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CUBIC for Fast Long-Distance NetworksNorth Carolina State UniversityDepartment of Computer ScienceRaleighNC27695-7534USrhee@ncsu.eduUniversity of Nebraska-LincolnDepartment of Computer Science and EngineeringLincolnNE68588-0115USxu@unl.eduUniversity of Colorado at BoulderDepartment of Computer ScienceBoulderCO80309-0430USsangtae.ha@colorado.edu+49 175 5766838alexander.zimmermann@rwth-aachen.deNetAppSonnenallee 1Kirchheim85551Germany+49 151 12055791lars@netapp.comrscheff@gmx.at
Transport
TCP Maintenance and Minor Extensions (TCPM) WGTCP Congestion ControlCUBIC is an extension to the current TCP standards. The protocol
differs from the current TCP standards only in the congestion
window adjustment function in the sender side. In particular, it
uses a cubic function instead of a linear window increase function of the
current TCP standards to improve scalability and stability under
fast and long distance networks. CUBIC and its predecessor algorithm have been adopted as
default by Linux and have been used for many years. This document provides a
specification of CUBIC to enable third party implementation and
to solicit the community feedback through experimentation on the
performance of CUBIC.The low utilization problem of TCP in fast long-distance networks
is well documented in .
This problem arises from a slow increase of congestion window
following a congestion event in a network with a large bandwidth
delay product (BDP). Our experience
indicates that this problem is frequently observed even in the
range of congestion window sizes over several hundreds of packets
(each packet is sized around 1000 bytes) especially under a network
path with over 100ms round-trip times (RTTs). This problem is
equally applicable to all Reno style TCP standards and their
variants, including TCP-RENO , TCP-NewReno
, SCTP
, TFRC that use
the same linear increase function for window growth, which we refer
to collectively as Standard TCP below. CUBIC is a modification to the congestion
control mechanism of Standard TCP, in particular, to the window
increase function of Standard TCP senders, to remedy this problem. Specifically,
it uses a cubic function instead of a linear window increase function of the
Standrad TCP to improve scalability and stability under
fast and long distance networks. BIC-TCP, a predecessor of CUBIC, has been selected as default TCP congestion
control algorithm by Linux in the year 2005 and been used for several years
by the Internet community at large. CUBIC uses a similar window growth function
as BIC-TCP and is designed to be less aggressive and fairer to TCP in
bandwidth usage than BIC-TCP while maintaining the strengths of BIC-TCP
such as stability, window scalability and RTT fairness.
CUBIC has already been deployed globally by Linux. Through
extensive testing in various Internet scenarios, we believe that
CUBIC is safe for testing and deployment in the global Internet.In the ensuing sections, we first brefly explain the design principle of CUBIC,
then provide the exact specification of
CUBIC, and finally discuss the safety features of CUBIC following the
guidelines specified in .The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL
NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
.CUBIC uses a cubic window increase function in terms of the elapsed time from
the last congestion event. While most alternative algorithms to
Standard TCP uses a convex increase function where during congestion avoidance
the window increment is always increasing, CUBIC uses both
the concave and convex profiles of a cubic function for window
increase. After a window reduction following a loss event detected by duplicate ACKs, it
registers the window size where it got the loss event as W_max and
performs a multiplicative decrease of congestion window and the
regular fast recovery and retransmit of Standard TCP. After it
enters into congestion avoidance from fast recovery, it starts to
increase the window using the concave profile of the cubic
function. The cubic function is set to have its plateau at W_max
so the concave growth continues until the window size becomes
W_max. After that, the cubic function turns into a convex profile
and the convex window growth begins. This style of window
adjustment (concave and then convex) improves protocol and network
stability while maintaining high network utilization . This is because the window size remains
almost constant, forming a plateau around W_max where network
utilization is deemed highest and under steady state, most window
size samples of CUBIC are close to W_max, thus promoting high
network utilization and protocol stability. Note that protocols
with convex increase functions have the maximum increments around
W_max and introduces a large number of packet bursts around the
saturation point of the network, likely causing frequent global
loss synchronizations.Another notable feature of CUBIC is that its window increase rate
is mostly independent of RTT, and follows a (cubic) function of the
elapsed time from the beginning of congestion avoidance. This feature promotes
per-flow fairness to Standard TCP as well as RTT-fairness. Note
that Standard TCP performs well under short RTT and small bandwidth
(or small BDP) networks. Only in a large long RTT and large
bandwidth (or large BDP) networks, it has the scalability problem.
An alternative protocol to Standard TCP designed to be friendly to
Standard TCP at a per-flow basis must operate to increase its
window much less aggressively in small BDP networks than in large
BDP networks. In CUBIC, its window growth rate is slowest around
the inflection point of the cubic function and this function does
not depend on RTT. In a smaller BDP network where Standard TCP
flows are working well, the absolute amount of the window decrease
at a loss event is always smaller because of the multiplicative
decrease. Therefore, in CUBIC, the starting window size after a
loss event from which the window starts to increase, is smaller in
a smaller BDP network, thus falling nearer to the plateau of the
cubic function where the growth rate is slowest. By setting
appropriate values of the cubic function parameters, CUBIC sets its
growth rate always no faster than Standard TCP around its
inflection point. When the cubic function grows slower than the
window of Standard TCP, CUBIC simply follows the window size of
Standard TCP to ensure fairness to Standard TCP in a small BDP
network. We call this region where CUBIC behaves like Standard TCP,
the TCP-friendly region.CUBIC maintains the same window growth rate independent of RTTs
outside of the TCP-friendly region, and flows with different RTTs
have the similar window sizes under steady state when they operate
outside the TCP-friendly region. This ensures CUBIC flows with
different RTTs to have their bandwidth shares (approximately,
window/RTT) linearly proportional to the inverse of their RTT ratio
(the longer RTT, the smaller the share). This behavior is the same
as that of Standard TCP under high statistical multiplexing
environments where packet losses are independent of individual flow
rates. However, under low statistical multiplexing environments,
the bandwidth share ratio of Standard TCP flows with different RTTs
is squarely proportional to the inverse of their RTT ratio . CUBIC always ensures the linear ratio independent of the
levels of statistical multiplexing. This is an improvement over
Standard TCP. While there is no consensus on a particular bandwidth
share ratios of different RTT flows, we believe that under wired
Internet, use of the linear share notion seems more reasonable than
equal share or a higher order shares. HTCP currently uses the
equal share.CUBIC sets the multiplicative window decrease factor to 0.7 while
Standard TCP uses 0.5. While this improves the scalability of the
protocol, a side effect of this decision is slower convergence
especially under low statistical multiplexing environments. This
design choice is following the observation that the author of HSTCP
has made along with other researchers
(e.g., ): the current Internet becomes more
asynchronous with less frequent loss synchronizations with high
statistical multiplexing. Under this environment, even strict Multiplicative-Increase Multiplicative-Decrease (MIMD)
can converge. CUBIC flows with the same RTT always converge to the
same share of bandwidth independent of statistical multiplexing,
thus achieving intra-protocol fairness. We also find that under the
environments with sufficient statistical multiplexing, the
convergence speed of CUBIC flows is reasonable.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.CUBIC maintains the acknowledgment (ACK) clocking of Standard
TCP by increasing congestion window only at the reception of
ACK. The protocol does not make any change to the fast
recovery and retransmit of TCP, such as TCP-NewReno . During congestion
avoidance after fast recovery, CUBIC changes the window update
algorithm of Standard TCP. Suppose that W_max is the window
size before the window is reduced in the last fast retransmit
and recovery.The window growth function of CUBIC uses the following
function:where C is a constant fixed to determine the aggressiveness
of window growth in high BDP networks, t is the elapsed time
from the last window reduction that is measured right after the fast recovery
in response to duplicate ACKs or after the congestion window reduction in response to ECN-Echo ACKs, and K is the time period that
the above function takes to increase the current window size
to W_max if there is no further loss event and is calculated
by using the following equation:where beta_cubic is the CUBIC multiplication decrease factor,
that is, when a packet loss detected by duplicate ACKs or a network congestion detected by ECN-Echo ACKs occurs, CUBIC reduces its current
window cwnd to W_cubic(0)=W_max*beta_cubic. We discuss how we set beta_cubic in Section 4.5 and how we set C
in Section 5.Upon receiving an ACK during congestion avoidance, CUBIC
computes the window growth rate during the next RTT period
using Eq. 1. It sets W_cubic(t+RTT) as the candidate target
value of congestion window, where RTT is the weithed average RTT calculated by the standard TCP. Depending on the value of the current window size cwnd,
CUBIC runs in three
different modes.
1) The TCP-friendly region, which ensures that
CUBIC achieves at least the same throughput as the standard TCP. 2) The concave region, if CUBIC is not in the TCP-friendly region and cwnd is less than W_max.3) The convex region, if CUBIC is not in the TCP-friendly region and cwnd is greater than W_max.
Below, we describe the exact actions taken by CUBIC in each region.Standard TCP performs well in certain types of networks, for example, under short RTT and small bandwidth (or
small BDP) networks. In these networks, we use the TCP-friendly region to ensure that
CUBIC achieves at least the same throughput as the standard TCP. The TCP-friendly region is designed according to the analysis described in .
The analysis studies the performance of an Additive Increase and Multiplicative
Decrease (AIMD) algorithm with an additive factor of alpha_aimd (segment per RTT)
and a multiplicative factor of beta_aimd, denoted by AIMD(alpha_aimd, beta_aimd).
Specifically, the average window size
of AIMD(alpha_aimd, beta_aimd) can be calculated using Eq. 3. The analysis
shows that AIMD(alpha_aimd, beta_aimd) with alpha_aimd=3*(1-beta_aimd)/(1+beta_aimd)
achieves the same average window size as
the standard TCP that uses AIMD(1, 0.5). Based on the above analysis, CUBIC uses Eq. 4 to estimate the window size W_est of
AIMD(alpha_aimd, beta_aimd) with alpha_aimd=3*(1-beta_cubic)/(1+beta_cubic) and beta_aimd=beta_cubic,
which achieves the same average window size as the standard TCP.
When receiving an ACK in congestion avoidance (cwnd could be greater than or less than W_max), CUBIC checks
whether W_cubic(t) is less than W_est(t). If so, CUBIC is in the
TCP-friendly region and cwnd SHOULD be set to W_est(t) at each
reception of ACK.When receiving an ACK in congestion avoidance, if the protocol
is not in the TCP-friendly region and cwnd is less than W_max,
then the protocol is in the concave region. In this region,
cwnd MUST be incremented by (W_cubic(t+RTT) - cwnd)/cwnd
for each received ACK, where W_cubic(t+RTT) is calculated using Eq. 1.When the current window size of CUBIC is larger than W_max,
it passes
the plateau of the cubic function after which CUBIC follows the
convex profile of the cubic function. Since cwnd is larger than
the previous saturation point W_max, this indicates that the
network conditions might have been perturbed since the last
loss event, possibly implying more available bandwidth after
some flow departures. Since the Internet is highly
asynchronous, some amount of perturbation is always possible
without causing a major change in available bandwidth. In this
phase, CUBIC is being very careful by very slowly increasing
its window size. The convex profile ensures that the window
increases very slowly at the beginning and gradually increases
its growth rate. We also call this phase as the maximum probing
phase since CUBIC is searching for a new W_max. In this region,
cwnd MUST be incremented by (W_cubic(t+RTT) - cwnd)/cwnd for
each received ACK, where W_cubic(t+RTT) is calculated using Eq. 1.When a packet loss detected by duplicate ACKs or a network congestion detected by ECN-Echo ACKs occurs, CUBIC updates its W_max, cwnd, and ssthresh (slow start threshold) as follows.
Parameter beta_cubic SHOULD be set to 0.7.A side effect of setting beta_cubic to a bigger value than 0.5 is
slower convergence. We believe that while a more adaptive
setting of beta_cubic could result in faster convergence, it will
make the analysis of the protocol much harder. This adaptive
adjustment of beta_cubic is an item for the next version of
CUBIC. To improve the convergence speed of CUBIC, we add a heuristic
in the protocol. When a new flow joins the network, existing
flows in the network need to give up their bandwidth shares to
allow the flow some room for growth if the existing flows have
been using all the bandwidth of the network. To increase this
release of bandwidth by existing flows, the following mechanism
called fast convergence SHOULD be implemented.With fast convergence, when a loss event occurs, before a
window reduction of congestion window, a flow remembers the
last value of W_max before it updates W_max for the current
loss event. Let us call the last value of W_max to be
W_last_max.At a loss event, if the current value of W_max is less than W_last_max, this indicates
that the saturation point experienced by this flow is getting reduced because of the
change in available bandwidth. Then we allow this flow to release more bandwidth
by reducing W_max further. This action effectively lengthens the time for this flow to
increase its window because the reduced W_max forces the flow to have the plateau earlier. This allows more time for the new flow to catch up its window sizeThe fast convergence is designed for network environments with multiple CUBIC flows. In network environments
with only a single CUBIC flow and without any other traffic, the fast convergence SHOULD be disabled. In case of timeout, CUBIC follows the standard TCP to reduce cwnd,
but sets ssthresh using beta_cubic (same as in Section 4.5).CUBIC MUST employ a slow start algorithm, when the cwnd is no more than ssthresh.
Among the slow start algorithms, CUBIC MAY choose the standard TCP slow start in general networks,
or the limited slow start or hybrid slow start for high-bandwidth and long-distance networks.In the case when CUBIC runs the hybrid slow start , it may exit the first slow start
without incurring any packet loss and thus W_max is undefined. In this special case, CUBIC switches to congestion avoidance
and increases its congestion window size
using Eq. 1 where K is set to 0 and W_max is set to the window size when CUBIC just exits the slow start.In this section, we further discuss the safety features of CUBIC following the
guidelines specified in .With a deterministic loss model where the number of packets
between two successive lost events is always 1/p, CUBIC always
operates with the concave window profile which greatly simplifies
the performance analysis of CUBIC. The average window size of CUBIC
can be obtained by the following function:With beta_cubic set to 0.7, the above formula is reduced to:We will determine the value of C in the following subsection
using Eq. 6.In environments where standard TCP is able to make reasonable
use of the available bandwidth, CUBIC does not significantly
change this state.Standard TCP performs well in the following two types of
networks:
1. networks with a small bandwidth-delay product
(BDP)2. networks with a short RTT, but not necessarily a
small BDPCUBIC is designed to behave very similarly to standard TCP
in the above two types of networks. The following two tables
show the average window size of standard TCP, HSTCP, and CUBIC.
The average window size of standard TCP and HSTCP is from . The average window size of CUBIC is
calculated by using Eq. 6 and CUBIC TCP friendly mode for three
different values of C.Loss Rate PTCPHSTCPCUBIC (C=0.04)CUBIC (C=0.4)CUBIC (C=4)10^-2121212121210^-3383838385910^-412026312018733310^-537917955931054187410^-6120012279333259261053810^-737958398118740333255926110^-812000574356105383187400333250Response function of standard TCP, HSTCP, and
CUBIC in networks with RTT = 0.1 seconds. The average window size
is in MSS-sized segments.Loss Rate PAverage TCP WAverage HSTCP WCUBIC (C=0.04)CUBIC (C=0.4)CUBIC (C=4)10^-2121212121210^-3383838383810^-412026312012012010^-5379179537937937910^-612001227912001200187410^-7379583981379559261053810^-812000574356187403332559261Response function of standard TCP, HSTCP, and
CUBIC in networks with RTT = 0.01 seconds. The average window size
is in MSS-sized segments.Both tables show that CUBIC with any of these three C values
is more friendly to TCP than HSTCP, especially in networks with
a short RTT where TCP performs reasonably well. For example, in
a network with RTT = 0.01 seconds and p=10^-6, TCP has an average
window of 1200 packets. If the packet size is 1500 bytes, then
TCP can achieve an average rate of 1.44 Gbps. In this case,
CUBIC with C=0.04 or C=0.4 achieves exactly the same rate as
Standard TCP, whereas HSTCP is about ten times more aggressive
than Standard TCP.We can see that C determines the aggressiveness of CUBIC in
competing with other protocols for the bandwidth. CUBIC is more
friendly to the Standard TCP, if the value of C is lower.
However, we do not recommend to set C to a very low value like
0.04, since CUBIC with a low C cannot efficiently use the
bandwidth in long RTT and high bandwidth networks. Based on
these observations and our experiments, we find C=0.4 gives a good balance between
TCP-friendliness and aggressiveness of window growth.
Therefore, C SHOULD be set to 0.4. With C set to 0.4, Eq. 6 is
reduced to:
AVG_W_cubic = 1.054 * (RTT^0.75) / (p^0.75) (Eq. 7)
Eq. 7 is then used in the next subsection to show the
scalability of CUBIC.CUBIC uses a more aggressive window growth function than
Standard TCP under long RTT and high bandwidth networks.The following table shows that to achieve 10Gbps rate,
standard TCP requires a packet loss rate of 2.0e-10, while
CUBIC requires a packet loss rate of 2.9e-8.Throughput(Mbps)Average WTCP PHSTCP PCUBIC P18.32.0e-22.0e-22.0e-21083.32.0e-43.9e-42.9e-4100833.32.0e-62.5e-51.4e-510008333.32.0e-81.5e-66.3e-71000083333.32.0e-101.0e-72.9e-8Required packet loss rate for Standard TCP, HSTCP,
and CUBIC to achieve a certain throughput. We use 1500-byte
packets and an RTT of 0.1 seconds.Our test results in indicate that
CUBIC uses the spare bandwidth left unused by existing Standard
TCP flows in the same bottleneck link without taking away much
bandwidth from the existing flows.CUBIC is designed to remedy the poor performance of TCP in
fast long-distance networks.CUBIC has been extensively studied by using both NS-2
simulation and test-bed experiments covering a wide range of
network environments. More information can be found in .Same as Standard TCP, CUBIC is a loss-based congestion control algorithm.
Because CUBIC is designed to be more aggressive (due to faster window growth function and
bigger multiplicative decrease factor)
than Standard TCP in fast and long distance networks,
it can fill large drop-tail buffers more quickly than Standard TCP and
increase the risk of a standing queue.
In this case,
proper queue sizing and management
could be used to reduce the packet queueing delay.With regard to the potential of causing congestion collapse, CUBIC behaves
like standard TCP since CUBIC modifies only the window
adjustment algorithm of TCP. Thus, it does not modify the ACK
clocking and Timeout behaviors of Standard TCP.CUBIC ensures convergence of competing CUBIC flows with the
same RTT in the same bottleneck links to an equal bandwidth
share. When competing flows have different RTTs, their
bandwidth shares are linearly proportional to the inverse of
their RTT ratios. This is true independent of the level of
statistical multiplexing in the link.This is not considered in the current CUBIC. CUBIC does not raise its congestion window size if the
flow is currently limited by the application instead of the
congestion window. In case of long periods when cwnd has not been
updated due to the application rate limit, such as idle periods, t in Eq. 1
MUST NOT include these periods; otherwise, W_cubic(t) might
be very high after restarting from these periods.In case that there is a sudden congestion, a routing change,
or a mobility event, CUBIC behaves the same as Standard
TCP.CUBIC requires only the change of TCP senders, and does not
require any assistant of routers.This proposal makes no changes to the underlying security of TCP.There are no IANA considerations regarding this document.Alexander Zimmermann and Lars Eggert have received funding from
the European Union's Horizon 2020 research and innovation program
2014-2018 under grant agreement No. 644866 (SSICLOPS). This
document reflects only the authors' views and the European
Commission is not responsible for any use that may be made of the
information it contains.
&RFC2119;
&RFC5681;
&RFC5348;
&RFC3649;
&RFC6582;
&RFC4960;
&RFC5033;
&RFC7567;
&RFC6675;
&RFC3742;
A Comparison of Equation-Based and AIMD Congestion ControlExtended Analysis of Binary Adjustment AlgorithmsScalable TCP: Improving Performance in HighSpeed Wide
Area NetworksBinary Increase Congestion Control for Fast, Long
Distance NetworksH-TCP: TCP Congestion Control for High
Bandwidth-Delay Product PathsA Step toward Realistic Performance Evaluation of
High-Speed TCP VariantsHybrid Slow Start for High-Bandwidth and Long-Distance NetworksCUBIC: A New TCP-Friendly High-Speed TCP VariantTCP Alternative Backoff with ECN (ABE)Stochastic Ordering for Internet Congestion Control
and its Applications