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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 EngineeringLincolnNE68588-01150USxu@unl.eduUniversity of Colorado at BoulderDepartment of Computer ScienceBoulderCO80309-0430USsangtae.ha@colorado.eduNetAppSonnenallee 1Kirchheim85551Germany+49 89 900594712alexander.zimmermann@netapp.comNetAppSonnenallee 1Kirchheim85551Germany+49 151 12055791lars@netapp.comNetAppAm Euro Platz 21120ViennaAustria+43 1 3676811 3146rs@netapp.com
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 of the
current TCP standards to improve scalability and stability under
fast and long distance networks. BIC-TCP, a predecessor of CUBIC,
has been a default TCP adopted by Linux since year 2005 and has
already been deployed globally and in use for several years by the
Internet community at large. CUBIC is using 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. Through extensive testing in various Internet scenarios,
we believe that CUBIC is safe for deployment and testing in the
global Internet. The intent of this document is to provide the
protocol specification of CUBIC for a third party implementation
and 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
, TCP-SACK , 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.
It uses a cubic 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 after a loss
event, 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, 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 since the last loss event. 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 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 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.In the ensuing sections, we provide the exact specification of
CUBIC and 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
.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-NewReno
and TCP-SACK . During congestion
avoidance after fast recovery, CUBIC changes the window update
algorithm of Standard TCP. Suppose that W_max is the window
size before the window is reduced in the last fast retransmit
and recovery.The window growth function of CUBIC uses the following
function:
W_cubic(t) = C*(t-K)^3 + W_max (Eq. 1)where C is a constant fixed to determine the aggressiveness
of window growth in high BDP networks, t is the elapsed time
from the last window reduction,and K is the time period that
the above function takes to increase the current window size
to W_max when there is no further loss event and is calculated
by using the following equation:
K = cubic_root(W_max*(1-beta_cubic)/C) (Eq. 2)where beta_cubic is the CUBIC multiplication decrease factor,
that is, when a packet loss occurs, CUBIC reduces its current
window cwnd to cwnd*beta_cubic. We discuss how we set C
in the next Section in more details.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. Depending on the value of the current window size cwnd,
CUBIC runs in three
different modes. First, if cwnd is less than the window size
that Standard TCP would reach at time t after the last loss
event, then CUBIC is in the TCP friendly region (we describe
below how to determine this window size of Standard TCP in term
of time t). Otherwise, if cwnd is less than W_max, then CUBIC
is the concave region, and if cwnd is larger than W_max, CUBIC
is in the convex region. Below, we describe the exact actions
taken by CUBIC in each region.When receiving an ACK in congestion avoidance, we first check
whether the protocol is in the TCP region or not. This is done
as follows. We can analyze the window size of a TCP-friendly AIMD
in terms of the elapsed time t. Using a simple analysis in , we can analyze the average window size of
additive increase and multiplicative decrease (AIMD) with an
additive factor alpha_aimd and a multiplicative factor
beta_aimd with the following function:
By the same analysis, the average window size of Standard TCP
is (1.5/p)^0.5, as the Standard TCP is a special case of AIMD
with alpha_aimd=1 and beta_aimd=0.5. Thus, for Eq. 3 to
be the same as that of Standard TCP, alpha_aimd must be equal to
3*(1-beta_aimd)/(1+beta_aimd). As AIMD increases its window by
alpha_aimd per RTT, we can get the window size of AIMD in terms of
the elapsed time t as follows:
If W_cubic(t) is less than W_aimd(t), then the protocol is
in the
TCP friendly region and cwnd SHOULD be set to W_aimd(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.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.When a packet loss occurs, CUBIC reduces its window size by a
factor of beta. 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.
This allows W_max to be slightly less than the original W_max.
Since flows spend most of time around their W_max, flows with
larger bandwidth shares tend to spend more time around the
plateau allowing more time for flows with smaller shares to
increase their windows.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:
AVG_W_cubic = (C*3.7/1.2)^0.25 * (RTT^0.75) / (p^0.75) (Eq. 6)
We will determine the value of C in the following subsection
using Eq. 6.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, 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. It is not designed for wireless
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 .In case that there is congestion collapse, CUBIC behaves
likely 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.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.
&RFC2018;
&RFC2119;
&RFC5681;
&RFC5348;
&RFC3649;
&RFC6582;
&RFC4960;
&RFC5033;
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 VariantsCUBIC: A New TCP-Friendly High-Speed TCP VariantStochastic Ordering for Internet Congestion Control
and its Applications