TCP Maintenance Working Group M. Mathis
Internet-Draft N. Dukkipati
Intended status: Experimental Y. Cheng
Expires: January 12, 2012 Google, Inc
July 11, 2011
Proportional Rate Reduction for TCP
draft-mathis-tcpm-proportional-rate-reduction-01.txt
Abstract
This document describes an experimental algorithm, Proportional Rate
Reduction (PPR) and related algorithms to improve the accuracy of the
amount of data sent by TCP during loss recovery. Standard Congestion
Control requires that TCP and other protocols reduce their congestion
window in response to losses. This window reduction naturally occurs
in the same round trip as the data retransmissions to repair the
losses, and is implemented by choosing not to transmit any data in
response to some ACKs arriving from the receiver. Two widely
deployed algorithms are used to implement this window reduction: Fast
Recovery and Rate Halving. Both algorithms are needlessly fragile
under a number of conditions, particularly when there is a burst of
losses that such that the number of ACKs returning to the sender is
so small that the effective window falls below the target congestion
window chosen by the congestion control algorithm. Proportional Rate
Reduction avoids these excess window reductions such that at the end
of recovery the actual window size will be as close as possible to
the window size determined by the congestion control algorithm. It
is patterned after rate halving, but using the fraction that is
appropriate for target window chosen by the congestion control
algorithm. In addition we propose two slightly different algorithms
to bound the total window reduction due to all mechanisms, including
application stalls, the losses themselves and inhibit further window
reductions when possible.
Status of this Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
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Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
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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 January 12, 2012.
Copyright Notice
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1. Examples . . . . . . . . . . . . . . . . . . . . . . . . . 7
4. Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5. Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 12
6. Conclusion and Recommendations . . . . . . . . . . . . . . . . 13
7. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 14
8. Security Considerations . . . . . . . . . . . . . . . . . . . 14
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 14
10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Appendix A. Packet Conservation Bound . . . . . . . . . . . . . . 15
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 16
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1. Introduction
This document describes an experimental algorithm, Proportional Rate
Reduction (PPR) and two slightly different reduction bound algorithms
to improve the accuracy of the amount of data sent by TCP during loss
recovery.
Standard Congestion Control [RFC 5681] requires that TCP (and other
protocols) reduce their congestion window in response to losses.
Fast Recovery, described in the same document, is the reference
algorithm for making this adjustment. It's stated goal is to recover
TCP's self clock by relying on returning ACKs during recovery to
clock more data into the network. Fast Recovery adjusts the window
by waiting for one half RTT of ACKs to pass before sending any data.
It is fragile because it can not compensate for the implicit window
reduction caused by the losses themselves, and is exposed to
timeouts. For example if half of the data or ACKs are lost, Fast
Recovery's expected behavior would be to reduce the window by not
sending in response to the first half window of ACKs, but then it
would not receive any additional ACKs and would timeout because it
failed to send anything at all.
The rate-halving algorithm improves this situation by sending data on
alternate ACKs during recovery, such that after one RTT the window
has been halved. Rate-having is implemented in Linux after only
being informally published [RHweb], including from an uncompleted
Internet-Draft[RHID]. Rate-halving also does not adequately
compensate for the implicit window reduction caused by the losses and
also assumes a 50% window reduction, which was completely standard at
the time it was written (several modern congestion control
algorithms, such as Cubic[CUBIC], can sometimes reduce the window by
much less than 50%.). As a consequence rate-halving often allows the
window to fall further than necessary, reducing performance and
increasing the risk of timeouts if there are any additional losses.
Proportional Rate Reduction (PPR) avoids these excess window
reductions such that at the end of recovery the actual window size
will be as close as possible to the window size determined by the
congestion control algorithm. It is patterned after Rate Halving,
but using the fraction that is appropriate for target window chosen
by the congestion control algorithm. During PRR one of two
additional reduction bound algorithms monitors the total window
reduction due to all mechanisms, including application stalls, the
losses themselves and attempts to inhibit further window reductions.
We describe two slightly different reduction bound algorithms:
conservative reduction bound (CRB), which meets a strict segment
conserving correctness critera; and a slow start reduction bound
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(SSRB), which is more aggressive than CRB by at most one segment per
ACK. CRB meets a conservative, philosophically pure and
aesthetically appealing notion of correct, however in real networks
it does not perform as well as the algorithms described in RFC 3517,
which prove to be non-conservative in a statistically significant
number of cases. SSRB offers a compromise by allowing TCP to send
one additional segment per ACK relative to CRB in some situations.
Although SSRB is less aggressive than RFC 3517 (transmitting fewer
segments or transmitting them later) it slightly outperforms it, due
to slightly lower probability of additional losses during recovery.
All three algorithms are based on common design principles, derived
from Van Jacobson's packet conservation principle: segments delivered
to the receiver are used as the clock to trigger sending additional
segments into the network. As much as possible Proportional Rate
Reduction and the reduction bound rely on this self clock process,
and are only slightly affected by the accuracy of other estimators,
such as pipe[RFC 3517] and cwnd. This is what gives the algorithms
their precision in the presence of events that cause uncertainty in
other estimators.
In Section 5, we summarize a companion paper[Recovery] with some
measurement experiments: PRR+SSRB outperforms both RFC 3517 and PRR+
CRB under authentic network traffic.
The algorithms are described as modifications to RFC 5681, TCP
Congestion Control, using concepts drawn from the pipe algorithm [RFC
3517]. They are most accurate and more easily implemented with
SACK[RFC 2018], but they do not require SACK.
2. Definitions
The following terms, parameters and state variables are used as they
are defined in earlier documents:
RFC 3517: covered (as in "covered sequence numbers")
RFC 5681: duplicate ACK, FlightSize, Sender Maximum Segment Size
(SMSS)
Voluntary Window Reductions: choosing not to send data in response to
some ACKs, for the purpose of reducing the sending window size or
data rate.
We define some additional variables:
SACKd: The total number of bytes that the scoreboard indicates has
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been delivered to the receiver. This can be computed by scanning the
scoreboard and counting the total number of bytes covered by all sack
blocks.
DeliveredData: The total number of bytes that the current ACK
indicates have been delivered to the receiver, relative to all past
ACKs. When not in recovery, DeliveredData is the change in snd.una.
With SACK, DeliveredData is not an estimator and can be computed
precisely as the change in snd.una plus the change in SACKd. Note
that if there are SACK blocks and snd.una advances, the change in
SACKd is typically negative. In recovery without SACK, DeliveredData
is estimated to be 1 SMSS on duplicate acknowledgements, and on a
subsequent partial or full ACK, DeliveredData is estimated to be the
change in snd.una, minus one SMSS for each preceding duplicate ACK.
Note that DeliveredData is robust: for TCP using SACK, DeliveredData
can be precisely computed anywhere in the network just by inspecting
the returning ACKs. The consequence of missing ACKs is that later
ACKs will show a larger DeliveredData. Furthermore, for any TCP
(with or without SACK) the sum of DeliveredData must agree with the
forward progress over the same time interval.
We introduce a local variable "sndcnt", which indicates exactly how
many bytes should be sent in response to each ACK. Note that the
decision of which data to send (e.g. retransmit missing data or send
more new data) is out of scope for this document.
3. Algorithms
Summary: If pipe (the estimated data is in flight) is larger than
ssthresh (the target cwnd at the end of recovery) then Proportional
Rate Reduction spreads the the voluntary window reductions across a
full RTT, such that as prr_delivered approaches RecoverFS (at the end
of recovery) prr_out approaches ssthresh, the target value for cwnd.
If there are excess losses such that pipe falls below ssthresh, the
selected reduction bound algorithm tries to hold pipe at ssthresh by
sending at most "limit" segments per ACK to catch up. For both
reduction bound algorithms the limit is first set to past voluntary
window reductions (prr_delivered - prr_out) permitting single ACKs to
trigger sending multiple segments. With PRR+CRB (conservative==True)
and if there are too many losses then prr_delivered - prr_out will be
exactly the same as DeliveredData for the current ACK, resulting in
sndcnt=DeliveredData. Therefore there will be no further Voluntary
Window Reductions. With PRR+SSRB (conservative==False) the same
situation results in sndcnt=DeliveredData+1, which ultimately causes
TCP to slowstart up to ssthresh.
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At the beginning of recovery initialize PRR state. This assumes a
modern congestion control algorithm, CongCtrlAlg(), that might set
ssthresh to something other than FlightSize/2:
ssthresh = CongCtrlAlg() // Target cwnd after recovery
prr_delivered = 0 // Total bytes delivered during recov
prr_out = 0 // Total bytes sent during recovery
RecoverFS = snd.nxt-snd.una // Flightsize at the start of recov
On every ACK during recovery compute:
DeliveredData = delta(snd.una) + delta(SACKd)
prr_delivered += DeliveredData
pipe = (RFC 3517 pipe algorithm)
if (pipe > ssthresh) {
// Proportional Rate Reduction
sndcnt = CEIL(prr_delivered * ssthresh / RecoverFS) - prr_out
} else {
// Two version of the reduction bound
if (conservative) { // PRR+CRB
limit = prr_delivered - prr_out
} else { // PRR+SSRB
limit = MAX(prr_delivered - prr_out, DeliveredData) + 1
}
sndcnt = MIN(ssthresh - pipe, limit)
}
sndcnt = MAX(sndcnt, 0) // positive
On any data transmission or retransmission:
prr_out += (data sent) // strictly less than or equal to sndcnt
The following examples will make these algorithms much clearer.
3.1. Examples
We illustrate these algorithms by showing their different behaviors
for two scenarios: TCP experiencing either a single loss or a burst
of 15 consecutive losses. In all cases we assume bulk data, standard
AIMD congestion control (the ssthresh is set to Flight Size/2) and
cwnd = FlightSIze = pipe = 20 segments, so ssthresh will be set to 10
at the beginning of recovery. We also assume standard Fast
Retransmit and Limited Transmit, so we send two new segments followed
by one retransmit on the first 3 duplicate ACKs after the losses.
Each of the diagrams below shows the per ACK response to the first
round trip for the various recovery algorithms when the zeroth
segment is lost. The top line indicates the transmitted segment
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number triggering the ACKs, with an X for the lost segment. "cwnd"
and "pipe" indicate the values of these algorithms after processing
each returning ACK. "Sent" indicates how much "N"ew or
"R"etransmitted data would be sent. Note that the algorithms for
deciding which data should be sent are out of scope of this document.
When there is a single loss, PRR with either of the reduction bound
algorithms has the same behavior. We show "RB", a flag indicating
which reduction bound subexpression ultimately determined the value
of sndcnt. When there is minimal losses "limit" (both algorithms)
will always be larger than ssthresh - pipe, so the sndcnt will be
ssthresh - pipe indicated by "s" in the "RB" row. PRR does not use
cwnd during recovery.
RFC 3517
ack# X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
cwnd: 20 20 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
pipe: 19 19 18 18 17 16 15 14 13 12 11 10 10 10 10 10 10 10 10
sent: N N R N N N N N N N N
Rate halving (Linux)
ack# X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
cwnd: 20 20 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11
pipe: 19 19 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11 10
sent: N N R N N N N N N N N
PRR
ack# X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
pipe: 19 19 18 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 10
sent: N N R N N N N N N N N
RB: s s
Note that all three algorithms send same total amount of data. RFC
3517 experiences a "half-window of silence", while the Rate Halving
and PRR spread the voluntary window reduction across an entire RTT.
Next we consider the same initial conditions when the first 15
packets (0-14) are lost. During the remainder of the lossy RTT, only
5 ACKs are returned to the sender. We examine each of these
algorithms in succession.
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RFC 3517
ack# X X X X X X X X X X X X X X X 15 16 17 18 19
cwnd: 20 20 11 11 11
pipe: 19 19 4 10 10
sent: N N 7R R R
Rate Halving (Linux)
ack# X X X X X X X X X X X X X X X 15 16 17 18 19
cwnd: 20 20 5 5 5
pipe: 19 19 4 4 4
sent: N N R R R
PRR-CRB
ack# X X X X X X X X X X X X X X X 15 16 17 18 19
pipe: 19 19 4 4 4
sent: N N R R R
RB: f f f
PRR-SSRB
ack# X X X X X X X X X X X X X X X 15 16 17 18 19
pipe: 19 19 4 5 6
sent: N N 2R 2R 2R
RB: d d d
In this situation, RFC 3517 is very non-conservative, because once
fast retransmit is triggered (on the ACK for segment 17) TCP
immediately retransmits sufficient data to bring pipe up to cwnd.
Our measurement data (see Section 5) indicates that RFC 3517
significantly outperforms Rate Halving, PRR-CRB and some other
similarly conservative algorithms that we tested, suggesting that it
is significantly common for the actual losses to exceed the window
reduction determined by the congestion control algorithm.
The Linux implementation of Rate Halving includes an early version of
the conservative reduction bound[RHweb]. In this situation each of
the five ACKs trigger exactly 5 transmissions (2 new data, 3 old
data), and cwnd is set to 5. At a window size of 5, it takes three
round trips to retransmit 15 lost segments. Rate Halving does not
raise the window during recovery, so when recovery finally completes,
TCP will slowstart cwnd from 5 up to 10. In this example, TCP
operates at half of the window chosen by the congestion control for
more than three RTTs, increasing the elapsed time and exposing it to
timeouts if there are additional losses.
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PRR-CRB implements conservative reduction bound. Since the total
losses bring pipe below ssthresh, data is sent such that the total
data transmitted, prr_out, follows the total data delivered to the
receiver as reported by returning ACKs. Transmission are controlled
by the sending limit, which was set to prr_delivered - prr_out. This
is indicated by the RB:f tagging in the figure. In this case PRR-CRB
is exposed to exactly the same problems as Rate Halving, taking
excessively long to recover from the losses and being exposed to
additional timeouts.
PRR-SSRB increases the window by exactly 1 segment per ACK until pipe
rises to sshthresh during recovery. This is accomplished by setting
limit to one greater than the data reported to have been delivered to
the receiver on this ACK, effectively implementing a slowstart during
recovery, and indicated by RB:d tagging in the figure. Although
increasing the window during recovery seems to be ill advised, it is
important to remember that this actually less aggressive than the
current standard which permits sending the same quantity of extra
data as a single burst in response to the ACK that triggered Fast
Retransmit
Under less extreme conditions, when the total losses are smaller than
the difference between Flight Size and ssthresh, PRR-CRB and PRR-SSRB
have identical behaviours.
4. Properties
The following properties are common to both PRR-CRB and PRR-SSRB:
Normally Proportional Rate Reduction will spread Voluntary Window
reductions out evenly across a full RTT. This has the potential to
generally reduce the burstiness of Internet traffic, and could be
considered to be a type of soft pacing. Theoretically any pacing
increases the probability that different flows are interleaved,
reducing the opportunity for ACK compression and other phenomena that
increase traffic burstiness. However these effects have not been
quantified.
If there are minimal losses, Proportional Rate Reduction will
converge to exactly the target window chosen by the congestion
control algorithm. Note that as TCP approaches the end of recovery
prr_delivered will approach RecoverFS and sndcnt will be computed
such that prr_out approaches ssthresh.
Implicit window reductions due to multiple isolated losses during
recovery cause later Voluntary Reductions to be skipped. For small
numbers of losses the window size ends at exactly the window chosen
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by the congestion control algorithm.
For burst losses, earlier Voluntary Window Reductions can be undone
by sending extra segments in response to ACKs arriving later during
recovery. Note that as long as some Voluntary Window Reductions are
not undone, the final value for pipe will be the same as ssthresh,
the target cwnd value chosen by the congestion control algorithm.
Proportional Rate Reduction with either reduction round improves the
situation when there are application stalls (e.g. when the sending
application does not queue data for transmission quickly enough or
the receiver stops advancing rwnd). When there is a application
stall early during recovery prr_out will fall behind the sum of the
transmissions permitted by sndcnt. The missed opportunities to send
due to stalls are treated like banked Voluntary Window Reductions:
specifically they cause prr_delivered-prr_out to be significantly
positive. If the application catches up while TCP is still in
recovery, TCP will send a partial window burst to catch up to exactly
where it would have been, had the application never stalled.
Although this burst might be viewed as being hard on the network,
this is exactly what happens every time there is a partial RTT
application stall while not in recovery. We have made the partial
RTT stall behavior uniform in all states. Changing this behavior is
out of scope for this document.
Proportional Rate Reduction with Reduction Bound is significantly
less sensitive to errors of the pipe estimator. While in recovery,
pipe is intrinsically an estimator, using incomplete information to
guess if un-SACKed segments are actually lost or out-of-order in the
network. Under some conditions pipe can have significant errors, for
example when a burst of reordered data is presumed to be lost and is
retransmitted, but then the original data arrives before the
retransmission. If the transmissions are regulated directly by pipe
as they are in RFC 3517, then errors and discontinuities in the value
of the pipe estimator can cause significant errors in the amount of
data sent. With Proportional Rate Reduction with Reduction Bound,
pipe merely determines how sndcnt is computed from DataDelivered.
Since short term errors in pipe are smoothed out across multiple ACKs
and both Proportional Rate Reduction and the reduction converge to
the same final window, errors in the pipe estimator have less impact
on the final outcome (This needs to be tested better).
Under all conditions and sequences of events during recovery, PRR-CRB
strictly bounds the data transmitted to be equal to or less than the
amount of data delivered to the receiver. We claim that this packet
conservation bound is the most aggressive algorithm that does not
lead to additional forced losses in some environments. It has the
property that if there is a standing queue at a bottleneck that is
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carrying no other traffic, the queue will maintain exactly constant
length for the entire recovery duration (except for +1/-1 fluctuation
due to differences in packet arrival and exit times) . See
Appendix A for a detailed discussion of this property.
Although the packet Packet Conserving Bound in very appealing for a
number of reasons, our measurements summarized in Section 5
demonstrate that it is less aggressive and does not perform as well
as RFC3517, which permits large bursts of data when there are bursts
of losses. PRR-SSRB is a compromise that permits TCP to send one
extra segment per ACK as compared to the packet conserving bound.
From the< perspective of the packet conserving bound, PRR-SSRB does
indeed open the window during recovery, however it is significantly
less aggressive than RFC3517 in the presence of burst losses.
5. Measurements
In a (to be published) companion paper[Recovery] we describe some
measurements comparing the various strategies for reducing the window
during recovery. The results presented in that paper are summarized
here.
The various window reduction algorithms and extensive instrumentation
were all implemented in a modified Linux 2.6.34 kernel. For all
experiments we used a uniform subset of the non-standard algorithms
present in the base Linux implementation. Specifically we disabled
threshold retransmit [FACK], which triggers Fast Retransmit earlier
than the standard algorithm. We left enabled CUBIC [CUBIC], limited
transmit [LT], and lost retransmission detection algorithms. This
subset was a compromise chosen such that the behaviors of both Rate
Halving (the Linux default) and RFC 3517 mode were authentic to their
respective specifications while at the same time the performance and
features were comparable to the kernels in production use. The
different window reduction algorithms were all present in the same
kernel and could be selected with a sysctl, such that we had an
absolutely uniform baseline for comparing RFC 3517, Rate Halving, and
PRR with various reduction bounds.
Our experiments included an additional algorithm, PRR with an
unlimited bound (PRR-UB), which sends ssthresh-pipe bursts when pipe
falls below ssthresh. This behavior parallels RFC 3517.
An important detail of this configuration is that CUBIC only reduces
the window by %, as opposed to the 50% reduction used by traditional
congestion control algorithms. This, in conjunction with using only
standard algorithms to trigger Fast Retransmit, accentuates the
tendency for RFC 3517 and PRR-UB to send a burst at the point when
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Fast Retransmit gets triggered if pipe is already below ssthresh.
All experiments were performed on servers carrying production traffic
for multiple Google services.
In this configuration is is observed that for 32% of the recovery
events, pipe falls below ssthresh before Fast Retransmit is
triggered, thus the various PRR algorithms start in the reduction
bound phase, and both PRR-UB and RFC 3517 send bursts of segments
with the fast retransmit.
In the companion paper we observe that PRR-SSRB spends the least time
in recovery of all the algorithms tested, largely because it
experiences fewer timeouts once it is already in recovery.
RFC 3517 experiences 29% more detected lost retransmissions and 2.6%
more timeouts (presumably due to undetected lost retransmissions)
than PRR-SSRB. These results are representative of PRR-UB and other
algorithms that send bursts when pipe falls below ssthresh.
Rate Halving experiences 5% more timeouts and significantly smaller
final cwnd values at the end of recovery. The smaller cwnd sometimes
causes the recovery itself to take extra round trips. These results
are representative of PRR-CRB and other algorithms that implement
strict packet conservation during recovery.
6. Conclusion and Recommendations
[This text assumes standards track. Experimental status would be
somewhat more reserved.]
Although the packet conserving bound in very appealing for a number
of reasons, our measurements summarized in Section 5 demonstrate that
it is less aggressive and does not perform as well as RFC3517, which
permits large bursts of data when there are bursts of losses. PRR-
SSRB is a compromise that permits TCP to send one extra segment per
ACK as compared to the packet conserving bound. From the perspective
of the packet conserving bound, PRR-SSRB does indeed open the window
during recovery, however it is significantly less aggressive than
RFC3517 in the presence of burst losses.
All TCP implementations SHOULD implement both PRR-CRB and PRR-SSRB,
with a control to select which algorithm is used. It is RECOMMENDED
that PRR-SSRB is the default algorithm.
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7. Acknowledgements
This draft is based in part on previous incomplete work by Matt
Mathis, Jeff Semke and Jamshid Mahdavi[RHID] and influenced by
several discussion with John Heffner.
Monia Ghobadi and Sivasankar Radhakrishnan helped analyze the
experiments.
8. Security Considerations
Proportional Rate Reduction does not change the risk profile for TCP.
Implementers that change PRR from counting bytes to segments have to
be cautious about the effects of ACK splitting attacks[SPLIT], where
the receiver acknowledges partial segments for the purpose of
confusing the sender's congestion accounting.
9. IANA Considerations
This document makes no request of IANA.
Note to RFC Editor: this section may be removed on publication as an
RFC.
10. References
TODO: A proper reference section.
[RFC 3517] "A Conservative Selective Acknowledgment (SACK)-based Loss
Recovery Algorithm for TCP". E. Blanton, M. Allman, K. Fall, L.
Wang. April 2003.
[RFC 5681] "TCP Congestion Control". M. Allman, V. Paxson, E.
Blanton. September 2009.
[RHweb] "TCP Rate-Halving with Bounding Parameters". M. Mathis, J.
Madavi, http://www.psc.edu/networking/papers/FACKnotes/971219/, Dec
1997.
[RHID] "The Rate-Halving Algorithm for TCP Congestion Control". M.
Mathis, J. Semke, J. Mahdavi, K. Lahey.
http://www.psc.edu/networking/ftp/papers/draft-ratehalving.txt, Work
in progress, last updated June 1999.
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[CUBIC] "CUBIC: A new TCP-friendly high-speed TCP variant". I. Rhee,
L. Xu, PFLDnet, Feb 2005.
[FACK] M. Mathis, J. Mahdavi, "Forward Acknowledgment: Refining TCP
Congestion Control", Proceedings of SIGCOMM'96, August, 1996,
Stanford, CA.
[Recovery] N. Dukkipati, M. Mathis, Y Cheng, "Improving TCP loss
recovery", to be published 2011.
Appendix A. Packet Conservation Bound
Under all conditions and sequences of events during recovery, PRR-CRB
strictly bounds the data transmitted to be equal to or less than the
amount of data delivered to the receiver. We claim that this packet
conservation bound is the most aggressive algorithm that does not
lead to additional forced losses in some environments. It has the
property that if there is a standing queue at a bottleneck that is
carrying no other traffic, the queue will maintain exactly constant
length for the entire recovery duration (except for +1/-1 fluctuation
due to differences in packet arrival and exit times) . Any less
aggressive algorithm will result in a declining queue at the
bottleneck. Any more aggressive algorithm will result in an
increasing queue or additional losses at the bottleneck.
We demonstrate this property with a little thought experiment:
Imagine a network path that has insignificant delays in both
directions, except the processing time and queue at a single
bottleneck in the forward path. By insignificant delay, I mean when
a packet is "served" at the head of the bottleneck queue, the
following events happen in much less than one packet time at the
bottleneck: the packet arrives at the receiver; the receiver sends an
ACK; which arrives at the sender; the sender processes the ACK and
sends some data; the data is queued at the bottleneck.
If sndcnt is set to DataDelivered and nothing else is inhibiting
sending data, then clearly the data arriving at the bottleneck queue
will exactly replace the data that was served at the head of the
queue, so the queue will have a constant length. If queue is drop
tail and full then the queue will stay exactly full, even in the
presence of losses or reordering on the ACK path, and independent of
whether the data is in order or out-of-order (e.g. simple reordering
or loss recovery from an earlier RTT). Any more aggressive algorithm
sending additional data will cause a queue overflow and loss. Any
less aggressive algorithm will under fill the queue. Therefore
setting sndcnt to DataDeliverd is the most aggressive algorithm that
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Internet-Draft Proportional Rate Reduction July 2011
does not cause forced losses in this simple network. Relaxing the
assumptions (e.g. making delays more authentic and adding more flows,
delayed ACKs, etc) increases the noise (jitter) in the system but
does not change it's basic behavior.
Note that the congestion control algorithm implements a broader
notion of optimal that includes appropriately sharing of the network.
PRR-CRB will choose to send the lessor of the data permitted by this
packet conserving bound and as determined by the congestion control
algorithm as PRR brings TCP's actual window down to ssthresh.
Authors' Addresses
Matt Mathis
Google, Inc
1600 Amphitheater Parkway
Mountain View, California 93117
USA
Email: mattmathis@google.com
Nandita Dukkipati
Google, Inc
1600 Amphitheater Parkway
Mountain View, California 93117
USA
Email: nanditad@google.com
Yuchung Cheng
Google, Inc
1600 Amphitheater Parkway
Mountain View, California 93117
USA
Email: ycheng@google.com
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