Network Working Group I. Rhee
Internet-Draft NCSU
Intended status: Experimental L. Xu
Expires: August 31, 2007 UNL
S. Ha
NCSU
February 27, 2007
CUBIC for Fast Long-Distance Networks
draft-rhee-tcp-cubic-00.txt
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Abstract
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.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. CUBIC Congestion Control . . . . . . . . . . . . . . . . . . . 7
2.1. Window growth function . . . . . . . . . . . . . . . . . . 7
2.2. TCP-friendly region . . . . . . . . . . . . . . . . . . . 7
2.3. Concave region . . . . . . . . . . . . . . . . . . . . . . 8
2.4. Convex region . . . . . . . . . . . . . . . . . . . . . . 8
2.5. Multiplicative decrease . . . . . . . . . . . . . . . . . 9
2.6. Fast convergence . . . . . . . . . . . . . . . . . . . . . 9
3. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1. Fairness to standard TCP . . . . . . . . . . . . . . . . . 11
3.2. Using Spare Capacity . . . . . . . . . . . . . . . . . . . 13
3.3. Difficult Environments . . . . . . . . . . . . . . . . . . 13
3.4. Investigating a Range of Environments . . . . . . . . . . 14
3.5. Protection against Congestion Collapse . . . . . . . . . . 14
3.6. Fairness within the Alternative Congestion Control
Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . 14
3.7. Performance with Misbehaving Nodes and Outside
Attackers . . . . . . . . . . . . . . . . . . . . . . . . 14
3.8. Responses to Sudden or Transient Events . . . . . . . . . 14
3.9. Incremental Deployment . . . . . . . . . . . . . . . . . . 14
4. Security Considerations . . . . . . . . . . . . . . . . . . . 15
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 16
6. References . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.1. Normative References . . . . . . . . . . . . . . . . . . . 17
6.2. Informative References . . . . . . . . . . . . . . . . . . 17
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 19
Intellectual Property and Copyright Statements . . . . . . . . . . 20
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1. Introduction
The low utilization problem of TCP in fast long-distance networks is
well documented in [K03][RFC3649]. 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
[H+06] 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 [RFC2581], TCP-NewReno [RFC3782], TCP-
SACK [RFC2018], SCTP [RFC2960], TFRC [RFC3448] 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 [C+07]. 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
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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 [XHR04]. 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 [LS05]
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
[RFC3649] has made along with other researchers (e.g., [GV02]): the
current Internet becomes more asynchronous with less frequent loss
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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 [FA06].
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2. CUBIC Congestion Control
2.1. Window growth function
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 [RFC3782] and TCP-SACK [RFC2018]. 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 CUBIC parameter, 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.
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.
2.2. TCP-friendly 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 [FHP00], 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:
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1/RTT (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 1/RTT (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 is set to W_tcp(t) at each reception of ACK.
2.3. Concave region
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 is
incremented by (W(t+RTT) - cwnd)/cwnd.
2.4. Convex region
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.
During the convex region, the window growth rate of CUBIC can be very
high at some time. While the convex window growth in this phase
seems appropriate (as most loss-based TCP alternative protocols use a
convex function), there is no consensus on what increase rate is
appropriate. For the time being, we clamp the growth rate to a
constant maximum rate, called max_increment_rate, not to cause too
much burst into the network. We set max_increment_rate to 160
packets per second. To be exact, if the protocol is the convex
region outside the TCP-friendly region, when receiving an ACK, we
uses the following code.
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W_inc = W(t+RTT) - cwnd;
if (W_inc > max_increment_rate * RTT) // max clamping
W_inc = max_increment_rate * RTT;
cwnd = cwnd + W_inc/cwnd;
Figure 1
We found this maximum increment rate is safe for the deployment of
the current Internet which is equivalent to 16 packets per RTT in a
100 ms RTT network, to 1.6 packets per RTT in a 10 ms RTT network
(since in this network, CUBIC is running in the TCP friendly region,
its increasing rate follows that of Standard TCP). Alternative to
this clamping, the increasing function of HSTCP can be considered
whose increase rate is a function of its current window size. Since
the scalability of CUBIC under steady state is mostly determined by
the concave profile of the cubic function where no clamping is
applied, the clamping does not affect the scalability of the protocol
under steady state.
2.5. Multiplicative decrease
When a packet loss occurs, CUBIC reduces its window size by a factor
of beta. We set beta to 0.2.
W_max = cwnd; // remember the window size before reduction
cwnd = cwnd * (1-beta); // window reduction
Figure 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.
2.6. Fast convergence
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, we add the following mechanism called fast
convergence.
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
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call the last value of W_max to be W_last_max.
if (W_max < W_last_max){ // check downward trend,
W_last_max = W_max; // remember the last W_max.
W_max = W_max*(2-beta)/2; // further reduce W_max.
} else // check upward trend.
W_last_max = W_max // remember the last W_max.
Figure 3
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.
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3. Discussion
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)
To ensure fairness to Standard TCP based on our argument in the
introduction, we set C to 0.4. We find that this value of C allows
the size of the TCP friendly region to be large enough to encompass
most of the environments where Standard TCP performs well while
preserving the scalability of the window growth function. With beta
set to 0.2, the above formula is reduced to:
1.17 * RTT^0.75 / p^0.75 (Eq. 6)
Eq. 6 is used to argue the fairness of CUBIC to Standard TCP and its
safety for deployment below.
3.1. Fairness to standard TCP
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 [RFC3649]. The average
window size of CUBIC is calculated by using Eq. 6 and CUBIC TCP
friendly mode.
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+-------------+---------------+-----------------+-----------------+
| Loss Rate P | Average TCP W | Average HSTCP W | Average CUBIC W |
+-------------+---------------+-----------------+-----------------+
| 10^-2 | 12 | 12 | 12 |
| | | | |
| 10^-3 | 38 | 38 | 38 |
| | | | |
| 10^-4 | 120 | 263 | 209 |
| | | | |
| 10^-5 | 379 | 1795 | 1175 |
| | | | |
| 10^-6 | 1200 | 12279 | 6609 |
| | | | |
| 10^-7 | 3795 | 83981 | 37165 |
| | | | |
| 10^-8 | 12000 | 574356 | 208058 |
+-------------+---------------+-----------------+-----------------+
Response function of standard TCP, HSTCP, and CUBIC in networks with
RTT = 100ms. The average window size W is in MSS-sized segments.
Table 1
+-------------+---------------+-----------------+-----------------+
| Loss Rate P | Average TCP W | Average HSTCP W | Average CUBIC W |
+-------------+---------------+-----------------+-----------------+
| 10^-2 | 12 | 12 | 12 |
| | | | |
| 10^-3 | 38 | 38 | 38 |
| | | | |
| 10^-4 | 120 | 263 | 120 |
| | | | |
| 10^-5 | 379 | 1795 | 379 |
| | | | |
| 10^-6 | 1200 | 12279 | 1200 |
| | | | |
| 10^-7 | 3795 | 83981 | 6588 |
| | | | |
| 10^-8 | 12000 | 574356 | 36996 |
+-------------+---------------+-----------------+-----------------+
Response function of standard TCP, HSTCP, and CUBIC in networks with
RTT = 10ms. The average window size W is in MSS-sized segments.
Table 2
Both tables show that CUBIC is more friendly to TCP than HSTCP,
especially in networks with a short RTT where TCP performs reasonably
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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 achieves exactly the same rate as Standard TCP, whereas HSTCP
is about ten times more aggressive than Standard TCP.
3.2. Using Spare Capacity
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 W | TCP P | HSTCP P | CUBIC P |
+------------------+-----------+---------+---------+---------+
| 1 | 8.3 | 2.0e-2 | 2.0e-2 | 2.0e-2 |
| | | | | |
| 10 | 83.3 | 2.0e-4 | 3.9e-4 | 3.3e-4 |
| | | | | |
| 100 | 833.3 | 2.0e-6 | 2.5e-5 | 1.6e-5 |
| | | | | |
| 1000 | 8333.3 | 2.0e-8 | 1.5e-6 | 7.3e-7 |
| | | | | |
| 10000 | 83333.3 | 2.0e-10 | 1.0e-7 | 3.4e-8 |
+------------------+-----------+---------+---------+---------+
Required 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.
Table 3
Our test results in [H+06] 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.
3.3. Difficult Environments
CUBIC is designed to remedy the poor performance of TCP in fast long-
distance networks. It is not designed for wireless networks.
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3.4. Investigating a Range of Environments
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 [H+06].
3.5. Protection against Congestion Collapse
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.
3.6. Fairness within the Alternative Congestion Control Algorithm.
CUBIC ensures convergence of competing CUBIC flows 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.
3.7. Performance with Misbehaving Nodes and Outside Attackers
This is not considered in the current CUBIC.
3.8. Responses to Sudden or Transient Events
In case that there is a sudden congestion, a routing change, or a
mobility event, CUBIC behaves the same as Standard TCP.
3.9. Incremental Deployment
CUBIC requires only the change of TCP senders, and does not require
any assistant of routers.
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4. Security Considerations
This proposal makes no changes to the underlying security of TCP.
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5. IANA Considerations
There are no IANA considerations regarding this document.
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6. References
6.1. Normative References
[RFC2018] Mathis, M., Mahdavi, J., Floyd, S., and A. Romanow, "TCP
Selective Acknowledgment Options", RFC 2018, October 1996.
[RFC2581] Allman, M., Paxson, V., and W. Stevens, "TCP Congestion
Control", RFC 2581, April 1999.
[RFC2960] Stewart, R., Xie, Q., Morneault, K., Sharp, C.,
Schwarzbauer, H., Taylor, T., Rytina, I., Kalla, M.,
Zhang, L., and V. Paxson, "Stream Control Transmission
Protocol", RFC 2960, October 2000.
[RFC3448] Handley, M., Floyd, S., Padhye, J., and J. Widmer, "TCP
Friendly Rate Control (TFRC): Protocol Specification",
RFC 3448, January 2003.
[RFC3782] Floyd, S., Henderson, T., and A. Gurtov, "The NewReno
Modification to TCP's Fast Recovery Algorithm", RFC 3782,
April 2004.
6.2. Informative References
[C+07] Cai, H., Eun, D., Ha, S., Rhee, I., and L. Xu, "Stochastic
Ordering for Internet Congestion Control and its
Applications", In Proceedings of IEEE INFOCOM , May 2007.
[FA06] Floyd, S. and M. Allman, "Specifying New Congestion
Control Algorithms", Internet-draft
draft-floyd-tsvwg-cc-alt-00.txt , December 2006.
[FHP00] Floyd, S., Handley, M., and J. Padhye, "A Comparison of
Equation-Based and AIMD Congestion Control", May 2000.
[GV02] Gorinsky, S. and H. Vin, "Extended Analysis of Binary
Adjustment Algorithms", Technical Report TR2002-29,
Department of Computer Sciences , The University of Texas
at Austin , August 2002.
[H+06] Ha, S., Kim, Y., Le, L., Rhee, I., and L. Xu, "A Step
toward Realistic Performance Evaluation of High-Speed TCP
Variants", International Workshop on Protocols for Fast
Long-Distance Networks , February 2006.
[K03] Kelly, T., "Scalable TCP: Improving Performance in
HighSpeed Wide Area Networks", ACM SIGCOMM Computer
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Communication Review , April 2003.
[LS05] Leith, D. and R. Shorten, "H-TCP: TCP Congestion Control
for High Bandwidth-Delay Product Paths", Internet-draft
draft-leith-tcp-htcp-00 , June 2005.
[RFC3649] Floyd, S., "HighSpeed TCP for Large Congestion Windows",
RFC 3649, December 2003.
[XHR04] Xu, L., Harfoush, K., and I. Rhee, "Binary Increase
Congestion Control for Fast, Long Distance Networks", In
Proceedings of IEEE INFOCOM , March 2004.
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Authors' Addresses
Injong Rhee
North Carolina State University
Department of Computer Science
Raleigh, NC 27695-7534
US
Email: rhee@ncsu.edu
Lisong Xu
University of Nebraska-Lincoln
Department of Computer Science and Engineering
Lincoln, NE 68588-0115
US
Email: xu@cse.unl.edu
Sangtae Ha
North Carolina State University
Department of Computer Science
Raleigh, NC 27695-7534
US
Email: sha2@ncsu.edu
Rhee, et al. Expires August 31, 2007 [Page 19]
Internet-Draft CUBIC February 2007
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