]>
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. We expect this document to be eventually published as an
experimental RFC.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 must 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 0.2 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
.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(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 W to W_max when there is no further
loss event and is calculated by using the following equation:
K = cubic_root(W_max*beta/C) (Eq. 2)where beta is the multiplication decrease factor. 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(t+RTT) as the candidate target value of
congestion window. Suppose that the current window size is cwnd.
Depending on the value of 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 Standard TCP 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 and a multiplicative factor beta to be the
following function:
(alpha/2 * (2-beta)/beta * 1/p)^0.5 (Eq. 3)By the same analysis, the average window size of Standard TCP
with alpha 1 and beta 0.5 is (3/2 *1/p)^0.5. Thus, for Eq. 3 to be
the same as that of Standard TCP, alpha must be equal to
3*beta/(2-beta). As Standard TCP increases its window by alpha per
RTT, we can get the window size of Standard TCP in terms of the
elapsed time t as follows:
W_tcp(t) = W_max*(1-beta) + 3*beta/(2-beta)* t/RTT (Eq. 4)If cwnd is less than W_tcp(t), then the protocol is in the TCP
friendly region and cwnd SHOULD be set to W_tcp(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(t+RTT) - cwnd)/cwnd.When the 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(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 SHOULD be set to 0.2.
A side effect of setting beta to a smaller value than 0.5 is
slower convergence. We believe that while a more adaptive setting
of beta could result in faster convergence, it will make the
analysis of the protocol much harder. This adaptive adjustment of
beta 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:
(C*(4-beta)/4/beta)^0.25 * RTT^0.75 / p^0.75 (Eq. 5)
With beta set to 0.2, the above formula is reduced to:
(C*3.8/0.8)^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^-3383838386610^-412026312020937110^-537917956601174208710^-6120012279371366021174010^-737958398120878371266602210^-812000574356117405208780371269Response function of standard TCP, HSTCP, and CUBIC
in networks with RTT = 100ms. The average window size W 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^-612001227912001200208710^-7379583981379566031174010^-812000574356208783712666022Response function of standard TCP, HSTCP, and CUBIC
in networks with RTT = 10ms. The average window size W 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 = 10ms 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:
1.17 * 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 3.4e-8.Throughput(Mbps)Average WTCP PHSTCP PCUBIC P18.32.0e-22.0e-22.0e-21083.32.0e-43.9e-43.3e-4100833.32.0e-62.5e-51.6e-510008333.32.0e-81.5e-67.3e-71000083333.32.0e-101.0e-73.4e-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