliness between AIMD Algorithms</title> <title>Friendliness between AIMD Algorithms</title>
<author initials="B." surname="Briscoe"> <author initials="B." surname="Briscoe">
<organization/> <organization/>
</author> </author>
<author initials="O." surname="Albisser"> <author initials="O." surname="Albisser">
<organization/> <organization/>
</author> </author>
<date year="2022" month="August" day="08"/> <date year="2023" month="May"/>
</front> </front>
<seriesInfo name="RFC Editor, please replace this URL with the permane nt arXiv one" value=""/> <seriesInfo name="DOI" value="10.48550/arXiv.2305.10581"/>
</reference> </reference>
<reference anchor="SXEZ19"> <reference anchor="SXEZ19">
<front> <front>
<title>Model-Agnostic and Efficient Exploration of Numerical Congest ion Control State Space of Real-World TCP Implementations</title> <title>Model-Agnostic and Efficient Exploration of Numerical Congest ion Control State Space of Real-World TCP Implementations</title>
<author fullname="Wei Sun" initials="W." surname="Sun"> <author fullname="Wei Sun" initials="W." surname="Sun">
<organization/> <organization/>
</author> </author>
<author fullname="Lisong Xu" initials="L." surname="Xu"> <author fullname="Lisong Xu" initials="L." surname="Xu">
<organization/> <organization/>
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<author fullname="Sebastian Elbaum" initials="S." surname="Elbaum"> <author fullname="Sebastian Elbaum" initials="S." surname="Elbaum">
<organization/> <organization/>
</author> </author>
<author fullname="Di Zhao" initials="D." surname="Zhao"> <author fullname="Di Zhao" initials="D." surname="Zhao">
<organization/> <organization/>
</author> </author>
<date month="October" year="2021"/> <date month="October" year="2021"/>
</front> </front>
<seriesInfo name="IEEE/ACM Transactions on Networking" value="vol. 29, no. 5, pp. 1990-2004"/> <refcontent>IEEE/ACM Transactions on Networking, vol. 29, no. 5, pp. 1 990-2004</refcontent>
<seriesInfo name="DOI" value="10.1109/tnet.2021.3078161"/> <seriesInfo name="DOI" value="10.1109/tnet.2021.3078161"/>
</reference> </reference>
<reference anchor="XHR04"> <reference anchor="XHR04">
<front> <front>
<title>Binary increase congestion control (BIC) for fast long-distan ce networks</title> <title>Binary increase congestion control (BIC) for fast long-distan ce networks</title>
<author fullname="Lisong Xu" initials="L." surname="Xu"> <author fullname="Lisong Xu" initials="L." surname="Xu">
<organization/> <organization/>
</author> </author>
<author fullname="K. Harfoush" initials="K." surname="Harfoush"> <author fullname="K. Harfoush" initials="K." surname="Harfoush">
<organization/> <organization/>
</author> </author>
<author fullname="Injong Rhee" initials="I." surname="Rhee"> <author fullname="Injong Rhee" initials="I." surname="Rhee">
<organization/> <organization/>
</author> </author>
<date month="February" year="2005"/> <date month="March" year="2004"/>
</front> </front>
<seriesInfo name="IEEE INFOCOM" value="2004"/> <refcontent>IEEE INFOCOM 2004</refcontent>
<seriesInfo name="DOI" value="10.1109/infcom.2004.1354672"/> <seriesInfo name="DOI" value="10.1109/infcom.2004.1354672"/>
</reference> </reference>
<reference anchor="HLRX07"> <reference anchor="HLRX07">
<front> <front>
<title>Impact of background traffic on performance of high-speed TCP variant protocols</title> <title>Impact of background traffic on performance of high-speed TCP variant protocols</title>
<author fullname="Sangtae Ha" initials="S." surname="Ha"> <author fullname="Sangtae Ha" initials="S." surname="Ha">
<organization/> <organization/>
</author> </author>
<author fullname="Long Le" initials="L." surname="Le"> <author fullname="Long Le" initials="L." surname="Le">
<organization/> <organization/>
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<organization/> <organization/>
</author> </author>
<author fullname="Lisong Xu" initials="L." surname="Xu"> <author fullname="Lisong Xu" initials="L." surname="Xu">
<organization/> <organization/>
</author> </author>
<date month="May" year="2007"/> <date month="May" year="2007"/>
</front> </front>
<seriesInfo name="Computer Networks" value="vol. 51, no. 7, pp. 1748-1 762"/> <refcontent>Computer Networks, vol. 51, no. 7, pp. 1748-1762</refconte nt>
<seriesInfo name="DOI" value="10.1016/j.comnet.2006.11.005"/> <seriesInfo name="DOI" value="10.1016/j.comnet.2006.11.005"/>
</reference> </reference>
<reference anchor="CEHRX09"> <reference anchor="CEHRX09">
<front> <front>
<title>Stochastic convex ordering for multiplicative decrease intern et congestion control</title> <title>Stochastic convex ordering for multiplicative decrease intern et congestion control</title>
<author fullname="Han Cai" initials="H." surname="Cai"> <author fullname="Han Cai" initials="H." surname="Cai">
<organization/> <organization/>
</author> </author>
<author fullname="Do Young Eun" initials="D." surname="Eun"> <author fullname="Do Young Eun" initials="D." surname="Eun">
<organization/> <organization/>
</author> </author>
<author fullname="Sangtae Ha" initials="S." surname="Ha"> <author fullname="Sangtae Ha" initials="S." surname="Ha">
<organization/> <organization/>
</author> </author>
<author fullname="Injong Rhee" initials="I." surname="Rhee"> <author fullname="Injong Rhee" initials="I." surname="Rhee">
<organization/> <organization/>
</author> </author>
<author fullname="Lisong Xu" initials="L." surname="Xu"> <author fullname="Lisong Xu" initials="L." surname="Xu">
<organization/> <organization/>
</author> </author>
<date month="February" year="2009"/> <date month="February" year="2009"/>
</front> </front>
<seriesInfo name="Computer Networks" value="vol. 53, no. 3, pp. 365-38 1"/> <refcontent>Computer Networks, vol. 53, no. 3, pp. 365-381</refcontent >
<seriesInfo name="DOI" value="10.1016/j.comnet.2008.10.012"/> <seriesInfo name="DOI" value="10.1016/j.comnet.2008.10.012"/>
</reference> </reference>
<reference anchor="HR11"> <reference anchor="HR11">
<front> <front>
<title>Taming the elephants: New TCP slow start</title> <title>Taming the elephants: New TCP slow start</title>
<author fullname="Sangtae Ha" initials="S." surname="Ha"> <author fullname="Sangtae Ha" initials="S." surname="Ha">
<organization/> <organization/>
</author> </author>
<author fullname="Injong Rhee" initials="I." surname="Rhee"> <author fullname="Injong Rhee" initials="I." surname="Rhee">
<organization/> <organization/>
</author> </author>
<date month="June" year="2011"/> <date month="June" year="2011"/>
</front> </front>
<seriesInfo name="Computer Networks" value="vol. 55, no. 9, pp. 2092-2 110"/> <refcontent>Computer Networks, vol. 55, no. 9, pp. 2092-2110</refconte nt>
<seriesInfo name="DOI" value="10.1016/j.comnet.2011.01.014"/> <seriesInfo name="DOI" value="10.1016/j.comnet.2011.01.014"/>
</reference> </reference>
<reference anchor="BSCLU13"> <reference anchor="BSCLU13">
<front> <front>
<title>Understanding TCP cubic performance in the cloud: A mean-fiel d approach</title> <title>Understanding TCP cubic performance in the cloud: A mean-fiel d approach</title>
<author fullname="Sonia Belhareth" initials="S." surname="Belhareth" > <author fullname="Sonia Belhareth" initials="S." surname="Belhareth" >
<organization/> <organization/>
</author> </author>
<author fullname="Lucile Sassatelli" initials="L." surname="Sassatel li"> <author fullname="Lucile Sassatelli" initials="L." surname="Sassatel li">
<organization/> <organization/>
</author> </author>
<author fullname="Denis Collange" initials="D." surname="Collange"> <author fullname="Denis Collange" initials="D." surname="Collange">
<organization/> <organization/>
</author> </author>
<author fullname="Dino Lopez-Pacheco" initials="D." surname="Lopez-P acheco"> <author fullname="Dino Lopez-Pacheco" initials="D." surname="Lopez-P acheco">
<organization/> <organization/>
</author> </author>
<author fullname="Guillaume Urvoy-Keller" initials="G." surname="Urv oy-Keller"> <author fullname="Guillaume Urvoy-Keller" initials="G." surname="Urv oy-Keller">
<organization/> <organization/>
</author> </author>
<date month="November" year="2013"/> <date month="November" year="2013"/>
</front> </front>
<seriesInfo name="2013 IEEE 2nd International Conference on Cloud Netw orking" value="(CloudNet)"/> <refcontent>2013 IEEE 2nd International Conference on Cloud Networking (CloudNet)</refcontent>
<seriesInfo name="DOI" value="10.1109/cloudnet.2013.6710576"/> <seriesInfo name="DOI" value="10.1109/cloudnet.2013.6710576"/>
</reference> </reference>
<reference anchor="LBEWK16"> <reference anchor="LBEWK16">
<front> <front>
<title>A Comparison of TCP Congestion Control Algorithms in 10G Netw orks</title> <title>A Comparison of TCP Congestion Control Algorithms in 10G Netw orks</title>
<author fullname="Thomas Lukaseder" initials="T." surname="Lukaseder "> <author fullname="Thomas Lukaseder" initials="T." surname="Lukaseder ">
<organization/> <organization/>
</author> </author>
<author fullname="Leonard Bradatsch" initials="L." surname="Bradatsc h"> <author fullname="Leonard Bradatsch" initials="L." surname="Bradatsc h">
<organization/> <organization/>
</author> </author>
<author fullname="Benjamin Erb" initials="B." surname="Erb"> <author fullname="Benjamin Erb" initials="B." surname="Erb">
<organization/> <organization/>
</author> </author>
<author fullname="Rens W. Van Der Heijden" initials="R." surname="Va n Der Heijden"> <author fullname="Rens W. Van Der Heijden" initials="R." surname="Va n Der Heijden">
<organization/> <organization/>
</author> </author>
<author fullname="Frank Kargl" initials="F." surname="Kargl"> <author fullname="Frank Kargl" initials="F." surname="Kargl">
<organization/> <organization/>
</author> </author>
<date month="November" year="2016"/> <date month="November" year="2016"/>
</front> </front>
<seriesInfo name="2016 IEEE 41st Conference on Local Computer Networks " value="(LCN)"/> <refcontent>2016 IEEE 41st Conference on Local Computer Networks (LCN) </refcontent>
<seriesInfo name="DOI" value="10.1109/lcn.2016.121"/> <seriesInfo name="DOI" value="10.1109/lcn.2016.121"/>
</reference> </reference>
<reference anchor="HRX08"> <reference anchor="HRX08">
<front> <front>
<title>CUBIC: a new TCP-friendly high-speed TCP variant</title> <title>CUBIC: a new TCP-friendly high-speed TCP variant</title>
<author fullname="Sangtae Ha" initials="S." surname="Ha"> <author fullname="Sangtae Ha" initials="S." surname="Ha">
<organization>North Carolina State University, Raleigh, NC</organi zation> <organization>North Carolina State University, Raleigh, NC</organi zation>
</author> </author>
<author fullname="Injong Rhee" initials="I." surname="Rhee"> <author fullname="Injong Rhee" initials="I." surname="Rhee">
<organization>North Carolina State University, Raleigh, NC</organi zation> <organization>North Carolina State University, Raleigh, NC</organi zation>
</author> </author>
<author fullname="Lisong Xu" initials="L." surname="Xu"> <author fullname="Lisong Xu" initials="L." surname="Xu">
<organization>University of Nebraska, Lincoln, Nebraska</organizat ion> <organization>University of Nebraska, Lincoln, Nebraska</organizat ion>
</author> </author>
<date month="July" year="2008"/> <date month="July" year="2008"/>
</front> </front>
<seriesInfo name="ACM SIGOPS Operating Systems Review" value="vol. 42, no. 5, pp. 64-74"/> <refcontent>ACM SIGOPS Operating Systems Review, vol. 42, no. 5, pp. 6 4-74</refcontent>
<seriesInfo name="DOI" value="10.1145/1400097.1400105"/> <seriesInfo name="DOI" value="10.1145/1400097.1400105"/>
</reference> </reference>
<reference anchor="K03"> <reference anchor="K03">
<front> <front>
<title>Scalable TCP: improving performance in highspeed wide area ne tworks</title> <title>Scalable TCP: improving performance in highspeed wide area ne tworks</title>
<author fullname="Tom Kelly" initials="T." surname="Kelly"> <author fullname="Tom Kelly" initials="T." surname="Kelly">
<organization>CERN-IT Division, Geneva, Switzerland</organization> <organization>CERN-IT Division, Geneva, Switzerland</organization>
</author> </author>
<date month="April" year="2003"/> <date month="April" year="2003"/>
</front> </front>
<seriesInfo name="ACM SIGCOMM Computer Communication Review" value="vo l. 33, no. 2, pp. 83-91"/> <refcontent>ACM SIGCOMM Computer Communication Review, vol. 33, no. 2, pp. 83-91</refcontent>
<seriesInfo name="DOI" value="10.1145/956981.956989"/> <seriesInfo name="DOI" value="10.1145/956981.956989"/>
</reference> </reference>
<reference anchor="LIU16"> <reference anchor="LIU16">
<front> <front>
<title>On Improving TCP Performance over Mobile Data Networks</title > <title>On Improving TCP Performance over Mobile Data Networks</title >
<author fullname="Ke Liu" initials="K." surname="Liu"> <author fullname="Ke Liu" initials="K." surname="Liu">
<organization/> <organization/>
</author> </author>
<author fullname="Jack Y.B. Lee" initials="J." surname="Lee"> <author fullname="Jack Y.B. Lee" initials="J." surname="Lee">
<organization/> <organization/>
</author> </author>
<date month="October" year="2016"/> <date month="October" year="2016"/>
</front> </front>
<seriesInfo name="IEEE Transactions on Mobile Computing" value="vol. 1 5, no. 10, pp. 2522-2536"/> <refcontent>IEEE Transactions on Mobile Computing, vol. 15, no. 10, pp . 2522-2536</refcontent>
<seriesInfo name="DOI" value="10.1109/tmc.2015.2500227"/> <seriesInfo name="DOI" value="10.1109/tmc.2015.2500227"/>
</reference> </reference>
<reference anchor="RFC9000">
<front>
<title>QUIC: A UDP-Based Multiplexed and Secure Transport</title>
<author fullname="J. Iyengar" initials="J." role="editor" surname="I
yengar">
<organization/>
</author>
<author fullname="M. Thomson" initials="M." role="editor" surname="T
homson">
<organization/>
</author>
<date month="May" year="2021"/>
<abstract>
<t>This document defines the core of the QUIC transport protocol.
QUIC provides applications with flow-controlled streams for structured communic
ation, low-latency connection establishment, and network path migration. QUIC in
cludes security measures that ensure confidentiality, integrity, and availabilit
y in a range of deployment circumstances. Accompanying documents describe the i
ntegration of TLS for key negotiation, loss detection, and an exemplary congesti
on control algorithm.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="9000"/>
<seriesInfo name="DOI" value="10.17487/RFC9000"/>
</reference>
<reference anchor="RFC9260">
<front>
<title>Stream Control Transmission Protocol</title>
<author fullname="R. Stewart" initials="R." surname="Stewart">
<organization/>
</author>
<author fullname="M. Tüxen" initials="M." surname="Tüxen">
<organization/>
</author>
<author fullname="K. Nielsen" initials="K." surname="Nielsen">
<organization/>
</author>
<date month="June" year="2022"/>
<abstract>
<t>This document describes the Stream Control Transmission Protoco
l (SCTP) and obsoletes RFC 4960. It incorporates the specification of the chunk
flags registry from RFC 6096 and the specification of the I bit of DATA chunks
from RFC 7053. Therefore, RFCs 6096 and 7053 are also obsoleted by this document
. In addition, RFCs 4460 and 8540, which describe errata for SCTP, are obsoleted
by this document. </t>
<t>SCTP was originally designed to transport Public Switched Telep
hone Network (PSTN) signaling messages over IP networks. It is also suited to be
used for other applications, for example, WebRTC.</t>
<t>SCTP is a reliable transport protocol operating on top of a con
nectionless packet network, such as IP. It offers the following services to its
users:</t>
<t>The design of SCTP includes appropriate congestion avoidance be
havior and resistance to flooding and masquerade attacks.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="9260"/>
<seriesInfo name="DOI" value="10.17487/RFC9260"/>
</reference>
<reference anchor="RFC3649">
<front>
<title>HighSpeed TCP for Large Congestion Windows</title>
<author fullname="S. Floyd" initials="S." surname="Floyd">
<organization/>
</author>
<date month="December" year="2003"/>
<abstract>
<t>The proposals in this document are experimental. While they ma
y be deployed in the current Internet, they do not represent a consensus that th
is is the best method for high-speed congestion control. In particular, we note
that alternative experimental proposals are likely to be forthcoming, and it is
not well understood how the proposals in this document will interact with such
alternative proposals. This document proposes HighSpeed TCP, a modification to
TCP's congestion control mechanism for use with TCP connections with large conge
stion windows. The congestion control mechanisms of the current Standard TCP co
nstrains the congestion windows that can be achieved by TCP in realistic environ
ments. For example, for a Standard TCP connection with 1500-byte packets and a
100 ms round-trip time, achieving a steady-state throughput of 10 Gbps would req
uire an average congestion window of 83,333 segments, and a packet drop rate of
at most one congestion event every 5,000,000,000 packets (or equivalently, at mo
st one congestion event every 1 2/3 hours). This is widely acknowledged as an u
nrealistic constraint. To address his limitation of TCP, this document proposes
HighSpeed TCP, and solicits experimentation and feedback from the wider communi
ty.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="3649"/>
<seriesInfo name="DOI" value="10.17487/RFC3649"/>
</reference>
<reference anchor="RFC8312">
<front>
<title>CUBIC for Fast Long-Distance Networks</title>
<author fullname="I. Rhee" initials="I." surname="Rhee">
<organization/>
</author>
<author fullname="L. Xu" initials="L." surname="Xu">
<organization/>
</author>
<author fullname="S. Ha" initials="S." surname="Ha">
<organization/>
</author>
<author fullname="A. Zimmermann" initials="A." surname="Zimmermann">
<organization/>
</author>
<author fullname="L. Eggert" initials="L." surname="Eggert">
<organization/>
</author>
<author fullname="R. Scheffenegger" initials="R." surname="Scheffene
gger">
<organization/>
</author>
<date month="February" year="2018"/>
<abstract>
<t>CUBIC is an extension to the current TCP standards. It differs
from the current TCP standards only in the congestion control algorithm on the
sender side. In particular, it uses a cubic function instead of a linear window
increase function of the current TCP standards to improve scalability and stabi
lity under fast and long-distance networks. CUBIC and its predecessor algorithm
have been adopted as defaults by Linux and have been used for many years. This
document provides a specification of CUBIC to enable third-party implementation
s and to solicit community feedback through experimentation on the performance o
f CUBIC.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="8312"/>
<seriesInfo name="DOI" value="10.17487/RFC8312"/>
</reference>
<reference anchor="RFC6937">
<front>
<title>Proportional Rate Reduction for TCP</title>
<author fullname="M. Mathis" initials="M." surname="Mathis">
<organization/>
</author>
<author fullname="N. Dukkipati" initials="N." surname="Dukkipati">
<organization/>
</author>
<author fullname="Y. Cheng" initials="Y." surname="Cheng">
<organization/>
</author>
<date month="May" year="2013"/>
<abstract>
<t>This document describes an experimental Proportional Rate Reduc
tion (PRR) algorithm as an alternative to the widely deployed Fast Recovery and
Rate-Halving algorithms. These algorithms determine the amount of data sent by
TCP during loss recovery. PRR minimizes excess window adjustments, and the actu
al window size at the end of recovery will be as close as possible to the ssthre
sh, as determined by the congestion control algorithm.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="6937"/>
<seriesInfo name="DOI" value="10.17487/RFC6937"/>
</reference>
<reference anchor="RFC7661">
<front>
<title>Updating TCP to Support Rate-Limited Traffic</title>
<author fullname="G. Fairhurst" initials="G." surname="Fairhurst">
<organization/>
</author>
<author fullname="A. Sathiaseelan" initials="A." surname="Sathiaseel
an">
<organization/>
</author>
<author fullname="R. Secchi" initials="R." surname="Secchi">
<organization/>
</author>
<date month="October" year="2015"/>
<abstract>
<t>This document provides a mechanism to address issues that arise
when TCP is used for traffic that exhibits periods where the sending rate is li
mited by the application rather than the congestion window. It provides an expe
rimental update to TCP that allows a TCP sender to restart quickly following a r
ate-limited interval. This method is expected to benefit applications that send
rate-limited traffic using TCP while also providing an appropriate response if
congestion is experienced.</t>
<t>This document also evaluates the Experimental specification of
TCP Congestion Window Validation (CWV) defined in RFC 2861 and concludes that RF
C 2861 sought to address important issues but failed to deliver a widely used so
lution. This document therefore reclassifies the status of RFC 2861 from Experi
mental to Historic. This document obsoletes RFC 2861.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="7661"/>
<seriesInfo name="DOI" value="10.17487/RFC7661"/>
</reference>
<reference anchor="RFC3522">
<front>
<title>The Eifel Detection Algorithm for TCP</title>
<author fullname="R. Ludwig" initials="R." surname="Ludwig">
<organization/>
</author>
<author fullname="M. Meyer" initials="M." surname="Meyer">
<organization/>
</author>
<date month="April" year="2003"/>
<abstract>
<t>The Eifel detection algorithm allows a TCP sender to detect a p
osteriori whether it has entered loss recovery unnecessarily. It requires that
the TCP Timestamps option defined in RFC 1323 be enabled for a connection. The
Eifel detection algorithm makes use of the fact that the TCP Timestamps option e
liminates the retransmission ambiguity in TCP. Based on the timestamp of the fi
rst acceptable ACK that arrives during loss recovery, it decides whether loss re
covery was entered unnecessarily. The Eifel detection algorithm provides a basi
s for future TCP enhancements. This includes response algorithms to back out of
loss recovery by restoring a TCP sender's congestion control state. This memo d
efines an Experimental Protocol for the Internet community.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="3522"/>
<seriesInfo name="DOI" value="10.17487/RFC3522"/>
</reference>
<reference anchor="RFC3708">
<front>
<title>Using TCP Duplicate Selective Acknowledgement (DSACKs) and St
ream Control Transmission Protocol (SCTP) Duplicate Transmission Sequence Number
s (TSNs) to Detect Spurious Retransmissions</title>
<author fullname="E. Blanton" initials="E." surname="Blanton">
<organization/>
</author>
<author fullname="M. Allman" initials="M." surname="Allman">
<organization/>
</author>
<date month="February" year="2004"/>
<abstract>
<t>TCP and Stream Control Transmission Protocol (SCTP) provide not
ification of duplicate segment receipt through Duplicate Selective Acknowledgeme
nt (DSACKs) and Duplicate Transmission Sequence Number (TSN) notification, respe
ctively. This document presents conservative methods of using this information
to identify unnecessary retransmissions for various applications. This memo def
ines an Experimental Protocol for the Internet community.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="3708"/>
<seriesInfo name="DOI" value="10.17487/RFC3708"/>
</reference>
<reference anchor="RFC3742">
<front>
<title>Limited Slow-Start for TCP with Large Congestion Windows</tit
le>
<author fullname="S. Floyd" initials="S." surname="Floyd">
<organization/>
</author>
<date month="March" year="2004"/>
<abstract>
<t>This document describes an optional modification for TCP's slow
-start for use with TCP connections with large congestion windows. For TCP conn
ections that are able to use congestion windows of thousands (or tens of thousan
ds) of MSS-sized segments (for MSS the sender's MAXIMUM SEGMENT SIZE), the curre
nt slow-start procedure can result in increasing the congestion window by thousa
nds of segments in a single round-trip time. Such an increase can easily result
in thousands of packets being dropped in one round-trip time. This is often co
unter-productive for the TCP flow itself, and is also hard on the rest of the tr
affic sharing the congested link. This note describes Limited Slow-Start as an
optional mechanism for limiting the number of segments by which the congestion w
indow is increased for one window of data during slow-start, in order to improve
performance for TCP connections with large congestion windows. This memo defin
es an Experimental Protocol for the Internet community.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="3742"/>
<seriesInfo name="DOI" value="10.17487/RFC3742"/>
</reference>
<reference anchor="RFC8511">
<front>
<title>TCP Alternative Backoff with ECN (ABE)</title>
<author fullname="N. Khademi" initials="N." surname="Khademi">
<organization/>
</author>
<author fullname="M. Welzl" initials="M." surname="Welzl">
<organization/>
</author>
<author fullname="G. Armitage" initials="G." surname="Armitage">
<organization/>
</author>
<author fullname="G. Fairhurst" initials="G." surname="Fairhurst">
<organization/>
</author>
<date month="December" year="2018"/>
<abstract>
<t>Active Queue Management (AQM) mechanisms allow for burst tolera
nce while enforcing short queues to minimise the time that packets spend enqueue
d at a bottleneck. This can cause noticeable performance degradation for TCP co
nnections traversing such a bottleneck, especially if there are only a few flows
or their bandwidth-delay product (BDP) is large. The reception of a Congestion
Experienced (CE) Explicit Congestion Notification (ECN) mark indicates that an
AQM mechanism is used at the bottleneck, and the bottleneck network queue is the
refore likely to be short. Feedback of this signal allows the TCP sender-side E
CN reaction in congestion avoidance to reduce the Congestion Window (cwnd) by a
smaller amount than the congestion control algorithm's reaction to inferred pack
et loss. Therefore, this specification defines an experimental change to the TCP
reaction specified in RFC 3168, as permitted by RFC 8311.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="8511"/>
<seriesInfo name="DOI" value="10.17487/RFC8511"/>
</reference>
</references>
</references>
<section anchor="acknowledgments">
<name>Acknowledgments</name>
<t>Richard Scheffenegger and Alexander Zimmermann originally co-authored
<xref target="RFC8312"/>.</t>
<t>These individuals suggested improvements to this document:</t>
<ul spacing="compact">
<li>
<t> <contact fullname="Bob Briscoe"/>
</t>
</li>
<li>
<t> <contact fullname="Christian Huitema"/>
</t>
</li>
<li>
<t> <contact fullname="Gorry Fairhurst"/>
</t>
</li>
<li>
<t> <contact fullname="Jonathan Morton"/>
</t>
</li>
<li>
<t> <contact fullname="Juhamatti Kuusisaari"/>
</t>
</li>
<li>
<t> <contact fullname="Junho Choi"/>
</t>
</li>
<li>
<t> <contact fullname="Markku Kojo"/>
</t>
</li>
<li>
<t> <contact fullname="Martin Duke"/>
</t>
</li>
<li>
<t> <contact fullname="Martin Thomson"/>
</t>
</li>
<li>
<t> <contact fullname="Matt Mathis"/>
</t>
</li>
<li>
<t> <contact fullname="Matt Olson"/>
</t>
</li>
<li>
<t> <contact fullname="Michael Welzl"/>
</t>
</li>
<li>
<t> <contact fullname="Mirja Kühlewind"/>
</t>
</li>
<li>
<t> <contact fullname="Mohit P. Tahiliani"/>
</t>
</li>
<li>
<t> <contact fullname="Neal Cardwell"/>
</t>
</li>
<li>
<t> <contact fullname="Praveen Balasubramanian"/>
</t>
</li>
<li>
<t> <contact fullname="Randall Stewart"/>
</t>
</li>
<li>
<t> <contact fullname="Richard Scheffenegger"/>
</t>
</li>
<li>
<t> <contact fullname="Rod Grimes"/>
</t>
</li>
<li>
<t> <contact fullname="Spencer Dawkins"/>
</t>
</li>
<li>
<t> <contact fullname="Tom Henderson"/>
</t>
</li>
<li>
<t> <contact fullname="Tom Petch"/>
</t>
</li>
<li>
<t> <contact fullname="Wesley Rosenblum"/>
</t>
</li>
<li>
<t> <contact fullname="Yoav Nir"/>
</t>
</li>
<li>
<t> <contact fullname="Yoshifumi Nishida"/>
</t>
</li>
<li>
<t> <contact fullname="Yuchung Cheng"/>
</t>
</li>
</ul>
<!-- Anyone else to acknowledge? -->
</section> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.9000.xml"
<section anchor="evolution-of-cubic"> />
<name>Evolution of CUBIC</name> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.9260.xml"
<!-- For future PRs, please include a bullet below that summarizes the cha />
nge <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3649.xml"
and link the issue number to the GitHub issue page. --> />
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8312.xml"
/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.6937.xml"
/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.7661.xml"
/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3522.xml"
/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3708.xml"
/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3742.xml"
/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8511.xml"
/>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-14"> </references>
<name>Since draft-ietf-tcpm-rfc8312bis-14</name> </references>
<ul spacing="normal">
<li>Specify how security considerations of TCP applies to CUBIC.</li>
<li>Elaborate differences between RFC 5681 and Cubic.</li>
<li>Tweak math for better plaintext rendering.
(<eref target="https://github.com/NTAP/rfc8312bis/pull/164">#164</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-13">
<name>Since draft-ietf-tcpm-rfc8312bis-13</name>
<ul spacing="normal">
<li>Add contents of <eref target="https://cse.unl.edu/~xu/avg_cubic_cw
nd.pdf"/> to
<xref target="proof-avg-window"/>.</li>
<li>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 <em>cwnd<sub>epoch</sub></em>.
(<eref target="https://github.com/NTAP/rfc8312bis/pull/158">#158</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-12">
<name>Since draft-ietf-tcpm-rfc8312bis-12</name>
<ul spacing="normal">
<li>Fix plaintext version of <xref target="eqssthresh"/>.</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-11">
<name>Since draft-ietf-tcpm-rfc8312bis-11</name>
<ul spacing="normal">
<li>Fix various nits.
(<eref target="https://github.com/NTAP/rfc8312bis/pull/157">#157</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-10">
<name>Since draft-ietf-tcpm-rfc8312bis-10</name>
<ul spacing="normal">
<li>Improve text related to <xref target="RFC7661"/>.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/149">#149</eref>)</li>
<li>Made variable naming a bit more consistent.
(<eref target="https://github.com/NTAP/rfc8312bis/pull/156">#156</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-09">
<name>Since draft-ietf-tcpm-rfc8312bis-09</name>
<ul spacing="normal">
<li>Improve text for Reno friendliness, multiplicative decrease and
reference to HLRX07.
(<eref target="https://github.com/NTAP/rfc8312bis/pull/152">#152</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-08">
<name>Since draft-ietf-tcpm-rfc8312bis-08</name>
<ul spacing="normal">
<li>Fix the text specifying when alpha_cubic <bcp14>SHOULD</bcp14> be
set to 1 to
indicate this should happen when cwnd &gt;= cwnd<sub>prior</sub> rather
than cwnd &gt;= W_max, since these are different in the
fast convergence case
(<eref target="https://github.com/NTAP/rfc8312bis/pull/146">#146</eref>)</li>
<li>Restrict use of <em>cwnd</em> directly on a congestion event
(<eref target="https://github.com/NTAP/rfc8312bis/pull/148">#148</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-07">
<name>Since draft-ietf-tcpm-rfc8312bis-07</name>
<ul spacing="normal">
<li>Document the WG discussion and decision around <xref target="RFC50
33"/> and
<xref target="RFC2914"/> (<eref target="https://github.com/NTAP/rfc8312bis/pull/
145">#145</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-06">
<name>Since draft-ietf-tcpm-rfc8312bis-06</name>
<ul spacing="normal">
<li>RFC7661 is safe even when cwnd grows beyond rwnd
(<eref target="https://github.com/NTAP/rfc8312bis/issues/143">#143</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-05">
<name>Since draft-ietf-tcpm-rfc8312bis-05</name>
<ul spacing="normal">
<li>Clarify meaning of "application-limited" in Section 5.8
(<eref target="https://github.com/NTAP/rfc8312bis/issues/137">#137</eref>)</li>
<li>Create new subsections for spurious timeouts and spurious loss via
ACK
(<eref target="https://github.com/NTAP/rfc8312bis/issues/90">#90</eref>)</li>
<li>Brief discussion of convergence in Section 5.6
(<eref target="https://github.com/NTAP/rfc8312bis/issues/96">#96</eref>)</li>
<li>Add more test results to Section 5 and update some references
(<eref target="https://github.com/NTAP/rfc8312bis/issues/91">#91</eref>)</li>
<li>Change wording around setting ssthresh
(<eref target="https://github.com/NTAP/rfc8312bis/issues/131">#131</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-04">
<name>Since draft-ietf-tcpm-rfc8312bis-04</name>
<ul spacing="normal">
<li>Fix incorrect math
(<eref target="https://github.com/NTAP/rfc8312bis/issues/106">#106</eref>)</li>
<li>Update RFC5681
(<eref target="https://github.com/NTAP/rfc8312bis/issues/99">#99</eref>)</li>
<li>Rephrase text around algorithmic alternatives, add HyStart++
(<eref target="https://github.com/NTAP/rfc8312bis/issues/85">#85</eref>,
<eref target="https://github.com/NTAP/rfc8312bis/issues/86">#86</eref>,
<eref target="https://github.com/NTAP/rfc8312bis/issues/90">#90</eref>)</li>
<li>Clarify what we mean by "new ACK" and use it in the text in more p
laces.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/101">#101</eref>)</li>
<li>Rewrite the Responses to Sudden or Transient Events section
(<eref target="https://github.com/NTAP/rfc8312bis/issues/98">#98</eref>)</li>
<li>Remove confusing text about <em>cwnd<sub>epoch</sub></em> in Secti
on 4.2
(<eref target="https://github.com/NTAP/rfc8312bis/issues/100">#100</eref>)</li>
<li>Change terminology from "AIMD" to "Reno"
(<eref target="https://github.com/NTAP/rfc8312bis/issues/108">#108</eref>)</li>
<li>Moved <bcp14>MUST NOT</bcp14> from app-limited section to main cub
ic AI section
(<eref target="https://github.com/NTAP/rfc8312bis/issues/97">#97</eref>)</li>
<li>Clarify cwnd decrease during multiplicative decrease
(<eref target="https://github.com/NTAP/rfc8312bis/issues/102">#102</eref>)</li>
<li>Clarify text around queuing and slow adaptation of CUBIC in wirele
ss environments
(<eref target="https://github.com/NTAP/rfc8312bis/issues/94">#94</eref>)</li>
<li>Set lower bound of cwnd to 1 MSS and use retransmit timer thereaft
er
(<eref target="https://github.com/NTAP/rfc8312bis/issues/83">#83</eref>)</li>
<li>Use FlightSize instead of cwnd to update ssthresh
(<eref target="https://github.com/NTAP/rfc8312bis/issues/114">#114</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-03">
<name>Since draft-ietf-tcpm-rfc8312bis-03</name>
<ul spacing="normal">
<li>Remove reference from abstract
(<eref target="https://github.com/NTAP/rfc8312bis/pull/82">#82</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-02">
<name>Since draft-ietf-tcpm-rfc8312bis-02</name>
<ul spacing="normal">
<li>Description of packet loss rate <em>p</em>
(<eref target="https://github.com/NTAP/rfc8312bis/issues/65">#65</eref>)</li>
<li>Clarification of TCP Friendly Equation for ABC and Delayed ACK
(<eref target="https://github.com/NTAP/rfc8312bis/issues/66">#66</eref>)</li>
<li>add applicability to QUIC and SCTP
(<eref target="https://github.com/NTAP/rfc8312bis/issues/61">#61</eref>)</li>
<li>clarity on setting <!--{{{&#945;}{}}}-->alpha<em><sub>aimd</sub></
em> to 1
(<eref target="https://github.com/NTAP/rfc8312bis/issues/68">#68</eref>)</li>
<li>introduce <!--{{{&#945;}{}}}-->alpha<em><sub>cubic</sub></em>
(<eref target="https://github.com/NTAP/rfc8312bis/issues/64">#64</eref>)</li>
<li>clarify <em>cwnd</em> growth in convex region
(<eref target="https://github.com/NTAP/rfc8312bis/issues/69">#69</eref>)</li>
<li>add guidance for using bytes and mention that segments count is de
cimal
(<eref target="https://github.com/NTAP/rfc8312bis/issues/67">#67</eref>)</li>
<li>add loss events detected by RACK and QUIC loss detection
(<eref target="https://github.com/NTAP/rfc8312bis/issues/62">#62</eref>)</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-01">
<name>Since draft-ietf-tcpm-rfc8312bis-01</name>
<ul spacing="normal">
<li>address Michael Scharf's editorial suggestions.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/59">#59</eref>)</li>
<li>add "Note to the RFC Editor" about removing underscores</li>
</ul>
</section>
<section anchor="since-draft-ietf-tcpm-rfc8312bis-00">
<name>Since draft-ietf-tcpm-rfc8312bis-00</name>
<ul spacing="normal">
<li>use updated xml2rfc with better text rendering of subscripts</li>
</ul>
</section>
<section anchor="since-draft-eggert-tcpm-rfc8312bis-03">
<name>Since draft-eggert-tcpm-rfc8312bis-03</name>
<ul spacing="normal">
<li>fix spelling nits</li>
<li>rename to draft-ietf</li>
<li>define <em>W<sub>max</sub></em> more clearly</li>
</ul>
</section>
<section anchor="since-draft-eggert-tcpm-rfc8312bis-02">
<name>Since draft-eggert-tcpm-rfc8312bis-02</name>
<ul spacing="normal">
<li>add definition for segments_acked and <!--{{{&#945;}{}}}-->alpha<e
m><sub>aimd</sub></em>.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/47">#47</eref>)</li>
<li>fix a mistake in <em>W<sub>max</sub></em> calculation in the fast
convergence section.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/51">#51</eref>)</li>
<li>clarity on setting <em>ssthresh</em> and <em>cwnd<sub>epoch</sub><
/em> during
multiplicative decrease.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/53">#53</eref>)</li>
</ul>
</section>
<section anchor="since-draft-eggert-tcpm-rfc8312bis-01">
<name>Since draft-eggert-tcpm-rfc8312bis-01</name>
<ul spacing="normal">
<li>rename TCP-Friendly to AIMD-Friendly and rename Standard TCP to AI
MD
TCP to avoid confusion as CUBIC has been widely used on the Internet.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/38">#38</eref>)</li>
<li>change introductory text to reflect the significant broader
deployment of CUBIC on the Internet.
(<eref target="https://github.com/NTAP/rfc8312bis/issues/39">#39</eref>)</li>
<li>rephrase introduction to avoid referring to variables that have no
t
been defined yet.</li>
</ul>
</section>
<section anchor="since-draft-eggert-tcpm-rfc8312bis-00">
<name>Since draft-eggert-tcpm-rfc8312bis-00</name>
<ul spacing="normal">
<li>acknowledge former co-authors
(<eref target="https://github.com/NTAP/rfc8312bis/issues/15">#15</eref>)</li>
<li>prevent <em>cwnd</em> from becoming less than two
(<eref target="https://github.com/NTAP/rfc8312bis/issues/7">#7</eref>)</li>
<li>add list of variables and constants
(<eref target="https://github.com/NTAP/rfc8312bis/issues/5">#5</eref>,
<eref target="https://github.com/NTAP/rfc8312bis/issues/6">#6</eref>)</li>
<li>update <em>K</em>'s definition and add bounds for CUBIC <em>target
</em> <em>cwnd</em>
<xref target="SXEZ19"/> (<eref target="https://github.com/NTAP/rfc83
12bis/issues/1">#1</eref>,
<eref target="https://github.com/NTAP/rfc8312bis/issues/14">#14</eref>)</li>
<li>update <em>W<sub>est</sub></em> to use AIMD approach
(<eref target="https://github.com/NTAP/rfc8312bis/issues/20">#20</eref>)</li>
</ul>
<!-- xml2rfc currently doesn't allow the &#945; Unicode symbol in bullet
lists -->
<ul spacing="normal">
<li>set <!--{{{&#945;}{}}}-->alpha<em><sub>aimd</sub></em> to 1 once
<em>W<sub>est</sub></em> reaches <em>W<sub>max</sub></em>
(<eref target="https://github.com/NTAP/rfc8312bis/issues/2">#2</eref>)</li>
<li>add Vidhi as co-author
(<eref target="https://github.com/NTAP/rfc8312bis/issues/17">#17</eref>)</li>
<li>note for Fast Recovery during <em>cwnd</em> decrease due to conges
tion
event (<eref target="https://github.com/NTAP/rfc8312bis/issues/11">#11</eref>)</
li>
<li>add section for spurious congestion events
(<eref target="https://github.com/NTAP/rfc8312bis/issues/23">#23</eref>)</li>
<li>initialize <em>W<sub>est</sub></em> after timeout and remove varia
ble
<em>W<sub>last_max</sub></em>
(<eref target="https://github.com/NTAP/rfc8312bis/issues/28">#28</eref>)</li>
</ul>
</section>
<section anchor="since-rfc8312">
<name>Since RFC8312</name>
<ul spacing="normal">
<li>converted to Markdown and xml2rfc v3</li>
<li>updated references (as part of the conversion)</li>
<li>updated author information</li>
<li>various formatting changes</li>
<li>move to Standards Track</li>
</ul>
</section>
<section anchor="since-the-original-paper"> <section anchor="since-the-original-paper">
<name>Since the Original Paper</name> <name>Evolution of CUBIC since the Original Paper</name>
<t>CUBIC has gone through a few changes since the initial release <t>CUBIC has gone through a few changes since the initial release
<xref target="HRX08"/> of its algorithm and implementation. This section highlig hts the <xref target="HRX08"/> of its algorithm and implementation. This appendix highli ghts the
differences between the original paper and <xref target="RFC8312"/>.</t> differences between the original paper and <xref target="RFC8312"/>.</t>
<ul spacing="normal"> <ul spacing="normal">
<li>The original paper <xref target="HRX08"/> includes the pseudocode of CUBIC <li>The original paper <xref target="HRX08"/> includes the pseudocode of CUBIC
implementation using Linux's pluggable congestion control framework, implementation using Linux's pluggable congestion control framework,
which excludes system-specific optimizations. The simplified which excludes system-specific optimizations. The simplified
pseudocode might be a good source to start with and understand CUBIC.</li> pseudocode might be a good starting point for learning about CUBIC.</li>
<li> <li>
<xref target="HRX08"/> also includes experimental results showing it s performance <xref target="HRX08"/> also includes experimental results showing it s performance
and fairness.</li> and fairness.</li>
</ul> </ul>
<!-- xml2rfc currently doesn't allow the &#946; Unicode symbol in bullet lists -->
<ul spacing="normal"> <ul spacing="normal">
<li>The definition of <!--{{{&#946;}{}}}-->beta<em><sub>cubic</sub></e m> constant <li><t>The definition of the β<em><sub>cubic</sub></em> constant
was changed in <xref target="RFC8312"/>. For example, was changed in <xref target="RFC8312"/>. For example,
<!--{{{&#946;}{}}}-->beta<em><sub>cubic</sub></em> in the original paper was the β<em><sub>cubic</sub></em> in the original paper was referred to as the
window decrease constant while <xref target="RFC8312"/> changed it to CUBIC window decrease constant, while <xref target="RFC8312"/> changed it to "CUBIC mu
multiplication decrease factor. With this change, the current ltiplicative decrease factor". With this change, the current
congestion window size after a congestion event in <xref target="RFC8312"/> was congestion window size after a congestion event as listed in <xref target="RFC83
<!--{{{&#946;}{}}}-->beta<em><sub>cubic</sub></em> * <em>W<sub>max</sub></em> wh 12"/> was
ile it was β<em><sub>cubic</sub></em> * <em>W<sub>max</sub></em>, while it was
(1-<!--{{{&#946;}{}}}-->beta<em><sub>cubic</sub></em>) * <em>W<sub>max</sub></em (1-β<em><sub>cubic</sub></em>) * <em>W<sub>max</sub></em> in the
> in the original paper.</t></li>
original paper.</li> <li><t>Its pseudocode used <em>W<sub>last_max</sub></em>, while <xref
<li>Its pseudocode used <em>W<sub>last_max</sub></em> while <xref targ target="RFC8312"/> used
et="RFC8312"/> used <em>W<sub>max</sub></em>.</t></li>
<em>W<sub>max</sub></em>.</li> <li><t>Its AIMD-friendly window was <em>W<sub>tcp</sub></em>, while <x
<li>Its AIMD-friendly window was <em>W<sub>tcp</sub></em> while <xref ref target="RFC8312"/> used
target="RFC8312"/> used <em>W<sub>est</sub></em>.</t></li>
<em>W<sub>est</sub></em>.</li>
</ul> </ul>
</section> </section>
</section>
<section anchor="proof-avg-window"> <section anchor="proof-avg-window">
<name>Proof of the Average CUBIC Window Size</name> <name>Proof of the Average CUBIC Window Size</name>
<t>This appendix contains a proof for the average CUBIC window <t>This appendix contains a proof for the average CUBIC window
size <em>AVG_W<sub>cubic</sub></em> in <xref target="eq5"/>.</t> size <em>AVG_W<sub>cubic</sub></em> in <xref target="eq5"/>.</t>
<t>We find <em>AVG_W<sub>cubic</sub></em> under a deterministic loss model , where the <t>We find <em>AVG_W<sub>cubic</sub></em> under a deterministic loss model , where the
number of packets between two successive packet losses is 1/<em>p</em>. With thi s number of packets between two successive packet losses is 1/<em>p</em>. &nbsp;Wi th this
model, CUBIC always operates with the concave window profile and the time period model, CUBIC always operates with the concave window profile and the time period
between two successive packet losses is <em>K</em>.</t> between two successive packet losses is <em>K</em>.</t>
<t>The average window size <em>AVG_W<sub>cubic</sub></em> is defined as fo llows, where the <t>The average window size <em>AVG_W<sub>cubic</sub></em> is defined as fo llows, where the
numerator 1/<em>p</em> is the total number of packets between two successive pac ket numerator 1/<em>p</em> is the total number of packets between two successive pac ket
losses, and the denominator <em>K</em>/<em>RTT</em> is the total number of RTTs between two losses and the denominator <em>K</em>/<em>RTT</em> is the total number of RTTs b etween two
successive packet losses.</t> successive packet losses.</t>
<figure anchor="peq1"> <figure anchor="peq1">
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<artwork type="ascii-art" align="center"><![CDATA[ 1 <artwork type="ascii-art" align="center"><![CDATA[ 1
─ ─
p p
AVG_W = ─── AVG_W = ───
cubic K cubic K
─── ───
RTT RTT
]]></artwork> ]]></artwork>
</artset> </artset>
</figure> </figure>
<t>Below, we find <em>K</em> as a function of CUBIC parameters <contact fu <t>Below, we find <em>K</em> as a function of CUBIC parameters β<em><sub>c
llname="β" asciiFullname=""/><em><sub>cubic</sub></em> ubic</sub></em>
and <em>C</em>, and network parameters <em>p</em> and <em>RTT</em>. According to and <em>C</em>, and network parameters <em>p</em> and <em>RTT</em>. &nbsp;Accord
the definition of ing to the definition of
<em>K</em> in <xref target="eq2"/>, we have</t> <em>K</em> in <xref target="eq2"/>, we have</t>
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<artwork type="ascii-art" align="center"><![CDATA[ ┌──────────── ────────┐ <artwork type="ascii-art" align="center"><![CDATA[ ┌──────────── ────────┐
3 │W - W * β 3 │W - W * β
╲ │ max max cubic ╲ │ max max cubic
K = ╲ │──────────────────── K = ╲ │────────────────────
╲│ C ╲│ C
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<t>The total number of packets between two successive packet losses can al so be <t>The total number of packets between two successive packet losses can al so be
obtained as follows using the window increase function in <xref target="eq1"/>. obtained as follows, using the window increase function in <xref target="eq1"/>.
Specifically, Specifically,
the window size in the first RTT (i.e., <em>n</em>=1 or equivalently <em>t</em>= the window size in the first RTT (i.e., <em>n</em>=1, or equivalently, <em>t</em
0) is >=0) is
<em>C</em>(-<em>K</em>)<sup>3</sup>+<em>W<sub>max</sub></em> and the window size in the last RTT <em>C</em>(-<em>K</em>)<sup>3</sup>+<em>W<sub>max</sub></em> and the window size in the last RTT
(i.e., <em>n</em>=<em>K</em>/<em>RTT</em> or equivalently <em>t</em>=<em>K</em>- <em>RTT</em>) is (i.e., <em>n</em>=<em>K</em>/<em>RTT</em>, or equivalently, <em>t</em>=<em>K</em >-<em>RTT</em>) is
<em>C</em>(-<em>RTT</em>)<sup>3</sup>+<em>W<sub>max</sub></em>.</t> <em>C</em>(-<em>RTT</em>)<sup>3</sup>+<em>W<sub>max</sub></em>.</t>
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<artwork type="ascii-art" align="center"><![CDATA[ K <artwork type="ascii-art" align="center"><![CDATA[ K
skipping to change at line 4915 skipping to change at line 4020
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
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<artwork type="ascii-art" align="center"><![CDATA[ ┌──────────── ──────────┐ <artwork type="ascii-art" align="center"><![CDATA[ ┌──────────── ──────────┐
│ 4 * ⎛1-β ⎞ │ 4 * ⎛1-β ⎞
4 │ ⎝ cubic⎠ RTT 4 │ ⎝ cubic⎠ RTT
K = ╲ │──────────────── * ─── K = ╲ │──────────────── * ───
╲ │C * ⎛3 + β ⎞ p ╲ │C * ⎛3 + β ⎞ p
╲│ ⎝ cubic⎠ ╲│ ⎝ cubic⎠
]]></artwork> ]]></artwork>
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</figure> </figure>
<t>The average CUBIC window size <em>AVG_W<sub>cubic</sub></em> can be obt ained by <t>The average CUBIC window size <em>AVG_W<sub>cubic</sub></em> can be obt ained by
substituting <em>K</em> with <xref target="peq4"/> in <xref target="peq1"/></t> substituting <em>K</em> from <xref target="peq4"/> in <xref target="peq1"/>.</t>
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</artwork> </artwork>
<artwork type="ascii-art" align="center"><![CDATA[ 1 ┌───────────────────────┐ <artwork type="ascii-art" align="center"><![CDATA[ 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
]]></artwork> ]]></artwork>
</artset> </artset>
</section> </section>
<section anchor="acknowledgments" numbered="false">
<name>Acknowledgments</name>
<t><contact fullname="Richard Scheffenegger"/> and <contact fullname="Alex
ander Zimmermann"/> originally coauthored
<xref target="RFC8312"/>.</t>
<t>These individuals suggested improvements to this document:</t>
<ul spacing="compact">
<li>
<t> <contact fullname="Bob Briscoe"/>
</t>
</li>
<li>
<t> <contact fullname="Christian Huitema"/>
</t>
</li>
<li>
<t> <contact fullname="Gorry Fairhurst"/>
</t>
</li>
<li>
<t> <contact fullname="Jonathan Morton"/>
</t>
</li>
<li>
<t> <contact fullname="Juhamatti Kuusisaari"/>
</t>
</li>
<li>
<t> <contact fullname="Junho Choi"/>
</t>
</li>
<li>
<t> <contact fullname="Markku Kojo"/>
</t>
</li>
<li>
<t> <contact fullname="Martin Duke"/>
</t>
</li>
<li>
<t> <contact fullname="Martin Thomson"/>
</t>
</li>
<li>
<t> <contact fullname="Matt Mathis"/>
</t>
</li>
<li>
<t> <contact fullname="Matt Olson"/>
</t>
</li>
<li>
<t> <contact fullname="Michael Welzl"/>
</t>
</li>
<li>
<t> <contact fullname="Mirja Kühlewind"/>
</t>
</li>
<li>
<t> <contact fullname="Mohit P. Tahiliani"/>
</t>
</li>
<li>
<t> <contact fullname="Neal Cardwell"/>
</t>
</li>
<li>
<t> <contact fullname="Praveen Balasubramanian"/>
</t>
</li>
<li>
<t> <contact fullname="Randall Stewart"/>
</t>
</li>
<li>
<t> <contact fullname="Richard Scheffenegger"/>
</t>
</li>
<li>
<t> <contact fullname="Rod Grimes"/>
</t>
</li>
<li>
<t> <contact fullname="Spencer Dawkins"/>
</t>
</li>
<li>
<t> <contact fullname="Tom Henderson"/>
</t>
</li>
<li>
<t> <contact fullname="Tom Petch"/>
</t>
</li>
<li>
<t> <contact fullname="Wesley Rosenblum"/>
</t>
</li>
<li>
<t> <contact fullname="Yoav Nir"/>
</t>
</li>
<li>
<t> <contact fullname="Yoshifumi Nishida"/>
</t>
</li>
<li>
<t> <contact fullname="Yuchung Cheng"/>
</t>
</li>
</ul>
</section>
</back> </back>
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