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Versions: 00 draft-rhee-tcpm-cubic

Network Working Group                                            I. Rhee
Internet-Draft                                                      NCSU
Intended status: Experimental                                      L. Xu
Expires: August 31, 2007                                             UNL
                                                                   S. Ha
                                                       February 27, 2007

                 CUBIC for Fast Long-Distance Networks

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Copyright Notice

   Copyright (C) The IETF Trust (2007).

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   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

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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

   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

   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

   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

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

   Email: rhee@ncsu.edu

   Lisong Xu
   University of Nebraska-Lincoln
   Department of Computer Science and Engineering
   Lincoln, NE  68588-0115

   Email: xu@cse.unl.edu

   Sangtae Ha
   North Carolina State University
   Department of Computer Science
   Raleigh, NC  27695-7534

   Email: sha2@ncsu.edu

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