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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@cse.unl.eduNorth Carolina State UniversityDepartment of Computer ScienceRaleighNC27695-7534USsha2@ncsu.eduInternet-Draft
CUBIC 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 soem 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 BDP
CUBIC 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 a Round-Trip Time 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 invese of their RTT ratios. This is true independent of
the level of stastistical 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.
TCP Selective Acknowledgment OptionsPittsburgh Supercomputing CenterPittsburgh Supercomputing CenterLawrence Berkeley National LaboratorySun Microsystems, Inc.Key words for use in RFCs to Indicate Requirement LevelsHarvard University1350 Mass. Ave.CambridgeMA 02138- +1 617 495 3864sob@harvard.eduTCP Congestion ControlNASA Glenn Research Center/Sterling SoftwareACIRI / ICSIStream Control Transmission Protocol
TCP Friendly Rate Control (TFRC): Protocol Specification
HighSpeed TCP for Large Congestion Windows
The NewReno Modification to TCP's Fast Recovery Algorithm
Specifying New Congestion Control Algorithms
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