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Versions: 00 01 02 03 04 05 draft-ietf-tcpm-newcwv

TCPM Working Group                                          G. Fairhurst
Internet-Draft                                           A. Sathiaseelan
Obsoletes: 2861 (if approved)                     University of Aberdeen
Updates: 5681 (if approved)                           September 14, 2012
Intended status: Standards Track
Expires: March 18, 2013


              Updating TCP to support Rate-Limited Traffic
                    draft-fairhurst-tcpm-newcwv-05

Abstract

   This document proposes an update to RFC 5681 to address issues that
   arise when TCP is used to support traffic that exhibits periods where
   the sending rate is limited by the application rather than the
   congestion window.  It updates TCP to allow a TCP sender to restart
   quickly following either an idle or rate-limited interval.  This
   method is expected to benefit applications that send rate-limited
   traffic using TCP, while also providing an appropriate response if
   congestion is experienced.

   It also evaluates TCP Congestion Window Validation, CWV, an IETF
   experimental specification defined in RFC 2861, and concludes that
   CWV sought to address important issues, but failed to deliver a
   widely used solution.  This document therefore proposes an update to
   the status of RFC 2861 by recommending it is moved from Experimental
   to Historic status, and that it is replaced by the current
   specification.

Status of this Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts 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 Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on March 18, 2013.

Copyright Notice



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   Copyright (c) 2012 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/license-info) 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.  Reviewing experience with TCP-CWV  . . . . . . . . . . . . . .  3
   3.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  4
   4.  An updated TCP response to idle and application-limited
       periods  . . . . . . . . . . . . . . . . . . . . . . . . . . .  5
     4.1.  A method for preserving cwnd during the idle and
           application-limited periods. . . . . . . . . . . . . . . .  6
     4.2.  The nonvalidated phase . . . . . . . . . . . . . . . . . .  6
     4.3.  TCP congestion control during the nonvalidated phase . . .  7
       4.3.1.  Response to congestion in the nonvalidated phase . . .  7
       4.3.2.  Adjustment at the end of the nonvalidated phase  . . .  8
   5.  Determining a safe period to preserve cwnd . . . . . . . . . .  9
   6.  Security Considerations  . . . . . . . . . . . . . . . . . . . 10
   7.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 10
   8.  Acknowledgments  . . . . . . . . . . . . . . . . . . . . . . . 10
   9.  Author Notes . . . . . . . . . . . . . . . . . . . . . . . . . 10
     9.1.  Other related work . . . . . . . . . . . . . . . . . . . . 11
     9.2.  Revision notes . . . . . . . . . . . . . . . . . . . . . . 12
   10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 13
     10.1. Normative References . . . . . . . . . . . . . . . . . . . 13
     10.2. Informative References . . . . . . . . . . . . . . . . . . 13
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 14













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1.  Introduction

   TCP is used to support a range of application behaviours.  The TCP
   congestion window (cwnd) controls the number of packets/bytes that a
   TCP flow may have in the network at any time.  The unacknowledged
   volume of data that a TCP flow has in the network at a specific time
   is known as the FlightSize [RFC5681].  A bulk application will always
   have data available to transmit.  The rate at which it sends is
   therefore limited by the maximum permitted by the receiver and
   congestion windows.  In contrast, a rate-limited application will
   experience periods when the sender is either idle or is unable to
   send at the maximum rate permitted by the cwnd.  This latter case is
   called rate-limited.  The focus of this document is on the operation
   of TCP in such an idle or rate-limited case.

   Standard TCP [RFC5681] requires the cwnd to be reset to the restart
   window (RW) when an application becomes idle.  [RFC2861] noted that
   this TCP behaviour was not always observed in current
   implementations.  Recent experiments [Bis08] confirm this to still be
   the case.

   Standard TCP does not impose additional restrictions on the growth of
   the cwnd when a TCP sender is rate-limited.  A rate-limited sender
   may therefore grow a cwnd far beyond that corresponding to the
   current transmit rate, resulting in a value that does not reflect
   current information about the state of the network path the flow is
   using.  Use of such an invalid cwnd may result in reduced application
   performance and/or could significantly contribute to network
   congestion.

   [RFC2861] proposed a solution to these issues in an experimental
   method known as Congestion Window Validation (CWV).  CWV was intended
   to help reduce cases where TCP accumulated an invalid cwnd.  The use
   and drawbacks of using CWV with an application are discussed in
   Section 2.

   Section 4 specifies an alternative to CWV that seeks to address the
   same issues, but does this in a way that is expected to mitigate the
   impact on an application that varies its sending rate.  The method
   described applies to both a rate-limited and an idle condition.


2.  Reviewing experience with TCP-CWV

   RFC 2861 described a simple modification to the TCP congestion
   control algorithm that decayed the cwnd after the transition to a
   "sufficiently-long" idle period.  This used the slow-start threshold
   (ssthresh) to save information about the previous value of the



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   congestion window.  The approach relaxed the standard TCP behaviour
   [RFC5681] for an idle session, intended to improve application
   performance.  CWV also modified the behaviour for a rate-limited
   session where a sender transmitted at a rate less than allowed by
   cwnd.

   RFC 2861 has been implemented in some mainstream operating systems as
   the default behaviour [Bis08].  Analysis (e.g.  [Bis10]) has shown
   that a TCP sender using CWV is able to use available capacity on a
   shared path after an idle period.  This can benefit some
   applications, especially over long delay paths, when compared to the
   slow-start restart specified by standard TCP.  However, CWV would
   only benefit an application if the idle period were less than several
   Retransmission Time Out (RTO) intervals [RFC6298], since the
   behaviour would otherwise be the same as for standard TCP, which
   resets the cwnd to the RTCP Restart Window (RW) after this period.

   Experience with CWV suggests that although CWV benefits the network
   in a rate-limited scenario (reducing the probability of network
   congestion), the behaviour can be too conservative for many common
   rate-limited applications.  This mechanism does not therefore offer
   the desirable increase in application performance for rate-limited
   applications and it is unclear whether applications actually use this
   mechanism in the general Internet.

   It is therefore concluded that CWV is often a poor solution for many
   rate-limited applications.  It has the correct motivation, but has
   the wrong approach to solving this problem.


3.  Terminology

   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].

   The document assumes familiarity with the terminology of TCP
   congestion control [RFC5681].

   The following new terminology is introduced:

   Validated phase: The phase where the cwnd reflects a current estimate
   of the available path capacity.

   Non-validated phase: The phase where the cwnd reflects a previous
   measurement of the available path capacity.

   Non-validated period, NVP: The maximum period for which cwnd is



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   preserved in the non-validated phase.

   Rate-limited: A TCP flow that does not consume more than one half of
   cwnd, and hence operates in the non-validated phase.

   pipe ACK: The measured volume of data that was acknowledged by the
   network per RTT.


4.  An updated TCP response to idle and application-limited periods

   This section proposes an update to the TCP congestion control
   behaviour during an idle or rate-limited period.  The new method
   permits a TCP sender to preserve the cwnd when an application becomes
   idle for a period of time (to be known as the non-validated period,
   NVP, see section 5).  This period, where actual usage is less than
   allowed by cwnd, is named as the non-validated phase.  This method
   allows an application to resume transmission at a previous rate
   without incurring the delay of slow-start.  However, if the TCP
   sender experiences congestion using the preserved cwnd, it is
   required to immediately reset the cwnd to an appropriate value
   specified by the method.  If a sender does not take advantage of the
   preserved cwnd within the NVP, the value of cwnd is reduced, ensuring
   the value better reflects the capacity that was recently actually
   used.

   The method requires that the TCP SACK option is enabled.  This allows
   the sender to select a cwnd following a congestion event that is
   based on the measured path capacity, better reflecting the fair-
   share.  A similar approach was proposed by TCP Jump Start [Liu07], as
   a congestion response after more rapid opening of a TCP connection.

   It is expected that this update will satisfy the requirements of many
   rate-limited applications and at the same time provide an appropriate
   method for use in the Internet.  It also reduces the incentive for an
   application to send data simply to keep transport congestion state.
   (This is sometimes known as "padding").

   The new method does not differentiate between times when the sender
   has become idle or rate-limited.  This is partly a response to
   recognition that some applications wish to transmit at a rate less
   than allowed by the sender cwnd, and that it can be hard to make a
   distinction between rate-limited and idle behaviour.  This is
   expected to encourage applications and TCP stacks to use standards-
   based congestion control methods.  It may also encourage the use of
   long-lived connections where this offers benefit (such as persistent
   http).




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   The method is specified in following subsections.

4.1.  A method for preserving cwnd during the idle and application-
      limited periods.

   The method described in this document updates [RFC5681].  Use of the
   method REQUIRES a TCP sender and the corresponding receiver to enable
   the TCP SACK option [RFC3517].

   [RFC5681] defines a variable FlightSize that indicates the amount of
   outstanding data in the network.  This is assumed to be equal to the
   value of Pipe calculated based on the pipe algorithm [RFC3517].  In
   RFC5681 this value is used during loss recovery, whereas in this
   method a new variable "pipeACK" is introduced and used to determine
   if the sender has validated the cwnd.

   A sender is not required to continuously track the pipeACK value, but
   MUST set this variable to the volume of data that was acknowledged by
   the network per measured Round Trip Time (RTT), with a sampling
   period of not less than one measurement for Min(RTT, 1 second).
   Using the variables defined in [RFC3517].  This could be implemented
   by caching the value of HighACK and after one RTT assigning pipeACK
   to the difference between the cached HighACK value and the current
   HighACK value.  Other equivalent methods may be used.

4.2.  The nonvalidated phase

   The updated method creates a new TCP sender phase that captures
   whether the cwnd reflects a validated or non-validated value.  The
   phases are defined as:

   o  Validated phase: pipeACK >=(1/2)*cwnd.  This is the normal phase,
      where cwnd is expected to be an approximate indication of the
      available capacity currently available along the network path, and
      the standard methods are used to increase cwnd (currently
      [RFC5681]).  The rule for transitioning to the non-validated phase
      is specified in section 4.3.

   o  Non-validated phase: pipeACK <(1/2)*cwnd.  This is the phase where
      the cwnd has a value based on a previous measurement of the
      available capacity, and the usage of this capacity has not been
      validated in the previous RTT.  That is, when it is not known
      whether the cwnd reflects the currently available capacity along
      the network path.  The mechanisms to be used in this phase seek to
      determine a safe value for cwnd and an appropriate reaction to
      congestion.  These mechanisms are specified in section 4.3.

   A sender starts a TCP connection in the Validated phase.



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   The values 1/2 was selected to reduce the effects of variations in
   the measured pipeACK, and to allow the sender some flexibility in
   when it sends data.

4.3.  TCP congestion control during the nonvalidated phase

   A TCP sender MUST enter the non-validated phase when the measured
   pipeACK is less than (1/2)*cwnd.

   A TCP sender that enters the non-validated phase will preserve the
   cwnd (i.e., this neither grows nor reduces while the sender remains
   in this phase).  The phase is concluded after a fixed period of time
   (the NVP, as explained in section 4.3.2) or when the sender transmits
   sufficient data so that pipeACK > (1/2)*cwnd (i.e. it is no longer
   rate-limited).

   The behaviour in the non-validated phase is specified as:

   o  The cwnd is not increased when ACK packets are received in this
      phase.

   o  If the sender receives an indication of congestion while in the
      non-validated phase (i.e. detects loss, or an Explicit Congestion
      Notification, ECN, mark [RFC3168]), the sender MUST exit the non-
      validated phase (reducing the cwnd as defined in section 4.3.1).

   o  If the Retransmission Time Out (RTO) expires while in the non-
      validated phase, the sender MUST exit the non-validated phase.  It
      then resumes using the Standard TCP RTO mechanism [RFC5681].  (The
      resulting reduction of cwnd described in section 4.3.2 is
      appropriate, since any accumulated path history is considered
      unreliable).

   o  A sender than measures a pipeACK greater than (1/2)*cwnd SHOULD
      enter the validated phase.  (A rate-limited sender will not
      normally be impacted by whether thit is in a validated or non-
      validate phase, since it will normally not consume the entire
      cwnd.  However a change to the validated phase will release the
      sender from constraints on the growth of cwnd, and restore the use
      of the standard congestion response.)

4.3.1.  Response to congestion in the nonvalidated phase

   Reception of congestion feedback while in the non-validated phase is
   interpreted as an indication that it was inappropriate for the sender
   to use the preserved cwnd.  The sender is therefore required to
   quickly reduce the rate to avoid further congestion.  Since the cwnd
   does not have a validated value, a new cwnd value must be selected



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   based on the utilised rate.

   A sender that detects a packet-drop or receives an ECN marked packet
   MUST calculate a safe cwnd, by setting it to the value specified in
   Section 3.2 of [RFC5681].

   At the end of the recovery phase, the TCP sender MUST reset the cwnd
   using the method below:
           cwnd = ((FlightSize - R)/2).

   Where, R is the volume of data that was reported as unacknowledged by
   the SACK information.  This follows the method proposed for Jump
   Start [[Liu07].

   The inclusion of the term R makes this adjustment more conservative
   than standard TCP.  (This is required, since the sender may have sent
   more segments than a Standard TCP sender would have done.  The
   additional reduction is beneficial when the FlightSize significantly
   overshoots the available path capacity incurring significant loss,
   for instance an intense traffic burst following a non-validated
   period.)

   If the sender implements a method that allows it to identify the
   number of ECN-marked segments within a window that were observed by
   the receiver, the sender SHOULD use the method above, further
   reducing R by the number of marked segments.

4.3.2.  Adjustment at the end of the nonvalidated phase

   During the non-validated phase, a sender can produce bursts of data
   of up to the cwnd in size.  While this is no different to standard
   TCP, it is desirable to control the maximum burst size, e.g. by
   setting a burst size limit, using a pacing algorithm, or some other
   method [Hug01].

   An application that remains in the non-validated phase for a period
   greater than the NVP is required to adjust its congestion control
   state.  If the sender exits the non-validated phase after this
   period, it MUST update the ssthresh:

         ssthresh = max(ssthresh, 3*cwnd/4).

   (This adjustment of ssthresh ensures that the sender records that it
   has safely sustained the present rate.  The change is beneficial to
   rate-limited flows that encounter occasional congestion, and could
   otherwise suffer an unwanted additional delay in recovering the
   sending rate.)




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   The sender MUST then update cwnd to be not greater than:

            cwnd = max(1/2*cwnd, IW).


   Where IW is the TCP inital window [RFC5681].

   (This adjustment ensures that sender responds conservatively at the
   end of the non-validated phase by reducing the cwnd to better reflect
   the current sending rate of the sender.  The cwnd update does not
   take into account FlightSize or pipeACK as these values only reflects
   the last RTT worth of data and do not reflect the average of peak
   sending rate.)

   After completing this adjustment, the sender MAY re-enter the non-
   validated phase, if required (see section 4.2).


5.  Determining a safe period to preserve cwnd

   This section documents the rationale for selecting the maximum period
   that cwnd may be preserved, known as the non-validated period, NVP.

   Preserving cwnd avoids undesirable side effects that would result if
   the cwnd were to be preserved for an arbitrary long period, which was
   a part of the problem that CWV originally attempted to address.  The
   period a sender may safely preserve the cwnd, is a function of the
   period that a network path is expected to sustain the capacity
   reflected by cwnd.  There is no ideal choice for this time.

   A period of five minutes was chosen for this NVP.  This is as a
   compromise that was larger than the idle intervals of common
   applications, but not sufficiently larger than the period for which
   the capacity of an Internet path may commonly be regarded as stable.
   The capacity of wired networks is usually relatively stable for
   periods of several minutes and that load stability increases with the
   capacity.  This suggests that cwnd may be preserved for at least a
   few minutes.

   There are cases where the TCP throughput exhibits significant
   variability over a time less than five minutes.  Examples could
   include wireless topologies, where TCP rate variations may fluctuate
   on the order of a few seconds as a consequence of medium access
   protocol instabilities.  Mobility changes may also impact TCP
   performance over short time scales.  Senders that observe such rapid
   changes in the path characteristic may also experience increased
   congestion with the new method, however such variation would likely
   also impact TCP's behaviour when supporting interactive and bulk



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   applications.

   Routing algorithms may modify the network path, disrupting the RTT
   measurement and changing the capacity available to a TCP connection,
   however such changes do not often occur within a time frame of a few
   minutes.

   The value of five minutes is therefore expected to be sufficient for
   most current applications.  Simulation studies also suggest that for
   many practical applications, the performance using this value will
   not be significantly different to that observed using a non-standard
   method that does not reset the cwnd after idle.

   Finally, other TCP sender mechanisms have used a 5 minute timer, and
   there could be simplifications in some implementations by reusing the
   same interval.  TCP defines a default user timeout of 5 minutes
   [RFC0793] i.e. how long transmitted data may remain unacknowledged
   before a connection is forcefully closed.


6.  Security Considerations

   General security considerations concerning TCP congestion control are
   discussed in [RFC5681].  This document describes an algorithm that
   updates one aspect of the congestion control procedures, and so the
   considerations described in RFC 5681 also apply to this algorithm.


7.  IANA Considerations

   There are no IANA considerations.


8.  Acknowledgments

   The authors acknowledge the contributions of Dr I Biswas and Dr R
   Secchi in supporting the evaluation of CWV and for their help in
   developing the mechanisms proposed in this draft.  We also
   acknowledge comments received from the Internet Congestion Control
   Research Group, in particular Yuchung Cheng, Mirja Kuehlewind, and
   Joe Touch.


9.  Author Notes







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9.1.  Other related work

   There are several issues to be discussed more widely:

      o Should the method explicitly state a procedure for limiting
      burstiness or pacing?



         This is often regarded as good practice, but is not presently a
         formal part of TCP. draft-hughes-restart-00.txt provides some
         discussion of this topic.

      o There are potential interaction with the proposal to raise the
      TCP initial Window to ten segments, do these cases need to be
      elaborated?



         This relates to draft-ietf-tcpm-initcwnd.

         The two methods have different functions and different response
         to loss/congestion.

         IW=10 proposes an experimental update to TCP that would allow
         faster opening of the cwnd, and also a large (same size)
         restart window.  This approach is based on the assumption that
         many forward paths can sustain bursts of up to ten segments
         without (appreciable) loss.  Such a significant increase in
         cwnd must be matched with an equally large reduction of cwnd if
         loss/congestion is detected, and such a congestion indication
         is likely to require future use of IW=10 to be disabled for
         this path for some time.  This guards against the unwanted
         behaviour of a series of short flows continuously flooding a
         network path without network congestion feedback.

         In contrast, new-CWV proposes a standards-track update with a
         rationale that relies on recent previous path history to select
         an appropriate cwnd after restart.

         The behaviour differs in three ways:

         1) For applications that send little initially, new-cwv may
         constrain more than IW=10, but would not require the connection
         to reset any path information when a restart incurred loss.  In
         contrast, new-cwv would allow the TCP connection to preserve
         the cached cwnd, any loss, would impact cwnd, but not impact
         other flows.



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         2) For applications that utilise more capacity than provided by
         a cwnd=10, this method would permit a larger restart window
         compared to a restart using IW=10.  This is justified by the
         recent path history.

         3) new-CWV is attended to also be used for rate-limited
         applications, where the application sends, but does not seek to
         fully utilise the cwnd.  In this case, new-cwv constrains the
         cwnd to that justified by the recent path history.  The
         performance trade-offs are hence different, and it would be
         possible to enable new-cwv when also using IW=10, and yield the
         benefits of this.

      o There is potential overlap with the Laminar proposal
      (draft-mathis-tcpm-tcp-laminar)



         The current draft was intended as a standards-track update to
         TCP, rather than a new transport variant.  At least, it would
         be good to understand how the two interact and whether there is
         a possibility of a single method.

9.2.  Revision notes

   Draft 03 was submitted to ICCRG to receive comments and feedback.

   Draft 04 contained the first set of clarifications after feedback:

   o  Changed name to application limited and used the term rate-limited
      in all places.

   o  Added justification and many minor changes suggested on the list.

   o  Added text to tie-in with more accurate ECN marking.

   o  Added ref to Hug01

   Draft 05 contained various updates:

   o  New text to redefine how to measure the acknowledged pipe,
      differentiating this from the FlightSize, and hence avoiding
      previous issues with infrequent large bursts of data not being
      validated.  A key point new feature is that pipeACK only triggers
      leaving the NVP after the size of the pipe has been acknowledged.
      This removed the need for hysteresis.





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   o  Reduction values were changed to 1/2, following analysis of
      suggestions from ICCRG.  This also sets the "target" cwnd as twice
      the used rate for non-validated case.

   o  Introduced a symbolic name (NVP) to denote the 5 minute period.


10.  References

10.1.  Normative References

   [RFC0793]  Postel, J., "Transmission Control Protocol", STD 7,
              RFC 793, September 1981.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC2861]  Handley, M., Padhye, J., and S. Floyd, "TCP Congestion
              Window Validation", RFC 2861, June 2000.

   [RFC3168]  Ramakrishnan, K., Floyd, S., and D. Black, "The Addition
              of Explicit Congestion Notification (ECN) to IP",
              RFC 3168, September 2001.

   [RFC3517]  Blanton, E., Allman, M., Fall, K., and L. Wang, "A
              Conservative Selective Acknowledgment (SACK)-based Loss
              Recovery Algorithm for TCP", RFC 3517, April 2003.

   [RFC5681]  Allman, M., Paxson, V., and E. Blanton, "TCP Congestion
              Control", RFC 5681, September 2009.

   [RFC6298]  Paxson, V., Allman, M., Chu, J., and M. Sargent,
              "Computing TCP's Retransmission Timer", RFC 6298,
              June 2011.

10.2.  Informative References

   [Bis08]    Biswas and Fairhurst, "A Practical Evaluation of
              Congestion Window Validation Behaviour, 9th Annual
              Postgraduate Symposium in the Convergence of
              Telecommunications, Networking and Broadcasting (PGNet),
              Liverpool, UK", June 2008.

   [Bis10]    Biswas, Sathiaseelan, Secchi, and Fairhurst, "Analysing
              TCP for Bursty Traffic, Int'l J. of Communications,
              Network and System Sciences, 7(3)", June 2010.

   [Hug01]    Hughes, Touch, and Heidemann, "Issues in TCP Slow-Start



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              Restart After Idle (Work-in-Progress)", December 2001.

   [Liu07]    Liu, Allman, Jiny, and Wang, "Congestion Control without a
              Startup Phase, 5th International Workshop on Protocols for
              Fast Long-Distance Networks (PFLDnet), Los Angeles,
              California, USA", February 2007.


Authors' Addresses

   Godred Fairhurst
   University of Aberdeen
   School of Engineering
   Fraser Noble Building
   Aberdeen, Scotland  AB24 3UE
   UK

   Email: gorry@erg.abdn.ac.uk
   URI:   http://www.erg.abdn.ac.uk


   Arjuna Sathiaseelan
   University of Aberdeen
   School of Engineering
   Fraser Noble Building
   Aberdeen, Scotland  AB24 3UE
   UK

   Email: arjuna@erg.abdn.ac.uk
   URI:   http://www.erg.abdn.ac.uk





















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