SEARCH -- a New Slow Start Algorithm for TCP and QUIC

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Table of Contents

1. Introduction

The TCP slow start mechanism starts sending data rates cautiously yet rapidly increases towards the congestion point, approximately doubling the congestion window (cwnd) each round-trip time (RTT). Unfortunately, default implementations of TCP slow start, such as TCP Cubic with HyStart [HYSTART] in Linux, often result in a premature exit from the slow start phase, or, if HyStart is disabled, excessive packet loss upon overshooting the congestion point. Exiting slow start too early curtails TCP's ability to capitalize on unused link capacity, a setback that is particularly pronounced in high bandwidth-delay product (BDP) networks (e.g., GEO satellites) where the time to grow the congestion window to the congestion point is substantial. Conversely, exiting slow start too late overshoots the link's capacity, inducing unnecessary congestion and packet loss, particularly problematic for links with large (bloated) bottleneck queues.¶

To determine the slow start exit point, we propose that the TCP sender monitor the acknowledged delivered bytes in an RTT and compare that to what is expected based on the bytes acknowledged as delivered during the previous RTT. Large differences between delivered bytes and expected delivered bytes is then the indicator that slow start has reached the network congestion point and the slow start phase should exit. We call our approach the Slow start Exit At Right CHokepoint (SEARCH) algorithm. SEARCH is based on the principle that during slow start, the congestion window expands by one maximum segment size (MSS) for each acknowledgment (ACK) received, prompting the transmission of two segments and effectively doubling the sending rate each RTT. However, when the network surpasses the congestion point, the delivery rate does not double as expected, signaling that the slow start phase should exit. Specifically, the current delivered bytes should be twice the delivered bytes one RTT ago. To accommodate links with a wide range in capacities, SEARCH normalizes the difference based on the current delivered bytes and since link latencies can vary over time independently of data rates (especially for wireless links), SEARCH smooths the measured delivered bytes over several RTTs.¶

This document describes the current version of the SEARCH algorithm, version 3. Active work on the SEARCH algorithm is continuing.¶

This document is organized as follows: Section 2 provides terminology and definitions relevant to this document; Section 3 describes the SEARCH algorithm in detail; Section 4 provides justification for the algorithm settings; Section 5 describes the implementation status; Section 6 describes security considerations; Section 7 notes that there are no IANA considerations; Section 8 closes with acknowledgments; and Section 9 provides references.¶

2. Terminology and Definitions

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, BCP 14 [RFC2119] and indicate requirement levels for compliant CoAP implementations.¶

In this document, the term "byte" is used in its now customary sense as a synonym for "octet".¶

ACK: a TCP acknowledgement.¶

bins: the aggregate (total) of acknowledged delivery bytes over a small time window.¶

congestion window (cwnd): A TCP state variable that limits the amount of data a TCP sender can send. At any given time, a TCP flow MUST NOT send data with a sequence number higher than the sum of the highest acknowledged sequence number and the minimum of the cwnd and the receiver window.¶

norm_diff: the normalized difference in current delivered bytes and previously delivered bytes.¶

round-trip time (RTT): the round-trip time for a segment sent until the acknowledgement is received.¶

THRESH: the norm_diff value above which SEARCH considers the congestion point reached and the slow start phase exits.¶

3. SEARCH Algorithm

The SEARCH algorithm core concept is that during the slow start phase, the delivered bytes should double each RTT until the congestion point is reached. In SEARCH, when the bytes delivered one RTT prior is half the bytes delivered currently, the bitrate is not yet at capacity, whereas when the bytes delivered prior are more than half the bytes delivered currently, the link capacity has been reached and TCP exits slow start.¶

One challenge in monitoring delivered data across multiple RTTs is latency variability for some links. Variable latency in the absence of congestion - common in some wireless links - can cause RTTs to differ over time even when the network is not yet at the congestion point. This variability complicates comparing delivered bytes one RTT prior to those delivered currently in that a lowered latency can make it seem like the total bytes delivered currently is too low compared to the total delivered one RTT ago, making it seem like the link is at the congestion point when it is not.¶

To counteract link latency variability, SEARCH tracks delivered data over several RTTs in a sliding window to provide a more stable basis for comparison. Since tracking individual segment delivery times is prohibitive in terms of memory use, the data within the sliding window is aggregated over bins representing small, fixed time periods. The window then slides over bin-by-bin, rather than sliding every acknowledgement (ACK), reducing both the computational load (since SEARCH only triggers at the bin boundary) and the memory requirements (since delivered bytes are kept for a bin-sized time interval instead of for each segment).¶

The SEARCH algorithm (that runs on the TCP sender only) is shown below.¶

The parameters in CAPS (lines 0-4) are constants.¶

The variables in Initialization (lines 5-9) are set once upon establishment of a TCP connection. The initial_rtt (line 1) obtained via the first round-trip time measured in the TCP connection.¶

The variable now on lines 9, 10 and 24 is the current system time when the code is called.¶

The variables sequence_num and rtt in the ACK_arrived() function are obtained upon arrival of an acknowledgement from the receiver.¶

The variable cwnd on lines 38 and 39 is the TCP congestion window.¶

Lines 0-4 set the predefined parameters for the SEARCH algorithm. The window factor (WINDOW_FACTOR) is a multiple of the initial RTT, set so as the SEARCH window will be 3.5 times the initial RTT (set upon initialization of the TCP flow in line 5). The delivered bytes over a SEARCH window is approximated using 10 bins (W), with an additional 15 additional bins (EXTRA_BINS) bins (for a total of 25 (NUM_BINS)) to allow comparison of the current delivered bytes to the previously delivered bytes one RTT earlier. The threshold (THRESH) is set to 0.35 and is the upper bound of the permissible difference between the previously delivered bytes and the current delivered bytes (normalized) above which slow start exits.¶

Lines 5-9 do one-time initialization of SEARCH variables when a TCP connection is established. The SEARCH window size (window_size) is set to be the initial RTT (initial_rtt) multiplied by the window factor (WINDOW_FACTOR). The bin duration (bin_duration) is then the window size divided by size (in bins) of the SEARCH window (W).¶

After initialization, SEARCH only acts when acknowledgements (ACKs) are received and even then, only when the current time (now) has passed the end of the latest bin boundary (stored in the variable bin_end). This check happens on line 10 and if the bin boundary is passed, the bin statistics are updated in the function update_bins(), lines 24-30.¶

In update_bins(), under most TCP connections, the time (now) is within the bin immediately after the previous bin, but in some cases (such as during an RTT spike or a TCP connection without data to send), more than one bin boundary may have been passed. Line 24 computes how many bins have been passed and line 25 updates the next bin boundary accordingly. In lines 26-28, for each bin passed, the bin[] variable is set to the previously-delivered bytes. In line 30, for the latest bin, the delivered bytes is updated to the latest sequence number (from the ACK).¶

Once the bins are updated, lines 12-14 check if enough bins have been filled to run SEARCH. This requires at least W (10) bins (i.e., a SEARCH window's worth of bytes-delivered data), but also enough bins to shift back by an RTT to compute a window (10) of bins one RTT ago, too.¶

If there is enough bin data to run SEARCH, lines 15 and 17 compute the current and previously delivered bytes over a window (W) of bins, respectively. This computation is done in the function compute_delv(), lines 32-38. For previously delivered bytes, shifting by an RTT may mean the SEARCH window lands between bin boundaries, so the fraction of the bin is computed in line 16 and passed into compute_delv() in line 17.¶

In the function compute_delv() over lines 31-35, idx1 and idx2 are the indices into the bin[] array for the start and end of the window as explained above, fraction is the proportion (from 0 to 1) of the end bins to use in the computation. Line 32 computes the bytes delivered (delv) over the inner part of the window (i.e., not counting the fractional bins on the end), and lines 33-34 compute the fractional parts of the end bins to add to delv.¶

Once delivered byes are computed, line 18 calculates the difference between the expected delivered bytes (2 x prev_delv) and the current delivered bytes (curr_delv), normalized by dividing by the expected delivered bytes. In line 19, this normalized difference value (norm_diff) is compared to the threshold (THRESH). If norm_diff is larger than THRESH, that means the current delivered bytes is lower than expected (i.e., the delivered bytes did not double over the previous RTT) and slow start exits.¶

Slow start exit is handled by the function exit_slow_start() on line 36. Setting the slow start threshold (ssthresh) to the congestion window (cwnd) at effectively exits slow start.¶

SEARCH 2.0 ALGORITHM¶

Parameters:
0: WINDOW_FACTOR = 3.5
1: W = 10
2: EXTRA_BINS = 15
3: NUM_BINS = W + EXTRA_BINS
4: THRESH = 0.35

Initialization():
5: window_size = *initial_rtt* x WINDOW_FACTOR
6: bin_duration = window_size / W
7: bin\[NUM_BINS\] = {}
8: curr_idx = -1
9: bin_end = *now* + bin_duration

ACK_arrived(sequence_num, rtt):

// Check if passed bin boundary.
10: if (*now* > bin_end) then
11:    update_bins()

// Check if enough data for SEARCH.
12:    prev_idx = curr_idx - (rtt / bin_duration)
13:    if (prev_idx >= W) and
14:       (curr_idx - prev_idx) <= EXTRA_BINS then

// Run SEARCH check.
15:       curr_delv = compute_delv(curr_idx - W, curr_idx)
16:       fraction = (rtt mod bin_duration) / bin_duration
17:       prev_delv = compute_delv(prev_idx - W, prev_idx, fraction)
18:       norm_diff = (2 x prev_delv - curr_delv) / (2 x prev_delv)
19:       if (norm_diff >= THRESH) then
20:          exit_slow_start()
21:       end if

22:    end if // Enough data for SEARCH.

23: end if // Each ACK.

// Update bin statistics, accounting for cases where more
// than one bin boundary might have been passed.
update_bins():
24: passed_bins = (*now* - bin_end) / bin_duration + 1
25: bin_end += passed_bins x bin_duration
26: for i = (curr_idx + 1) to (curr_idx + passed_bins)
27:    if (curr_idx >= 0) bin\[i mod NUM_BINS\] = bin\[curr_idx\]
28: end for
29: curr_idx += passed_bins
30: bin\[curr_idx mod NUM_BINS\] = sequence_num

// Compute delivered bytes over the window of bins, interpolating a
// fraction of each bin on the end (default is 0).
compute_delv(idx1, idx2, fraction = 0):
31: delv = 0
32: delv = bin[(idx2 - 1) mod NUM_BINS] - bin[idx1 mod NUM_BINS]
33: delv += (bin[idx1 mod NUM_BINS] - bin[(idx1 - 1) mod NUM_BINS]) x (1 - fraction)
34: delv += (bin[idx2 mod NUM_BINS] - bin[(idx2 - 1) mod NUM_BINS]) x fraction
35: return delv

// Exit slow start by setting ssthresh.
exit_slow_start():
36: ssthresh = *cwnd*

4. SEARCH Parameters

This section provides justification and some sensitivity analysis for key SEARCH algorithm constants.¶

Window Size (window_size)¶

The SEARCH window smooths over RTT fluctuations in a connection that are unrelated to congestion. The window size must be large enough to encapsulate meaningful link RTT variation, yet small in order to allow SEARCH to respond near when slow start reaches link capacity. In order to determine an appropriate window size, we analyzed RTT variation over time for GEO, LEO, and 4G LTE links for TCP during slow start. See [KCL24] for details.¶

The SEARCH window size needs to be large enough to capture the observed periodic oscillations in the RTT values. In order to determine the oscillation period, we use a Fast Fourier Transform (FFT) to convert measured RTT values from the time domain to the frequency domain. For GEO satellites, the primary frequency peak is at 0.5 Hz, meaning there is a large, periodic cycle that occurs about every 2 seconds. Given the minimum RTT for a GEO connection of about 600 ms, this means an RTT cycle occurs about every 3.33 RTTs. Thus, a SEARCH window size of about 3.5 times the minimum RTT should smooth out the latency variation for this type of link.¶

While the RTT periodicity for LEO links is not as pronounced as in GEO links, the analysis yields a similar window size. The FFT of LEO RTTs has a dominant peak at 10 Hz, so a period of about 0.1 seconds. With LEO's minimum RTT of about 30 ms, the period is about 3.33 RTTs, similar to that for GEO links. Thus, a window size of about 3.5 times the minimum RTT should smooth out the latency variation for this type of link, too.¶

Similarly to the LEO link, the LTE network does not have a strong RTT periodicity. The FFT of LTE RTTs has a dominant peak at 6 Hz, with a period of about 0.17 seconds. With the minimum RTT of the LTE network of about 60 ms, this means a window size of about 2.8 times the minimum RTT is needed. A SEARCH default of 3.5 times the minimum RTT exceeds this, so should smooth out the variance for this type of link as well.¶

** Threshold (THRESH) **¶

The threshold (THRESH) determines when the difference between the bytes delivered currently and the bytes delivered during the previous RTT is large enough to exit the slow start phase. A small threshold is desirable to exit slow start close to the "at capacity" point (i.e., without overshooting too much), but the threshold must be large enough not to trigger an exit from slow start prematurely due to noise in the measurements.¶

During slow start, the congestion window doubles each RTT. In ideal conditions and with an initial cwnd of 1 (1 is used as an example, but typical congestion windows start at 10 or more), this results in a sequence of delivered bytes that follows a doubling pattern (1, 2, 4, 8, 16, ...). Once the link capacity is reached, the delivered bytes each RTT cannot increase despite cwnd growth. For example, consider a SEARCH window that is 4x the size of the RTT. After 5 RTTs, the current delivered window comprises 2, 4, 8, 16, while the previous delivered window is 1, 2, 4, 8. The current delivered bytes is 30, exactly double the bytes delivered in the previous window. Thus, SEARCH would compute the normalized difference as zero.¶

Once the cwnd ramps up to meet full link capacity, the delivered bytes plateau. Continuing the example, if the link capacity is reached when cwnd is 16, the delivered bytes growth would be 1, 2, 4, 8, 16, 16. The current delivered window is 4+8+16+16 = 44, while the previously delivered window is 2+4+8+16 = 30. Here, the normalized difference between 2x the previously delivered window and the current delivered window is about (60-44)/60 = 0.27. After 5 more RTTs, the previous delivered and current delivered bytes would both be 16 + 16 + 16 + 16 = 64 and the normalized difference would be (128 - 64) / 64 = 0.5.¶

Thus, the norm values typically range from 0 (before the congestion point) to 0.5 (well after the congestion point) with values between 0 and 0.5 when the congestion point has been reached but not surpassed by the full window.¶

To generalize this relationship, the theoretical underpinnings of this behavior can be quantified by integrating the area under the congestion window curve over time for a closed-form equation for both the current delivered bytes (curr_delv) and the previously delivered bytes (prev_delv). The normalized difference can be computed based on the RTT round relative to the "at capacity" round. While SEARCH seeks to detect the "at capacity" point as soon as possible after reaching it, it must also avoid premature exit in the case of noise on the link. The 0.35 threshold value chosen does this and can be detected about 2 RTTs of reaching capacity.¶

Number of Bins (NUM_BINS)¶

Dividing the delivered byte window into bins reduces the sender's memory use by aggregating data across multiple ACKs instead of tracking each ACK. This approach simplifies data handling and minimizes the frequency of SEARCH window updates, enhancing sender efficiency. However, more bins provide more fidelity to actual delivered byte totals and allow SEARCH to make decisions (i.e., compute if it should exit slow start) more often, but require more memory for each TCP flow. Sensitivity analysis previously conducted aimed to identify the impact of the number of bins used by SEARCH and the ability to exit slow start in a timely fashion.¶

Using a window size of 3.5x the initial RTT and a threshold of 0.35, we varied the number of bins from 5 to 40 and observed the impact on SEARCH's performance over GEO, LEO and 4G LTE downloads. For all three link types, a bin size of 10 provides nearly identical performance as SEARCH running with more bins, while 10 also minimizes early exits from slow start while having an "at chokepoint" percentage that is close to the maximum.¶

5. SEARCH Options

This section describes optional adjustments to the SEARCH algorithm.¶

A) The interpolation code in lines 16-17 and 33-34 gives a more precise computation of the previously delivered bytes by computing a fraction of the adjacent bins. If saving the computation time required for interpolation is desired, interpolation could be disabled, effectively "rounding down" the previous delivered window to the lowest bin (the same as running SEARCH with fraction of 0). While this would sacrifice some accuracy for the SEARCH check computations, at least it errs on the side of not exiting slow start too early.¶

B) In exit_slow_start(), since SEARCH had to pass the congestion point in order to ascertain that it had, in fact, been reached, the congestion window (cwnd) could be reduced to the value at the congestion point instead of above it. Since with a THRESHOLD setting of 0.35, detection of the congestion point is delayed by almost exactly two RTTs, so the extra bytes (past the congestion point) that had been added to the congestion window could be subtracted from the congestion window. Code to do so is below:¶

36: cong_idx = curr_idx - 2 x *initial_rtt* / bin_duration
37: overshoot = compute_delv(cong_idx, curr_idx)
38: *cwnd* -= overshoot

C) If the RTT grows such that the previous window can not be computed due to overlapping the bins used for the current window (line 14), SEARCH cannot run and instead must wait for the RTT to decrease enough until there is no such overlap. Instead, SEARCH could reduce the size of the window to prevent this overlap. If this is done, instead of shifting back 3.5x the initial RTT (the WINDOW_FACTOR), SEARCH could shift back less (e.g., 2.0x). While this smaller window has the disadvantage of not smoothing over RTT variance as well as the default window, it has the advantage of allowing the SEARCH check to still run (lines 15-21), possibly with an adjusted THRESHOLD.¶

6. Deployment and Performance Evaluation

Evaluation of hundreds of downloads of TCP with SEARCH across GEO, LEO, and 4G LTE network links compared to TCP with HyStart and TCP without HyStart shows SEARCH almost always exits after capacity has been reached but before packet loss has occurred. This results in capacity limits being reached quickly while avoiding inefficiencies caused by lost packets.¶

Evaluation of a SEARCH implementation in an open source QUIC library (QUICly) over an emulated GEO satellite link validates the implementation, illustrating how SEARCH detects the congestion point and exits slow start before packet loss occurs. Evaluation over a commercial GEO satellite link shows SEARCH can provide a median improvement of up to 3 seconds (14%) compared to the baseline by limiting cwnd growth when capacity is reached and delaying any packet loss due to congestion.¶

Details can be found at [KCL24] and [CKC24], respectively.¶

7. Implementation Status

This section records the status of known implementations of the algorithm defined by this specification at the time of posting of this Internet-Draft, and is based on a proposal described in [RFC7942]. The description of implementations in this section is intended to assist the IETF in its decision processes in progressing drafts to RFCs. Please note that the listing of any individual implementation here does not imply endorsement by the IETF. Furthermore, no effort has been spent to verify the information presented here that was supplied by IETF contributors. This is not intended as, and must not be construed to be, a catalog of available implementations or their features. Readers are advised to note that other implementations may exist.¶

According to [RFC7942], "this will allow reviewers and working groups to assign due consideration to documents that have the benefit of running code, which may serve as evidence of valuable experimentation and feedback that have made the implemented protocols more mature. It is up to the individual working groups to use this information as they see fit".¶

As of the time of writing, the following implementations of SEARCH have been publicly released:¶

Linux TCP¶

Source code URL:¶

https://github.com/Project-Faster/tcp_ss_search.git¶

Source: WPI Maturity: production License: GPL? Contact: [email protected] Last updated: May 2024¶

QUIC¶

Source code URLs:¶

https://github.com/Project-Faster/quicly/tree/generic-slowstart https://github.com/AmberCronin/quicly https://github.com/AmberCronin/qperf¶

Source: WPI Maturity: production License: BSD-style Contact: [email protected] Last updated: May 2024¶

8. Security Considerations

This proposal makes no changes to the underlying security of transport protocols or congestion control algorithms. SEARCH shares the same security considerations as the existing standard congestion control algorithm [RFC5681].¶

9. IANA Considerations

This document has no IANA actions. Here we are using that phrase, suggested by [RFC8126], because SEARCH does not modify or extend the wire format of any network protocol, nor does it add new dependencies on assigned numbers. SEARCH involves only a change to the slow start part of the congestion control algorithm of a transport sender, and does not involve changes in the network, the receiver, or any network protocol.¶

Note to RFC Editor: this section may be removed on publication as an RFC.¶

10. Acknowledgements

Much of the content of this draft is the result of discussions with the Congestion Control Research Group (CCRG) at WPI https://web.cs.wpi.edu/~claypool/ccrg. In addition, feedback and discussions of early versions of SEARCH with the technical group at Viasat has been invaluable.¶

11. References

Appendix A. Historical Note

Authors' Addresses