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RFC 5827

Early Retransmit for TCP and Stream Control Transmission Protocol (SCTP)

Pages: 15

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Internet Engineering Task Force (IETF)                         M. Allman
Request for Comments: 5827                                          ICSI
Category: Experimental                                    K. Avrachenkov
ISSN: 2070-1721                                                    INRIA
                                                               U. Ayesta
                                           BCAM-IKERBASQUE and LAAS-CNRS
                                                              J. Blanton
                                                         Ohio University
                                                               P. Hurtig
                                                     Karlstad University
                                                              April 2010

                        Early Retransmit for TCP
            and Stream Control Transmission Protocol (SCTP)


This document proposes a new mechanism for TCP and Stream Control Transmission Protocol (SCTP) that can be used to recover lost segments when a connection's congestion window is small. The "Early Retransmit" mechanism allows the transport to reduce, in certain special circumstances, the number of duplicate acknowledgments required to trigger a fast retransmission. This allows the transport to use fast retransmit to recover segment losses that would otherwise require a lengthy retransmission timeout. Status of This Memo This document is not an Internet Standards Track specification; it is published for examination, experimental implementation, and evaluation. This document defines an Experimental Protocol for the Internet community. This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Not all documents approved by the IESG are a candidate for any level of Internet Standard; see Section 2 of RFC 5741. Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at
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Copyright Notice

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1. Introduction

Many researchers have studied the problems with TCP's loss recovery [RFC793, RFC5681] when the congestion window is small, and they have outlined possible mechanisms to mitigate these problems [Mor97, BPS+98, Bal98, LK98, RFC3150, AA02]. SCTP's [RFC4960] loss recovery and congestion control mechanisms are based on TCP, and therefore the same problems impact the performance of SCTP connections. When the transport detects a missing segment, the connection enters a loss recovery phase. There are several variants of the loss recovery phase depending on the TCP implementation. TCP can use slow-start-based recovery or fast recovery [RFC5681], NewReno [RFC3782], and loss recovery, based on selective acknowledgments (SACKs) [RFC2018, FF96, RFC3517]. SCTP's loss recovery is not as varied due to the built-in selective acknowledgments. All of the above variants have two methods for invoking loss recovery. First, if an acknowledgment (ACK) for a given segment is not received in a certain amount of time, a retransmission timer fires, and the segment is resent [RFC2988, RFC4960]. Second, the "fast retransmit" algorithm resends a segment when three duplicate
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   ACKs arrive at the sender [Jac88, RFC5681].  Duplicate ACKs are
   triggered by out-of-order arrivals at the receiver.  However, because
   duplicate ACKs from the receiver are triggered by both segment loss
   and segment reordering in the network path, the sender waits for
   three duplicate ACKs in an attempt to disambiguate segment loss from
   segment reordering.  When the congestion window is small, it may not
   be possible to generate the required number of duplicate ACKs to
   trigger fast retransmit when a loss does happen.

   Small congestion windows can occur in a number of situations, such

   (1) The connection is constrained by end-to-end congestion control
       when the connection's share of the path is small, the path has a
       small bandwidth-delay product, or the transport is ascertaining
       the available bandwidth in the first few round-trip times of slow

   (2) The connection is "application limited" and has only a limited
       amount of data to send.  This can happen any time the application
       does not produce enough data to fill the congestion window.  A
       particular case when all connections become application limited
       is as the connection ends.

   (3) The connection is limited by the receiver's advertised window.

   The transport's retransmission timeout (RTO) is based on measured
   round-trip times (RTT) between the sender and receiver, as specified
   in [RFC2988] (for TCP) and [RFC4960] (for SCTP).  To prevent spurious
   retransmissions of segments that are only delayed and not lost, the
   minimum RTO is conservatively chosen to be 1 second.  Therefore, it
   behooves TCP senders to detect and recover from as many losses as
   possible without incurring a lengthy timeout during which the
   connection remains idle.  However, if not enough duplicate ACKs
   arrive from the receiver, the fast retransmit algorithm is never
   triggered -- this situation occurs when the congestion window is
   small, if a large number of segments in a window are lost, or at the
   end of a transfer as data drains from the network.  For instance,
   consider a congestion window of three segments' worth of data.  If
   one segment is dropped by the network, then at most two duplicate
   ACKs will arrive at the sender.  Since three duplicate ACKs are
   required to trigger fast retransmit, a timeout will be required to
   resend the dropped segment.  Note that delayed ACKs [RFC5681] may
   further reduce the number of duplicate ACKs a receiver sends.
   However, we assume that receivers send immediate ACKs when there is a
   gap in the received sequence space per [RFC5681].
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   [BPS+98] shows that roughly 56% of retransmissions sent by a busy Web
   server are sent after the RTO timer expires, while only 44% are
   handled by fast retransmit.  In addition, only 4% of the RTO timer-
   based retransmissions could have been avoided with SACK, which has to
   continue to disambiguate reordering from genuine loss.  Furthermore,
   [All00] shows that for one particular Web server, the median number
   of bytes carried by a connection is less than four segments,
   indicating that more than half of the connections will be forced to
   rely on the RTO timer to recover from any losses that occur.  Thus,
   loss recovery that does not rely on the conservative RTO is likely to
   be beneficial for short TCP transfers.

   The limited transmit mechanism introduced in [RFC3042] and currently
   codified in [RFC5681] allows a TCP sender to transmit previously
   unsent data upon receipt of each of the two duplicate ACKs that
   precede a fast retransmit.  SCTP [RFC4960] uses SACK information to
   calculate the number of outstanding segments in the network.  Hence,
   when the first two duplicate ACKs arrive at the sender, they will
   indicate that data has left the network, and they will allow the
   sender to transmit new data (if available), similar to TCP's limited
   transmit algorithm.  In the remainder of this document, we use
   "limited transmit" to include both TCP and SCTP mechanisms for
   sending in response to the first two duplicate ACKs.  By sending
   these two new segments, the sender is attempting to induce additional
   duplicate ACKs (if appropriate), so that fast retransmit will be
   triggered before the retransmission timeout expires.  The sender-side
   "Early Retransmit" mechanism outlined in this document covers the
   case when previously unsent data is not available for transmission
   (case (2) above) or cannot be transmitted due to an advertised window
   limitation (case (3) above).

   Note: This document is being published as an experimental RFC, as
   part of the process for the TCPM working group and the IETF to assess
   whether the proposed change is useful and safe in the heterogeneous
   environments, including which variants of the mechanism are the most
   effective.  In the future, this specification may be updated and put
   on the standards track if its safeness and efficacy can be

2. 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 RFC 2119 [RFC2119]. The reader is expected to be familiar with the definitions given in [RFC5681].
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3. Early Retransmit Algorithm

The Early Retransmit algorithm calls for lowering the threshold for triggering fast retransmit when the amount of outstanding data is small and when no previously unsent data can be transmitted (such that limited transmit could be used). Duplicate ACKs are triggered by each arriving out-of-order segment. Therefore, fast retransmit will not be invoked when there are less than four outstanding segments (assuming only one segment loss in the window). However, TCP and SCTP are not required to track the number of outstanding segments, but rather the number of outstanding bytes or messages. (Note that SCTP's message boundaries do not necessarily correspond to segment boundaries.) Therefore, applying the intuitive notion of a transport with less than four segments outstanding is more complicated than it first appears. In Section 3.1, we describe a "byte-based" variant of Early Retransmit that attempts to roughly map the number of outstanding bytes to a number of outstanding segments that is then used when deciding whether to trigger Early Retransmit. In Section 3.2, we describe a "segment-based" variant that represents a more precise algorithm for triggering Early Retransmit. This precision comes at the cost of requiring additional state to be kept by the TCP sender. In both cases, we describe SACK-based and non- SACK-based versions of the scheme (of course, the non-SACK version will not apply to SCTP). This document explicitly does not prefer one variant over the other, but leaves the choice to the implementer.

3.1. Byte-Based Early Retransmit

A TCP or SCTP sender MAY use byte-based Early Retransmit. Upon the arrival of an ACK, a sender employing byte-based Early Retransmit MUST use the following two conditions to determine when an Early Retransmit is sent: (2.a) The amount of outstanding data (ownd) -- data sent but not yet acknowledged -- is less than 4*SMSS bytes (as defined in [RFC5681]). Note that in the byte-based variant of Early Retransmit, "ownd" is equivalent to "FlightSize" (defined in [RFC5681]). We use different notation, because "ownd" is not consistent with FlightSize throughout this document. Also note that in SCTP, messages will have to be converted to bytes to make this variant of Early Retransmit work.
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   (2.b) There is either no unsent data ready for transmission at the
         sender, or the advertised receive window does not permit new
         segments to be transmitted.

   When the above two conditions hold and a TCP connection does not
   support SACK, the duplicate ACK threshold used to trigger a
   retransmission MUST be reduced to:

                ER_thresh = ceiling (ownd/SMSS) - 1                 (1)

   duplicate ACKs, where ownd is expressed in terms of bytes.  We call
   this reduced ACK threshold enabling "Early Retransmission".

   When conditions (2.a) and (2.b) hold and a TCP connection does
   support SACK or SCTP is in use, Early Retransmit MUST be used only
   when "ownd - SMSS" bytes have been SACKed.

   If either (or both) condition (2.a) and/or (2.b) does not hold, the
   transport MUST NOT use Early Retransmit, but rather prefer the
   standard mechanisms, including fast retransmit and limited transmit.

   As noted above, the drawback of this byte-based variant is precision
   [HB08].  We illustrate this with two examples:

      + Consider a non-SACK TCP sender that uses an SMSS of 1460 bytes
        and transmits three segments, each with 400 bytes of payload.
        This is a case where Early Retransmit could aid loss recovery if
        one segment is lost.  However, in this case, ER_thresh will
        become zero, per Equation (1), because the number of outstanding
        bytes is a poor estimate of the number of outstanding segments.
        A similar problem occurs for senders that employ SACK, as the
        expression "ownd - SMSS" will become negative.

      + Next, consider a non-SACK TCP sender that uses an SMSS of
        1460 bytes and transmits 10 segments, each with 400 bytes of
        payload.  In this case, ER_thresh will be 2 per Equation (1).
        Thus, even though there are enough segments outstanding to
        trigger fast retransmit with the standard duplicate ACK
        threshold, Early Retransmit will be triggered.  This could cause
        or exacerbate performance problems caused by segment reordering
        in the network.
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3.2. Segment-Based Early Retransmit

A TCP or SCTP sender MAY use segment-based Early Retransmit. Upon the arrival of an ACK, a sender employing segment-based Early Retransmit MUST use the following two conditions to determine when an Early Retransmit is sent: (3.a) The number of outstanding segments (oseg) -- segments sent but not yet acknowledged -- is less than four. (3.b) There is either no unsent data ready for transmission at the sender, or the advertised receive window does not permit new segments to be transmitted. When the above two conditions hold and a TCP connection does not support SACK, the duplicate ACK threshold used to trigger a retransmission MUST be reduced to: ER_thresh = oseg - 1 (2) duplicate ACKs, where oseg represents the number of outstanding segments. (We discuss tracking the number of outstanding segments below.) We call this reduced ACK threshold enabling "Early Retransmission". When conditions (3.a) and (3.b) hold and a TCP connection does support SACK or SCTP is in use, Early Retransmit MUST be used only when "oseg - 1" segments have been SACKed. A segment is considered to be SACKed when all of its data bytes (TCP) or data chunks (SCTP) have been indicated as arrived by the receiver. If either (or both) condition (3.a) and/or (3.b) does not hold, the transport MUST NOT use Early Retransmit, but rather prefer the standard mechanisms, including fast retransmit and limited transmit. This version of Early Retransmit solves the precision issues discussed in the previous section. As noted previously, the cost is that the implementation will have to track segment boundaries to form an understanding as to how many actual segments have been transmitted, but not acknowledged. This can be done by the sender tracking the boundaries of the three segments on the right side of the current window (which involves tracking four sequence numbers in TCP). This could be done by keeping a circular list of the segment boundaries, for instance. Cumulative ACKs that do not fall within this region indicate that at least four segments are outstanding, and therefore Early Retransmit MUST NOT be used. When the outstanding window becomes small enough that Early Retransmit can be invoked, a
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   full understanding of the number of outstanding segments will be
   available from the four sequence numbers retained.  (Note: the
   implicit sequence number consumed by the TCP FIN bit can also be
   included in the tracking of segment boundaries.)

4. Discussion

In this section, we discuss a number of issues surrounding the Early Retransmit algorithm.

4.1. SACK vs. Non-SACK

The SACK variant of the Early Retransmit algorithm is preferred to the non-SACK variant in TCP due to its robustness in the face of ACK loss (since SACKs are sent redundantly), and due to interactions with the delayed ACK timer (SCTP does not have a non-SACK mode and therefore naturally supports SACK-based Early Retransmit). Consider a flight of three segments, S1...S3, with S2 being dropped by the network. When S1 arrives, it is in order, and so the receiver may or may not delay the ACK, leading to two scenarios: (A) The ACK for S1 is delayed: In this case, the arrival of S3 will trigger an ACK to be transmitted, covering S1 (which was previously unacknowledged). In this case, Early Retransmit without SACK will not prevent an RTO because no duplicate ACKs will arrive. However, with SACK, the ACK for S1 will also include SACK information indicating that S3 has arrived at the receiver. The sender can then invoke Early Retransmit on this ACK because only one segment remains outstanding. (B) The ACK for S1 is not delayed: In this case, the arrival of S1 triggers an ACK of previously unacknowledged data. The arrival of S3 triggers a duplicate ACK (because it is out of order). Both ACKs will cover the same segment (S1). Therefore, regardless of whether SACK is used, Early Retransmit can be performed by the sender (assuming no ACK loss).

4.2. Segment Reordering

Early Retransmit is less robust in the face of reordered segments than when using the standard fast retransmit threshold. Research shows that a general reduction in the number of duplicate ACKs required to trigger fast retransmit to two (rather than three) leads to a reduction in the ratio of good to bad retransmits by a factor of three [Pax97]. However, this analysis did not include the additional conditioning on the event that the ownd was smaller than four segments and that no new data was available for transmission.
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   A number of studies have shown that network reordering is not a rare
   event across some network paths.  Various measurement studies have
   shown that reordering along most paths is negligible, but along
   certain paths can be quite prevalent [Pax97, BPS99, BS02, Pir05].
   Evaluating Early Retransmit in the face of real segment reordering is
   part of the experiment we hope to instigate with this document.

4.3. Worst Case

Next, we note two "worst case" scenarios for Early Retransmit: (1) Persistent reordering of segments coupled with an application that does not constantly send data can result in large numbers of needless retransmissions when using Early Retransmit. For instance, consider an application that sends data two segments at a time, followed by an idle period when no data is queued for delivery. If the network consistently reorders the two segments, the sender will needlessly retransmit one out of every two unique segments transmitted when using the above algorithm (meaning that one-third of all segments sent are needless retransmissions). However, this would only be a problem for long-lived connections from applications that transmit in spurts. (2) Similar to the above, consider the case of that consist of two segment each and always experience reordering. Just as in (1) above, one out of every two unique data segments will be retransmitted needlessly; therefore, one-third of the traffic will be spurious. Currently, this document offers no suggestion on how to mitigate the above problems. However, the worst cases are likely pathological. Part of the experiments that this document hopes to trigger would involve better understanding of whether such theoretical worst-case scenarios are prevalent in the network, and in general, to explore the trade-off between spurious fast retransmits and the delay imposed by the RTO. Appendix A does offer a survey of possible mitigations that call for curtailing the use of Early Retransmit when it is making poor retransmission decisions.

5. Related Work

There are a number of similar proposals in the literature that attempt to mitigate the same problem that Early Retransmit addresses. Deployment of Explicit Congestion Notification (ECN) [Flo94, RFC3168] may benefit connections with small congestion window sizes [RFC2884]. ECN provides a method for indicating congestion to the end-host without dropping segments. While some segment drops may still occur,
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   ECN may allow a transport to perform better with small congestion
   window sizes because the sender will be required to detect less
   segment loss [RFC2884].

   [Bal98] outlines another solution to the problem of having no new
   segments to transmit into the network when the first two duplicate
   ACKs arrive.  In response to these duplicate ACKs, a TCP sender
   transmits zero-byte segments to induce additional duplicate ACKs.
   This method preserves the robustness of the standard fast retransmit
   algorithm at the cost of injecting segments into the network that do
   not deliver any data, and therefore are potentially wasting network
   resources (at a time when there is a reasonable chance that the
   resources are scarce).

   [RFC4653] also defines an orthogonal method for altering the
   duplicate ACK threshold.  The mechanisms proposed in this document
   decrease the duplicate ACK threshold when a small amount of data is
   outstanding.  Meanwhile, the mechanisms in [RFC4653] increase the
   duplicate ACK threshold (over the standard of 3) when the congestion
   window is large in an effort to increase robustness to segment

6. Security Considerations

The security considerations found in [RFC5681] apply to this document. No additional security problems have been identified with Early Retransmit at this time.

7. Acknowledgments

We thank Sally Floyd for her feedback in discussions about Early Retransmit. The notion of Early Retransmit was originally sketched in an Internet-Draft co-authored by Sally Floyd and Hari Balakrishnan. Armando Caro, Joe Touch, Alexander Zimmermann, and many members of the TSVWG and TCPM working groups provided good discussions that helped shape this document. Our thanks to all!

8. References

8.1. Normative References

[RFC793] Postel, J., "Transmission Control Protocol", STD 7, RFC 793, September 1981. [RFC2018] Mathis, M., Mahdavi, J., Floyd, S., and A. Romanow, "TCP Selective Acknowledgment Options", RFC 2018, October 1996.
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   [RFC2119]   Bradner, S., "Key words for use in RFCs to Indicate
               Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC2883]   Floyd, S., Mahdavi, J., Mathis, M., and M. Podolsky, "An
               Extension to the Selective Acknowledgement (SACK) Option
               for TCP", RFC 2883, July 2000.

   [RFC2988]   Paxson, V. and M. Allman, "Computing TCP's Retransmission
               Timer", RFC 2988, November 2000.

   [RFC3042]   Allman, M., Balakrishnan, H., and S. Floyd, "Enhancing
               TCP's Loss Recovery Using Limited Transmit", RFC 3042,
               January 2001.

   [RFC4960]   Stewart, R., Ed., "Stream Control Transmission Protocol",
               RFC 4960, September 2007.

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

8.2. Informative References

[AA02] Urtzi Ayesta, Konstantin Avrachenkov, "The Effect of the Initial Window Size and Limited Transmit Algorithm on the Transient Behavior of TCP Transfers", In Proc. of the 15th ITC Internet Specialist Seminar, Wurzburg, July 2002. [All00] Mark Allman. A Web Server's View of the Transport Layer. ACM Computer Communication Review, October 2000. [Bal98] Hari Balakrishnan. Challenges to Reliable Data Transport over Heterogeneous Wireless Networks. Ph.D. Thesis, University of California at Berkeley, August 1998. [BPS+98] Hari Balakrishnan, Venkata Padmanabhan, Srinivasan Seshan, Mark Stemm, and Randy Katz. TCP Behavior of a Busy Web Server: Analysis and Improvements. Proc. IEEE INFOCOM Conf., San Francisco, CA, March 1998. [BPS99] Jon Bennett, Craig Partridge, Nicholas Shectman. Packet Reordering is Not Pathological Network Behavior. IEEE/ACM Transactions on Networking, December 1999. [BS02] John Bellardo, Stefan Savage. Measuring Packet Reordering, ACM/USENIX Internet Measurement Workshop, November 2002.
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   [FF96]      Kevin Fall, Sally Floyd.  Simulation-based Comparisons of
               Tahoe, Reno, and SACK TCP.  ACM Computer Communication
               Review, July 1996.

   [Flo94]     Sally Floyd.  TCP and Explicit Congestion Notification.
               ACM Computer Communication Review, October 1994.

   [HB08]      Per Hurtig, Anna Brunstrom.  Enhancing SCTP Loss
               Recovery: An Experimental Evaluation of Early Retransmit.
               Elsevier Computer Communications, Vol. 31(16),
               October 2008, pp. 3778-3788.

   [Jac88]     Van Jacobson.  Congestion Avoidance and Control.  ACM
               SIGCOMM 1988.

   [LK98]      Dong Lin, H.T. Kung.  TCP Fast Recovery Strategies:
               Analysis and Improvements.  Proc. IEEE INFOCOM Conf.,
               San Francisco, CA, March 1998.

   [Mor97]     Robert Morris.  TCP Behavior with Many Flows.  Proc.
               Fifth IEEE International Conference on Network Protocols,
               October 1997.

   [Pax97]     Vern Paxson.  End-to-End Internet Packet Dynamics.  ACM
               SIGCOMM, September 1997.

   [Pir05]     N. M. Piratla, "A Theoretical Foundation, Metrics and
               Modeling of Packet Reordering and Methodology of Delay
               Modeling using Inter-packet Gaps," Ph.D. Dissertation,
               Department of Electrical and Computer Engineering,
               Colorado State University, Fort Collins, CO, Fall 2005.

   [RFC2884]   Hadi Salim, J. and U. Ahmed, "Performance Evaluation of
               Explicit Congestion Notification (ECN) in IP Networks",
               RFC 2884, July 2000.

   [RFC3150]   Dawkins, S., Montenegro, G., Kojo, M., and V. Magret,
               "End-to-end Performance Implications of Slow Links",
               BCP 48, RFC 3150, July 2001.

   [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.
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   [RFC3522]   Ludwig, R. and M. Meyer, "The Eifel Detection Algorithm
               for TCP", RFC 3522, April 2003.

   [RFC3782]   Floyd, S., Henderson, T., and A. Gurtov, "The NewReno
               Modification to TCP's Fast Recovery Algorithm", RFC 3782,
               April 2004.

   [RFC4653]   Bhandarkar, S., Reddy, A., Allman, M., and E. Blanton,
               "Improving the Robustness of TCP to Non-Congestion
               Events", RFC 4653, August 2006.
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Appendix A. Research Issues in Adjusting the Duplicate ACK Threshold

Decreasing the number of duplicate ACKs required to trigger fast retransmit, as suggested in Section 3, has the drawback of making fast retransmit less robust in the face of minor network reordering. Two egregious examples of problems caused by reordering are given in Section 4. This appendix outlines several schemes that have been suggested to mitigate the problems caused by Early Retransmit in the face of segment reordering. These methods need further research before they are suggested for general use (and current consensus is that the cases that make Early Retransmit unnecessarily retransmit a large amount of data are pathological, and therefore, these mitigations are not generally required). MITIGATION A.1: Allow a connection to use Early Retransmit as long as the algorithm is not injecting "too much" spurious data into the network. For instance, using the information provided by TCP's D-SACK option [RFC2883] or SCTP's Duplicate Transmission Sequence Number (Duplicate-TSN) notification, a sender can determine when segments sent via Early Retransmit are needless. Likewise, using Eifel [RFC3522], the sender can detect spurious Early Retransmits. Once spurious Early Retransmits are detected, the sender can either eliminate the use of Early Retransmit, or limit the use of the algorithm to ensure that an acceptably small fraction of the connection's transmissions are not spurious. For example, a connection could stop using Early Retransmit after the first spurious retransmit is detected. MITIGATION A.2: If a sender cannot reliably determine whether an Early-Retransmitted segment is spurious or not, the sender could simply limit Early Retransmits, either to some fixed number per connection (e.g., Early Retransmit is allowed only once per connection), or to some small percentage of the total traffic being transmitted. MITIGATION A.3: Allow a connection to trigger Early Retransmit using the criteria given in Section 3, in addition to a "small" timeout [Pax97]. For instance, a sender may have to wait for two duplicate ACKs and then T msec before Early Retransmit is invoked. The added time gives reordered acknowledgments time to arrive at the sender and avoid a needless retransmit. Designing a method for choosing an appropriate timeout is part of the research that would need to be involved in this scheme.
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Authors' Addresses

Mark Allman International Computer Science Institute 1947 Center Street, Suite 600 Berkeley, CA 94704-1198 USA Phone: 440-235-1792 EMail: Konstantin Avrachenkov INRIA 2004 route des Lucioles, B.P.93 06902, Sophia Antipolis France Phone: 00 33 492 38 7751 EMail: Urtzi Ayesta BCAM-IKERBASQUE LAAS-CNRS Bizkaia Technology Park, Building 500 7 Avenue Colonel Roche 48160 Derio 31077, Toulouse Spain France EMail: Josh Blanton Ohio University 301 Stocker Center Athens, OH 45701 USA EMail: Per Hurtig Karlstad University Department of Computer Science Universitetsgatan 2 651 88 Karlstad Sweden EMail: