 1/draftietftcpmcubic00.txt 20160118 08:15:20.459043777 0800
+++ 2/draftietftcpmcubic01.txt 20160118 08:15:20.491044539 0800
@@ 1,25 +1,25 @@
TCP Maintenance and Minor Extensions (TCPM) WG I. Rhee
InternetDraft NCSU
Intended status: Informational L. Xu
Expires: December 20, 2015 UNL
+Expires: July 21, 2016 UNL
S. Ha
 NCSU
+ Colorado
A. Zimmermann
L. Eggert
R. Scheffenegger
NetApp
 June 18, 2015
+ January 18, 2016
CUBIC for Fast LongDistance Networks
 draftietftcpmcubic00
+ draftietftcpmcubic01
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. BICTCP, a predecessor of CUBIC, has been a
default TCP adopted by Linux since year 2005 and has already been
@@ 42,68 +42,67 @@
InternetDrafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as InternetDrafts. The list of current Internet
Drafts is at http://datatracker.ietf.org/drafts/current/.
InternetDrafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use InternetDrafts as reference
material or to cite them other than as "work in progress."
 This InternetDraft will expire on December 20, 2015.
+ This InternetDraft will expire on July 21, 2016.
Copyright Notice
 Copyright (c) 2015 IETF Trust and the persons identified as the
+ Copyright (c) 2016 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/licenseinfo) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Conventions . . . . . . . . . . . . . . . . . . . . . . . . . 5
3. CUBIC Congestion Control . . . . . . . . . . . . . . . . . . 5
3.1. Window growth function . . . . . . . . . . . . . . . . . 5
3.2. TCPfriendly region . . . . . . . . . . . . . . . . . . . 6
 3.3. Concave region . . . . . . . . . . . . . . . . . . . . . 6
+ 3.3. Concave region . . . . . . . . . . . . . . . . . . . . . 7
3.4. Convex region . . . . . . . . . . . . . . . . . . . . . . 7
3.5. Multiplicative decrease . . . . . . . . . . . . . . . . . 7
3.6. Fast convergence . . . . . . . . . . . . . . . . . . . . 7
4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.1. Fairness to standard TCP . . . . . . . . . . . . . . . . 8
4.2. Using Spare Capacity . . . . . . . . . . . . . . . . . . 10
 4.3. Difficult Environments . . . . . . . . . . . . . . . . . 10
+ 4.3. Difficult Environments . . . . . . . . . . . . . . . . . 11
4.4. Investigating a Range of Environments . . . . . . . . . . 11
4.5. Protection against Congestion Collapse . . . . . . . . . 11
4.6. Fairness within the Alternative Congestion Control
Algorithm. . . . . . . . . . . . . . . . . . . . . . . . 11
4.7. Performance with Misbehaving Nodes and Outside Attackers 11
4.8. Responses to Sudden or Transient Events . . . . . . . . . 11
4.9. Incremental Deployment . . . . . . . . . . . . . . . . . 11
 5. Security Considerations . . . . . . . . . . . . . . . . . . . 11
 6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 11
+ 5. Security Considerations . . . . . . . . . . . . . . . . . . . 12
+ 6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 12
7. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 12
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 12
8.1. Normative References . . . . . . . . . . . . . . . . . . 12
 8.2. Informative References . . . . . . . . . . . . . . . . . 12
+ 8.2. Informative References . . . . . . . . . . . . . . . . . 13
 Appendix A. ToDo List . . . . . . . . . . . . . . . . . . . . . 13
 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 13
+ Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 14
1. Introduction
The low utilization problem of TCP in fast longdistance 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
[HKLRX06] 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
@@ 144,22 +143,22 @@
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 RTTfairness. 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 perflow basis must operate must increase its
 window much less aggressively in small BDP networks than in large BDP
+ Standard TCP at a perflow 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
@@ 181,21 +180,21 @@
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 [LS08]
currently uses the equal share.
 CUBIC sets the multiplicative window decrease factor to 0.2 while
+ 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
[RFC3649] has made along with other researchers (e.g., [GV02]): 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 intraprotocol fairness.
@@ 207,163 +206,173 @@
specified in [RFC5033].
2. Conventions
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 [RFC2119].
3. CUBIC Congestion Control
+ 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.
+
3.1. 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 TCPNewReno [RFC6582] and TCPSACK [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*(tK)^3 + W_max (Eq. 1)
+ W_cubic(t) = C*(tK)^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:
+ 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*beta/C) (Eq. 2)
+ K = cubic_root(W_max*(1beta_cubic)/C) (Eq. 2)
 where beta is the multiplication decrease factor. We discuss how we
 set C in the next Section in more details.
+ 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(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.
+ 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.
3.2. TCPfriendly 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
+ We can analyze the window size of a TCPfriendly AIMD 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:
+ decrease (AIMD) with an additive factor alpha_aimd and a
+ multiplicative factor beta_aimd with the following function:
 (alpha/2 * (2beta)/beta * 1/p)^0.5 (Eq. 3)
+ AVG_W_aimd = [ alpha_aimd * (1+beta_aimd) /
+ (2*(1beta_aimd)*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/(2beta).
 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:
+ 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*(1beta_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:
 W_tcp(t) = W_max*(1beta) + 3*beta/(2beta)* t/RTT (Eq. 4)
+ W_aimd(t) = W_max*beta_aimd +
+ [3*(1beta_aimd)/(1+beta_aimd)] * (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
+ 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.
3.3. Concave region
When receiving an ACK in congestion avoidance, if the protocol is not
in the TCPfriendly 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.
+ incremented by (W_cubic(t+RTT)  cwnd)/cwnd for each received ACK.
3.4. 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
+ 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(t+RTT)  cwnd)/cwnd for each
 received ACK.
+ region, cwnd MUST be incremented by (W_cubic(t+RTT)  cwnd)/cwnd for
+ each received ACK.
3.5. Multiplicative decrease
When a packet loss occurs, CUBIC reduces its window size by a factor
 of beta. Parameter beta SHOULD be set to 0.2.
+ of beta. Parameter beta_cubic SHOULD be set to 0.7.
W_max = cwnd; // save window size before reduction
 cwnd = cwnd * (1beta); // window reduction
+ cwnd = cwnd * beta_cubic; // window reduction
 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.
+ 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.
3.6. 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, 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.
if (W_max < W_last_max){ // check downward trend
W_last_max = W_max; // remember the last W_max
 W_max = W_max*(2beta)/2; // further reduce W_max
+ W_max = W_max*(1+beta_cubic)/2; // further reduce W_max
} else { // check upward trend
W_last_max = W_max // remember the last W_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.
4. 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*(4beta)/4/beta)^0.25 * RTT^0.75 / p^0.75 (Eq. 5)
+ AVG_W_cubic = [C*(3+beta_cubic)/(4*(1beta_cubic))]^0.25 *
+ (RTT^0.75) / (p^0.75) (Eq. 5)
 With beta set to 0.2, the above formula is reduced to:
+ With beta_cubic set to 0.7, the above formula is reduced to:
 (C*3.8/0.8)^0.25 * RTT^0.75 / p^0.75 (Eq. 6)
+ 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.
4.1. 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.
@@ 378,92 +387,93 @@
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 for three different values of C.
+++++++
 Loss  TCP  HSTCP  CUBIC  CUBIC  CUBIC 
 Rate P    (C=0.04)  (C=0.4)  (C=4) 
+++++++
 10^2  12  12  12  12  12 
  10^3  38  38  38  38  66 
  10^4  120  263  120  209  371 
  10^5  379  1795  660  1174  2087 
  10^6  1200  12279  3713  6602  11740 
  10^7  3795  83981  20878  37126  66022 
  10^8  12000  574356  117405  208780  371269 
+  10^3  38  38  38  38  59 
+  10^4  120  263  120  187  333 
+  10^5  379  1795  593  1054  1874 
+  10^6  1200  12279  3332  5926  10538 
+  10^7  3795  83981  18740  33325  59261 
+  10^8  12000  574356  105383  187400  333250 
+++++++
Response function of standard TCP, HSTCP, and CUBIC in networks with
 RTT = 100ms. The average window size W is in MSSsized segments.
+ RTT = 0.1 seconds. The average window size is in MSSsized segments.
Table 1
+++++++
 Loss  Average  Average  CUBIC  CUBIC  CUBIC 
 Rate P  TCP W  HSTCP W  (C=0.04)  (C=0.4)  (C=4) 
+++++++
 10^2  12  12  12  12  12 
 10^3  38  38  38  38  38 
 10^4  120  263  120  120  120 
 10^5  379  1795  379  379  379 
  10^6  1200  12279  1200  1200  2087 
  10^7  3795  83981  3795  6603  11740 
  10^8  12000  574356  20878  37126  66022 
+  10^6  1200  12279  1200  1200  1874 
+  10^7  3795  83981  3795  5926  10538 
+  10^8  12000  574356  18740  33325  59261 
+++++++
Response function of standard TCP, HSTCP, and CUBIC in networks with
 RTT = 10ms. The average window size W is in MSSsized segments.
+ RTT = 0.01 seconds. The average window size is in MSSsized
+ segments.
Table 2
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.
+ 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 TCPfriendliness 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)
+ 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.
4.2. 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 2.0e10, while CUBIC requires a packet
 loss rate of 3.4e8.
+ loss rate of 2.9e8.
++++++
 Throughput(Mbps)  Average W  TCP P  HSTCP P  CUBIC P 
++++++
 1  8.3  2.0e2  2.0e2  2.0e2 
  10  83.3  2.0e4  3.9e4  3.3e4 
  100  833.3  2.0e6  2.5e5  1.6e5 
  1000  8333.3  2.0e8  1.5e6  7.3e7 
  10000  83333.3  2.0e10  1.0e7  3.4e8 
+  10  83.3  2.0e4  3.9e4  2.9e4 
+  100  833.3  2.0e6  2.5e5  1.4e5 
+  1000  8333.3  2.0e8  1.5e6  6.3e7 
+  10000  83333.3  2.0e10  1.0e7  2.9e8 
++++++
Required packet loss rate for Standard TCP, HSTCP, and CUBIC to
achieve a certain throughput. We use 1500byte packets and an RTT of
0.1 seconds.
Table 3
Our test results in [HKLRX06] indicate that CUBIC uses the spare
bandwidth left unused by existing Standard TCP flows in the same
@@ 526,44 +536,55 @@
20142018 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.
8. References
8.1. Normative References
[RFC2018] Mathis, M., Mahdavi, J., Floyd, S., and A. Romanow, "TCP
 Selective Acknowledgment Options", RFC 2018, October 1996.
+ Selective Acknowledgment Options", RFC 2018,
+ DOI 10.17487/RFC2018, October 1996,
+ .
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
 Requirement Levels", BCP 14, RFC 2119, March 1997.
+ Requirement Levels", BCP 14, RFC 2119,
+ DOI 10.17487/RFC2119, March 1997,
+ .
[RFC3649] Floyd, S., "HighSpeed TCP for Large Congestion Windows",
 RFC 3649, December 2003.
+ RFC 3649, DOI 10.17487/RFC3649, December 2003,
+ .
 [RFC4960] Stewart, R., "Stream Control Transmission Protocol", RFC
 4960, September 2007.
+ [RFC4960] Stewart, R., Ed., "Stream Control Transmission Protocol",
+ RFC 4960, DOI 10.17487/RFC4960, September 2007,
+ .
[RFC5033] Floyd, S. and M. Allman, "Specifying New Congestion
 Control Algorithms", BCP 133, RFC 5033, August 2007.
+ Control Algorithms", BCP 133, RFC 5033,
+ DOI 10.17487/RFC5033, August 2007,
+ .
[RFC5348] Floyd, S., Handley, M., Padhye, J., and J. Widmer, "TCP
 Friendly Rate Control (TFRC): Protocol Specification", RFC
 5348, September 2008.
+ Friendly Rate Control (TFRC): Protocol Specification",
+ RFC 5348, DOI 10.17487/RFC5348, September 2008,
+ .
[RFC5681] Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
 Control", RFC 5681, September 2009.
+ Control", RFC 5681, DOI 10.17487/RFC5681, September 2009,
+ .
[RFC6582] Henderson, T., Floyd, S., Gurtov, A., and Y. Nishida, "The
NewReno Modification to TCP's Fast Recovery Algorithm",
 RFC 6582, April 2012.
+ RFC 6582, DOI 10.17487/RFC6582, April 2012,
+ .
8.2. Informative References
[CEHRX07] 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.
[FHP00] Floyd, S., Handley, M., and J. Padhye, "A Comparison of
EquationBased and AIMD Congestion Control", May 2000.
@@ 586,37 +607,30 @@
Communication Review , April 2003.
[LS08] Leith, D. and R. Shorten, "HTCP: TCP Congestion Control
for High BandwidthDelay Product Paths", Internetdraft
draftleithtcphtcp06 , April 2008.
[XHR04] Xu, L., Harfoush, K., and I. Rhee, "Binary Increase
Congestion Control for Fast, Long Distance Networks", In
Proceedings of IEEE INFOCOM , March 2004.
Appendix A. ToDo List

 o Incorporate ICCRG's feedback (see
 http://trac.tools.ietf.org/group/irtf/trac/wiki/ICCRG_cubic)

 o ncorporate feedback from Neal Cardwell (see http://www.ietf.org/
 mailarchive/web/tcpm/current/msg09508.html)

Authors' Addresses
Injong Rhee
North Carolina State University
Department of Computer Science
Raleigh, NC 276957534
US
Email: rhee@ncsu.edu
+
Lisong Xu
University of NebraskaLincoln
Department of Computer Science and Engineering
Lincoln, NE 6858801150
US
Email: xu@unl.edu
Sangtae Ha
University of Colorado at Boulder