CUBIC for Fast and Long-Distance Networks

Internet-Draft	CUBIC	July 2021
Xu, et al.	Expires 27 January 2022	[Page]

Abstract

CUBIC is a standard TCP congestion control algorithm that uses a cubic function instead of the linear window increase function on the sender side to improve scalability and stability over fast and long-distance networks. CUBIC has been adopted as the default TCP congestion control algorithm by the Linux, Windows, and Apple stacks.¶

This document updates the specification of CUBIC to include algorithmic improvements based on these implementations and recent academic work. Based on the extensive deployment experience with CUBIC, it also moves the specification to the Standards Track, obsoleting [RFC8312].¶

3. Design Principles of CUBIC

CUBIC is designed according to the following design principles:¶

Principle 1:: For better network utilization and stability, CUBIC uses both the concave and convex profiles of a cubic function to increase the congestion window size, instead of using just a convex function.¶
Principle 2:: To be AIMD-friendly, CUBIC is designed to behave like AIMD TCP in networks with short RTTs and small bandwidth where AIMD TCP performs well.¶
Principle 3:: For RTT-fairness, CUBIC is designed to achieve linear bandwidth sharing among flows with different RTTs.¶
Principle 4:: CUBIC appropriately sets its multiplicative window decrease factor in order to balance between the scalability and convergence speed.¶

3.1. Principle 1 for the CUBIC Increase Function

For better network utilization and stability, CUBIC [HRX08] uses a cubic window increase function in terms of the elapsed time from the last congestion event. While most alternative congestion control algorithms to AIMD TCP increase the congestion window using convex functions, CUBIC uses both the concave and convex profiles of a cubic function for window growth.¶

After a window reduction in response to a congestion event detected by duplicate ACKs, Explicit Congestion Notification-Echo (ECN-Echo, ECE) ACKs [RFC3168], TCP RACK [RFC8985] or QUIC loss detection [RFC9002], CUBIC remembers the congestion window size at which it received the congestion event and performs a multiplicative decrease of the congestion window. When CUBIC enters into congestion avoidance, it starts to increase the congestion window using the concave profile of the cubic function. The cubic function is set to have its plateau at the remembered congestion window size, so that the concave window increase continues until then. After that, the cubic function turns into a convex profile and the convex window increase begins.¶

This style of window adjustment (concave and then convex) improves the algorithm stability while maintaining high network utilization [CEHRX07]. This is because the window size remains almost constant, forming a plateau around the remembered congestion window size of the last congestion event, where network utilization is deemed highest. Under steady state, most window size samples of CUBIC are close to that remembered congestion window size, thus promoting high network utilization and stability.¶

Note that congestion control algorithms that only use convex functions to increase the congestion window size have their maximum increments around the remembered congestion window size of the last congestion event, and thus introduce many packet bursts around the saturation point of the network, likely causing frequent global loss synchronizations.¶

3.2. Principle 2 for AIMD Friendliness

CUBIC promotes per-flow fairness to AIMD TCP. Note that AIMD TCP performs well over paths with short RTTs and small bandwidths (or small BDPs). There is only a scalability problem in networks with long RTTs and large bandwidths (or large BDPs).¶

A congestion control algorithm designed to be friendly to AIMD TCP on a per-flow basis must increase its congestion window less aggressively in small BDP networks than in large BDP networks.¶

The aggressiveness of CUBIC mainly depends on the maximum window size before a window reduction, which is smaller in small-BDP networks than in large-BDP networks. Thus, CUBIC increases its congestion window less aggressively in small-BDP networks than in large-BDP networks.¶

Furthermore, in cases when the cubic function of CUBIC would increase the congestion window less aggressively than AIMD TCP, CUBIC simply follows the window size of AIMD TCP to ensure that CUBIC achieves at least the same throughput as AIMD TCP in small-BDP networks. We call this region where CUBIC behaves like AIMD TCP the "AIMD-friendly region".¶

3.3. Principle 3 for RTT Fairness

Two CUBIC flows with different RTTs have a throughput ratio that is linearly proportional to the inverse of their RTT ratio, where the throughput of a flow is approximately the size of its congestion window divided by its RTT.¶

Specifically, CUBIC maintains a window increase rate independent of RTTs outside the AIMD-friendly region, and thus flows with different RTTs have similar congestion window sizes under steady state when they operate outside the AIMD-friendly region.¶

This notion of a linear throughput ratio is similar to that of AIMD TCP under high statistical multiplexing where packet loss is independent of individual flow rates. However, under low statistical multiplexing, the throughput ratio of AIMD TCP flows with different RTTs is quadratically proportional to the inverse of their RTT ratio [XHR04].¶

CUBIC always ensures a linear throughput ratio independent of the amount of statistical multiplexing. This is an improvement over AIMD TCP. While there is no consensus on particular throughput ratios for different RTT flows, we believe that over wired Internet paths, use of a linear throughput ratio seems more reasonable than equal throughputs (i.e., the same throughput for flows with different RTTs) or a higher-order throughput ratio (e.g., a quadratical throughput ratio of AIMD TCP under low statistical multiplexing environments).¶

3.4. Principle 4 for the CUBIC Decrease Factor

To balance between scalability and convergence speed, CUBIC sets the multiplicative window decrease factor to 0.7, whereas AIMD TCP uses 0.5.¶

While this improves the scalability of CUBIC, a side effect of this decision is slower convergence, especially under low statistical multiplexing. This design choice is following the observation that HighSpeed TCP (HSTCP) [RFC3649] and other approaches (e.g., [GV02]) made: the current Internet becomes more asynchronous with less frequent loss synchronizations under high statistical multiplexing.¶

In such environments, even strict Multiplicative-Increase Multiplicative-Decrease (MIMD) can converge. CUBIC flows with the same RTT always converge to the same throughput independent of statistical multiplexing, thus achieving intra-algorithm fairness. We also find that in environments with sufficient statistical multiplexing, the convergence speed of CUBIC is reasonable.¶

4. CUBIC Congestion Control

In this section, we discuss how the congestion window is updated during the different stages of the CUBIC congestion controller.¶

4.1. Definitions

The unit of all window sizes in this document is segments of the maximum segment size (MSS), and the unit of all times is seconds. Implementations can use bytes to express window sizes, which would require factoring in the maximum segment size wherever necessary and replacing segments_acked with the number of bytes acknowledged in Figure 4.¶

4.1.1. Constants of Interest

β_cubic: CUBIC multiplication decrease factor as described in Section 4.6.¶

α_cubic: CUBIC additive increase factor used in AIMD-friendly region as described in Section 4.3.¶

C: constant that determines the aggressiveness of CUBIC in competing with other congestion control algorithms in high BDP networks. Please see Section 5 for more explanation on how it is set. The unit for C is¶

4.1.2. Variables of Interest

This section defines the variables required to implement CUBIC:¶

RTT: Smoothed round-trip time in seconds, calculated as described in [RFC6298].¶

cwnd: Current congestion window in segments.¶

ssthresh: Current slow start threshold in segments.¶

W_max: Size of cwnd in segments just before cwnd was reduced in the last congestion event when fast convergence is disabled. However, if fast convergence is enabled, the size may be further reduced based on the current saturation point.¶

K: The time period in seconds it takes to increase the congestion window size at the beginning of the current congestion avoidance stage to W_max.¶

current_time: Current time of the system in seconds.¶

epoch_start: The time in seconds at which the current congestion avoidance stage started.¶

cwnd_start: The cwnd at the beginning of the current congestion avoidance stage, i.e., at time epoch_start.¶

W_cubic(t): The congestion window in segments at time t in seconds based on the cubic increase function, as described in Section 4.2.¶

target: Target value of congestion window in segments after the next RTT, that is, W_cubic(t + RTT), as described in Section 4.2.¶

W_est: An estimate for the congestion window in segments in the AIMD-friendly region, that is, an estimate for the congestion window of AIMD TCP.¶

segments_acked: Number of MSS-sized segments acked when an ACK is received. This number will be a decimal value when an ACK acknowledges an amount of data that is not MSS-sized. Specifically, it can be less than 1 when an ACK acknowledges a segment smaller than the MSS.¶

4.2. Window Increase Function

CUBIC maintains the acknowledgment (ACK) clocking of AIMD TCP by increasing the congestion window only at the reception of an ACK. It does not make any changes to the TCP Fast Recovery and Fast Retransmit algorithms [RFC6582][RFC6675].¶

During congestion avoidance, after a congestion event is detected by mechanisms described in Section 3.1, CUBIC changes the window increase function of AIMD TCP.¶

CUBIC uses the following window increase function:¶

Figure 1

where t is the elapsed time in seconds from the beginning of the current congestion avoidance stage, that is,¶

and where epoch_start is the time at which the current congestion avoidance stage starts. K is the time period that the above function takes to increase the congestion window size at the beginning of the current congestion avoidance stage to W_max if there are no further congestion events and is calculated using the following equation:¶

Figure 2

where cwnd_start is the congestion window at the beginning of the current congestion avoidance stage. For example, right after a congestion event, cwnd_start is equal to the new cwnd calculated as described in Section 4.6.¶

Upon receiving an ACK during congestion avoidance, CUBIC computes the target congestion window size after the next RTT using Figure 1 as follows, where RTT is the smoothed round-trip time. The lower and upper bounds below ensure that CUBIC's congestion window increase rate is non-decreasing and is less than the increase rate of slow start.¶

Depending on the value of the current congestion window size cwnd, CUBIC runs in three different regions:¶

The AIMD-friendly region, which ensures that CUBIC achieves at least the same throughput as AIMD TCP.¶
The concave region, if CUBIC is not in the AIMD-friendly region and cwnd is less than W_max.¶
The convex region, if CUBIC is not in the AIMD-friendly region and cwnd is greater than W_max.¶

Below, we describe the exact actions taken by CUBIC in each region.¶

4.3. AIMD-Friendly Region

AIMD TCP performs well in certain types of networks, for example, under short RTTs and small bandwidths (or small BDPs). In these networks, CUBIC remains in the AIMD-friendly region to achieve at least the same throughput as AIMD TCP.¶

The AIMD-friendly region is designed according to the analysis in [FHP00], which studies the performance of an AIMD algorithm with an additive factor of α (segments per RTT) and a multiplicative factor of β, denoted by AIMD(α, β). p is the packet loss rate. Specifically, the average congestion window size of AIMD(α, β) can be calculated using Figure 3.¶

Figure 3

By the same analysis, to achieve the same average window size as AIMD TCP that uses AIMD(1, 0.5), α must be equal to,¶

Thus, CUBIC uses Figure 4 to estimate the window size W_est in the AIMD-friendly region with¶

which achieves the same average window size as AIMD TCP. When receiving an ACK in congestion avoidance (where cwnd could be greater than or less than W_max), CUBIC checks whether W_cubic(t) is less than W_est. If so, CUBIC is in the AIMD-friendly region and cwnd SHOULD be set to W_est at each reception of an ACK.¶

W_est is set equal to cwnd_start at the start of the congestion avoidance stage. After that, on every ACK, W_est is updated using Figure 4. Note that this equation is for a connection where Appropriate Byte Counting (ABC) [RFC3465] is disabled. For a connection with ABC enabled, this equation SHOULD be adjusted by using the number of acknowledged bytes instead of acknowledged segments. Also note that this equation works for connections with enabled or disabled Delayed ACKs [RFC5681], as segments_acked will be different based on the segments actually acknowledged by an ACK.¶

Figure 4

Note that once W_est reaches W_max, that is, W_est >= W_max, CUBIC needs to start probing to determine the new value of W_max. At this point, α_cubic SHOULD be set to 1 to ensure that CUBIC can achieve the same congestion window increment as AIMD TCP, which uses AIMD(1, 0.5).¶

4.4. Concave Region

When receiving an ACK in congestion avoidance, if CUBIC is not in the AIMD-friendly region and cwnd is less than W_max, then CUBIC is in the concave region. In this region, cwnd MUST be incremented by¶

for each received ACK, where target is calculated as described in Section 4.2.¶

4.5. Convex Region

When receiving an ACK in congestion avoidance, if CUBIC is not in the AIMD-friendly region and cwnd is larger than or equal to W_max, then CUBIC is in the convex region.¶

The convex region indicates that the network conditions might have changed since the last congestion event, possibly implying more available bandwidth after some flow departures. Since the Internet is highly asynchronous, some amount of perturbation is always possible without causing a major change in available bandwidth.¶

Unless it is overridden by the AIMD window increase, CUBIC is very careful in this region. The convex profile aims to increase the window very slowly at the beginning when cwnd is around W_max and then gradually increases its rate of increase. We also call this region the "maximum probing phase", since CUBIC is searching for a new W_max. In this region, cwnd MUST be incremented by¶

for each received ACK, where target is calculated as described in Section 4.2.¶

4.6. Multiplicative Decrease

When a congestion event is detected by mechanisms described in Section 3.1, CUBIC updates W_max and reduces cwnd and ssthresh immediately as described below. An implementation MAY set a smaller ssthresh than suggested below to accommodate rate-limited applications as described in [RFC7661]. For both packet loss and congestion detection through ECN, the sender MAY employ a Fast Recovery algorithm to gradually adjust the congestion window to its new reduced ssthresh value. The parameter β_cubic SHOULD be set to 0.7.¶

A side effect of setting β_cubic to a value bigger than 0.5 is slower convergence. We believe that while a more adaptive setting of β_cubic could result in faster convergence, it will make the analysis of CUBIC much harder.¶

4.7. Fast Convergence

To improve convergence speed, CUBIC uses a heuristic. When a new flow joins the network, existing flows need to give up some of their bandwidth to allow the new flow some room for growth, if the existing flows have been using all the network bandwidth. To speed up this bandwidth release by existing flows, the following "Fast Convergence" mechanism SHOULD be implemented.¶

With Fast Convergence, when a congestion event occurs, we update W_max as follows, before the window reduction as described in Section 4.6.¶

At a congestion event, if the current cwnd is less than W_max, this indicates that the saturation point experienced by this flow is getting reduced because of a change in available bandwidth. Then we allow this flow to release more bandwidth by reducing W_max further. This action effectively lengthens the time for this flow to increase its congestion window, because the reduced W_max forces the flow to plateau earlier. This allows more time for the new flow to catch up to its congestion window size.¶

Fast Convergence is designed for network environments with multiple CUBIC flows. In network environments with only a single CUBIC flow and without any other traffic, Fast Convergence SHOULD be disabled.¶

4.8. Timeout

In case of a timeout, CUBIC follows AIMD TCP to reduce cwnd [RFC5681], but sets ssthresh using β_cubic (same as in Section 4.6) in a way that is different from AIMD TCP [RFC5681].¶

During the first congestion avoidance stage after a timeout, CUBIC increases its congestion window size using Figure 1, where t is the elapsed time since the beginning of the current congestion avoidance, K is set to 0, and W_max is set to the congestion window size at the beginning of the current congestion avoidance stage. In addition, for the AIMD-friendly region, W_est SHOULD be set to the congestion window size at the beginning of the current congestion avoidance.¶

4.9. Spurious Congestion Events

In cases where CUBIC reduces its congestion window in response to having detected packet loss via duplicate ACKs or timeouts, there is a possibility that the missing ACK would arrive after the congestion window reduction and a corresponding packet retransmission. For example, packet reordering could trigger this behavior. A high degree of packet reordering could cause multiple congestion window reduction events, where spurious losses are incorrectly interpreted as congestion signals, thus degrading CUBIC's performance significantly.¶

When there is a congestion event, a CUBIC implementation SHOULD save the current value of the following variables before the congestion window reduction.¶

CUBIC MAY implement an algorithm to detect spurious retransmissions, such as DSACK [RFC3708], Forward RTO-Recovery [RFC5682] or Eifel [RFC3522]. Once a spurious congestion event is detected, CUBIC SHOULD restore the original values of above-mentioned variables as follows if the current cwnd is lower than prior_cwnd. Restoring the original values ensures that CUBIC's performance is similar to what it would be without spurious losses.¶

In rare cases, when the detection happens long after a spurious loss event and the current cwnd is already higher than prior_cwnd, CUBIC SHOULD continue to use the current and the most recent values of these variables.¶

4.10. Slow Start

CUBIC MUST employ a slow-start algorithm, when cwnd is no more than ssthresh. Among the slow-start algorithms, CUBIC MAY choose the AIMD TCP slow start [RFC5681] in general networks, or the limited slow start [RFC3742] or hybrid slow start [HR08] for fast and long-distance networks.¶

When CUBIC uses hybrid slow start [HR08], it may exit the first slow start without incurring any packet loss and thus W_max is undefined. In this special case, CUBIC switches to congestion avoidance and increases its congestion window size using Figure 1, where t is the elapsed time since the beginning of the current congestion avoidance, K is set to 0, and W_max is set to the congestion window size at the beginning of the current congestion avoidance stage.¶

5. Discussion

In this section, we further discuss the safety features of CUBIC following the guidelines specified in [RFC5033].¶

With a deterministic loss model where the number of packets between two successive packet losses is always 1/p, CUBIC always operates with the concave window profile, which greatly simplifies the performance analysis of CUBIC. The average window size of CUBIC can be obtained by the following function:¶

Figure 5

With β_cubic set to 0.7, the above formula reduces to:¶

Figure 6

We will determine the value of C in the following subsection using Figure 6.¶

5.1. Fairness to AIMD TCP

In environments where AIMD TCP is able to make reasonable use of the available bandwidth, CUBIC does not significantly change this state.¶

AIMD TCP performs well in the following two types of networks:¶

networks with a small bandwidth-delay product (BDP)¶
networks with a short RTTs, but not necessarily a small BDP¶

CUBIC is designed to behave very similarly to AIMD TCP in the above two types of networks. The following two tables show the average window sizes of AIMD TCP, HSTCP, and CUBIC. The average window sizes of AIMD TCP and HSTCP are from [RFC3649]. The average window size of CUBIC is calculated using Figure 6 and the CUBIC AIMD-friendly region for three different values of C.¶

Table 1: AIMD TCP, HSTCP, and CUBIC with RTT = 0.1 seconds
Loss Rate P	AIMD	HSTCP	CUBIC (C=0.04)	CUBIC (C=0.4)	CUBIC (C=4)
1.0e-02	12	12	12	12	12
1.0e-03	38	38	38	38	59
1.0e-04	120	263	120	187	333
1.0e-05	379	1795	593	1054	1874
1.0e-06	1200	12280	3332	5926	10538
1.0e-07	3795	83981	18740	33325	59261
1.0e-08	12000	574356	105383	187400	333250

Table 1 describes the response function of AIMD TCP, HSTCP, and CUBIC in networks with RTT = 0.1 seconds. The average window size is in MSS-sized segments.¶

Table 2: AIMD TCP, HSTCP, and CUBIC with RTT = 0.01 seconds
Loss Rate P	AIMD	HSTCP	CUBIC (C=0.04)	CUBIC (C=0.4)	CUBIC (C=4)
1.0e-02	12	12	12	12	12
1.0e-03	38	38	38	38	38
1.0e-04	120	263	120	120	120
1.0e-05	379	1795	379	379	379
1.0e-06	1200	12280	1200	1200	1874
1.0e-07	3795	83981	3795	5926	10538
1.0e-08	12000	574356	18740	33325	59261

Table 2 describes the response function of AIMD TCP, HSTCP, and CUBIC in networks with RTT = 0.01 seconds. The average window size is in MSS-sized segments.¶

Both tables show that CUBIC with any of these three C values is more friendly to AIMD TCP than HSTCP, especially in networks with a short RTT where AIMD TCP performs reasonably well. For example, in a network with RTT = 0.01 seconds and p=10^-6, AIMD TCP has an average window of 1200 packets. If the packet size is 1500 bytes, then AIMD TCP can achieve an average rate of 1.44 Gbps. In this case, CUBIC with C=0.04 or C=0.4 achieves exactly the same rate as AIMD TCP, whereas HSTCP is about ten times more aggressive than AIMD TCP.¶

We can see that C determines the aggressiveness of CUBIC in competing with other congestion control algorithms for bandwidth. CUBIC is more friendly to AIMD TCP, if the value of C is lower. However, we do not recommend setting C to a very low value like 0.04, since CUBIC with a low C cannot efficiently use the bandwidth in fast and long-distance networks. Based on these observations and extensive deployment experience, we find C=0.4 gives a good balance between AIMD- friendliness and aggressiveness of window increase. Therefore, C SHOULD be set to 0.4. With C set to 0.4, Figure 6 is reduced to:¶

Figure 7

Figure 7 is then used in the next subsection to show the scalability of CUBIC.¶

5.2. Using Spare Capacity

CUBIC uses a more aggressive window increase function than AIMD TCP for fast and long-distance networks.¶

The following table shows that to achieve the 10 Gbps rate, AIMD TCP requires a packet loss rate of 2.0e-10, while CUBIC requires a packet loss rate of 2.9e-8.¶

Table 3: Required packet loss rate for AIMD TCP, HSTCP, and CUBIC to achieve a certain throughput
Throughput (Mbps)	Average W	AIMD P	HSTCP P	CUBIC P
1	8.3	2.0e-2	2.0e-2	2.0e-2
10	83.3	2.0e-4	3.9e-4	2.9e-4
100	833.3	2.0e-6	2.5e-5	1.4e-5
1000	8333.3	2.0e-8	1.5e-6	6.3e-7
10000	83333.3	2.0e-10	1.0e-7	2.9e-8

Table 3 describes the required packet loss rate for AIMD TCP, HSTCP, and CUBIC to achieve a certain throughput. We use 1500-byte packets and an RTT of 0.1 seconds.¶

Our test results in [HKLRX06] indicate that CUBIC uses the spare bandwidth left unused by existing AIMD TCP flows in the same bottleneck link without taking away much bandwidth from the existing flows.¶

5.3. Difficult Environments

CUBIC is designed to remedy the poor performance of AIMD TCP in fast and long-distance networks.¶

5.4. Investigating a Range of Environments

There is decade-long deployment experience with CUBIC on the Internet. CUBIC has also been extensively studied by using both NS-2 simulation and testbed experiments, covering a wide range of network environments. More information can be found in [HKLRX06].¶

Same as AIMD TCP, CUBIC is a loss-based congestion control algorithm. Because CUBIC is designed to be more aggressive (due to a faster window increase function and bigger multiplicative decrease factor) than AIMD TCP in fast and long-distance networks, it can fill large drop-tail buffers more quickly than AIMD TCP and increases the risk of a standing queue [RFC8511]. In this case, proper queue sizing and management [RFC7567] could be used to reduce the packet queuing delay.¶

5.5. Protection against Congestion Collapse

With regard to the potential of causing congestion collapse, CUBIC behaves like AIMD TCP, since CUBIC modifies only the window adjustment algorithm of AIMD TCP. Thus, it does not modify the ACK clocking and timeout behaviors of AIMD TCP.¶

5.6. Fairness within the Alternative Congestion Control Algorithm

CUBIC ensures convergence of competing CUBIC flows with the same RTT in the same bottleneck links to an equal throughput. When competing flows have different RTT values, their throughput ratio is linearly proportional to the inverse of their RTT ratios. This is true independently of the level of statistical multiplexing on the link.¶

5.7. Performance with Misbehaving Nodes and Outside Attackers

This is not considered in the current CUBIC design.¶

5.8. Behavior for Application-Limited Flows

CUBIC does not increase its congestion window size if a flow is currently limited by the application instead of the congestion window. In case of long periods during which cwnd has not been updated due to such an application limit, such as idle periods, t in Figure 1 MUST NOT include these periods; otherwise, W_cubic(t) might be very high after restarting from these periods.¶

5.9. Responses to Sudden or Transient Events

If there is a sudden congestion, a routing change, or a mobility event, CUBIC behaves the same as AIMD TCP.¶

5.10. Incremental Deployment

CUBIC requires only changes to TCP senders, and it does not require any changes at TCP receivers. That is, a CUBIC sender works correctly with the AIMD TCP receivers. In addition, CUBIC does not require any changes to routers and does not require any assistance from routers.¶

8. References

8.1. Normative References

[RFC2119]: Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, <https://www.rfc-editor.org/rfc/rfc2119>.
[RFC3168]: Ramakrishnan, K., Floyd, S., and D. Black, "The Addition of Explicit Congestion Notification (ECN) to IP", RFC 3168, DOI 10.17487/RFC3168, September 2001, <https://www.rfc-editor.org/rfc/rfc3168>.
[RFC5033]: Floyd, S. and M. Allman, "Specifying New Congestion Control Algorithms", BCP 133, RFC 5033, DOI 10.17487/RFC5033, August 2007, <https://www.rfc-editor.org/rfc/rfc5033>.
[RFC5348]: Floyd, S., Handley, M., Padhye, J., and J. Widmer, "TCP Friendly Rate Control (TFRC): Protocol Specification", RFC 5348, DOI 10.17487/RFC5348, September 2008, <https://www.rfc-editor.org/rfc/rfc5348>.
[RFC5681]: Allman, M., Paxson, V., and E. Blanton, "TCP Congestion Control", RFC 5681, DOI 10.17487/RFC5681, September 2009, <https://www.rfc-editor.org/rfc/rfc5681>.
[RFC6298]: Paxson, V., Allman, M., Chu, J., and M. Sargent, "Computing TCP's Retransmission Timer", RFC 6298, DOI 10.17487/RFC6298, June 2011, <https://www.rfc-editor.org/rfc/rfc6298>.
[RFC6582]: Henderson, T., Floyd, S., Gurtov, A., and Y. Nishida, "The NewReno Modification to TCP's Fast Recovery Algorithm", RFC 6582, DOI 10.17487/RFC6582, April 2012, <https://www.rfc-editor.org/rfc/rfc6582>.
[RFC6675]: Blanton, E., Allman, M., Wang, L., Jarvinen, I., Kojo, M., and Y. Nishida, "A Conservative Loss Recovery Algorithm Based on Selective Acknowledgment (SACK) for TCP", RFC 6675, DOI 10.17487/RFC6675, August 2012, <https://www.rfc-editor.org/rfc/rfc6675>.
[RFC7567]: Baker, F., Ed. and G. Fairhurst, Ed., "IETF Recommendations Regarding Active Queue Management", BCP 197, RFC 7567, DOI 10.17487/RFC7567, July 2015, <https://www.rfc-editor.org/rfc/rfc7567>.
[RFC8174]: Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.
[RFC8985]: Cheng, Y., Cardwell, N., Dukkipati, N., and P. Jha, "The RACK-TLP Loss Detection Algorithm for TCP", RFC 8985, DOI 10.17487/RFC8985, February 2021, <https://www.rfc-editor.org/rfc/rfc8985>.
[RFC9002]: Iyengar, J., Ed. and I. Swett, Ed., "QUIC Loss Detection and Congestion Control", RFC 9002, DOI 10.17487/RFC9002, May 2021, <https://www.rfc-editor.org/rfc/rfc9002>.

8.2. Informative References

[CEHRX07]: Cai, H., Eun, D., Ha, S., Rhee, I., and L. Xu, "Stochastic Ordering for Internet Congestion Control and its Applications", IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications, DOI 10.1109/infcom.2007.111, 2007, <https://doi.org/10.1109/infcom.2007.111>.
[FHP00]: Floyd, S., Handley, M., and J. Padhye, "A Comparison of Equation-Based and AIMD Congestion Control", May 2000, <https://www.icir.org/tfrc/aimd.pdf>.
[GV02]: Gorinsky, S. and H. Vin, "Extended Analysis of Binary Adjustment Algorithms", Technical Report TR2002-29, Department of Computer Sciences, The University of Texas at Austin, 11 August 2002, <https://www.cs.utexas.edu/ftp/techreports/tr02-39.ps.gz>.
[HKLRX06]: Ha, S., Kim, Y., Le, L., Rhee, I., and L. Xu, "A Step toward Realistic Performance Evaluation of High-Speed TCP Variants", International Workshop on Protocols for Fast Long-Distance Networks, February 2006, <https://pfld.net/2006/paper/s2_03.pdf>.
[HR08]: Ha, S. and I. Rhee, "Hybrid Slow Start for High-Bandwidth and Long-Distance Networks", International Workshop on Protocols for Fast Long-Distance Networks, March 2008, <http://www.hep.man.ac.uk/g/GDARN-IT/pfldnet2008/paper/Sangate_Ha%20Final.pdf>.
[HRX08]: Ha, S., Rhee, I., and L. Xu, "CUBIC: a new TCP-friendly high-speed TCP variant", ACM SIGOPS Operating Systems Review Vol. 42, pp. 64-74, DOI 10.1145/1400097.1400105, July 2008, <https://doi.org/10.1145/1400097.1400105>.
[K03]: Kelly, T., "Scalable TCP: improving performance in highspeed wide area networks", ACM SIGCOMM Computer Communication Review Vol. 33, pp. 83-91, DOI 10.1145/956981.956989, April 2003, <https://doi.org/10.1145/956981.956989>.
[RFC3465]: Allman, M., "TCP Congestion Control with Appropriate Byte Counting (ABC)", RFC 3465, DOI 10.17487/RFC3465, February 2003, <https://www.rfc-editor.org/rfc/rfc3465>.
[RFC3522]: Ludwig, R. and M. Meyer, "The Eifel Detection Algorithm for TCP", RFC 3522, DOI 10.17487/RFC3522, April 2003, <https://www.rfc-editor.org/rfc/rfc3522>.
[RFC3649]: Floyd, S., "HighSpeed TCP for Large Congestion Windows", RFC 3649, DOI 10.17487/RFC3649, December 2003, <https://www.rfc-editor.org/rfc/rfc3649>.
[RFC3708]: Blanton, E. and M. Allman, "Using TCP Duplicate Selective Acknowledgement (DSACKs) and Stream Control Transmission Protocol (SCTP) Duplicate Transmission Sequence Numbers (TSNs) to Detect Spurious Retransmissions", RFC 3708, DOI 10.17487/RFC3708, February 2004, <https://www.rfc-editor.org/rfc/rfc3708>.
[RFC3742]: Floyd, S., "Limited Slow-Start for TCP with Large Congestion Windows", RFC 3742, DOI 10.17487/RFC3742, March 2004, <https://www.rfc-editor.org/rfc/rfc3742>.
[RFC4960]: Stewart, R., Ed., "Stream Control Transmission Protocol", RFC 4960, DOI 10.17487/RFC4960, September 2007, <https://www.rfc-editor.org/rfc/rfc4960>.
[RFC5682]: Sarolahti, P., Kojo, M., Yamamoto, K., and M. Hata, "Forward RTO-Recovery (F-RTO): An Algorithm for Detecting Spurious Retransmission Timeouts with TCP", RFC 5682, DOI 10.17487/RFC5682, September 2009, <https://www.rfc-editor.org/rfc/rfc5682>.
[RFC7661]: Fairhurst, G., Sathiaseelan, A., and R. Secchi, "Updating TCP to Support Rate-Limited Traffic", RFC 7661, DOI 10.17487/RFC7661, October 2015, <https://www.rfc-editor.org/rfc/rfc7661>.
[RFC8312]: Rhee, I., Xu, L., Ha, S., Zimmermann, A., Eggert, L., and R. Scheffenegger, "CUBIC for Fast Long-Distance Networks", RFC 8312, DOI 10.17487/RFC8312, February 2018, <https://www.rfc-editor.org/rfc/rfc8312>.
[RFC8511]: Khademi, N., Welzl, M., Armitage, G., and G. Fairhurst, "TCP Alternative Backoff with ECN (ABE)", RFC 8511, DOI 10.17487/RFC8511, December 2018, <https://www.rfc-editor.org/rfc/rfc8511>.
[RFC9000]: Iyengar, J., Ed. and M. Thomson, Ed., "QUIC: A UDP-Based Multiplexed and Secure Transport", RFC 9000, DOI 10.17487/RFC9000, May 2021, <https://www.rfc-editor.org/rfc/rfc9000>.
[SXEZ19]: Sun, W., Xu, L., Elbaum, S., and D. Zhao, "Model-Agnostic and Efficient Exploration of Numerical State Space of Real-World TCP Congestion Control Implementations", USENIX NSDI 2019, February 2019, <https://www.usenix.org/system/files/nsdi19-sun.pdf>.
[XHR04]: Xu, L., Harfoush, K., and I. Rhee, "Binary Increase Congestion Control (BIC) for Fast Long-Distance Networks", IEEE INFOCOM 2004, DOI 10.1109/infcom.2004.1354672, March 2004, <https://doi.org/10.1109/infcom.2004.1354672>.

Appendix B. Evolution of CUBIC

B.1. Since draft-ietf-tcpm-rfc8312bis-02

Decription of packet loss rate p (#65)¶
Clarification of TCP Friendly Equation for ABC and Delayed ACK (#66)¶
add applicability to QUIC and SCTP (#61)¶
clarity on setting alpha_aimd to 1 (#68)¶
introduce alpha_cubic (#64)¶
clarify cwnd growth in convex region (#69)¶
add guidance for using bytes and mention that segments count is decimal (#67)¶
add loss events detected by RACK and QUIC loss detection (#62)¶

B.2. Since draft-ietf-tcpm-rfc8312bis-01

address Michael Scharf's editorial suggestions. (#59)¶
add "Note to the RFC Editor" about removing underscores¶

B.3. Since draft-ietf-tcpm-rfc8312bis-00

use updated xml2rfc with better text rendering of subscripts¶

B.4. Since draft-eggert-tcpm-rfc8312bis-03

fix spelling nits¶
rename to draft-ietf¶
define W_max more clearly¶

B.5. Since draft-eggert-tcpm-rfc8312bis-02

add definition for segments_acked and alpha_aimd. (#47)¶
fix a mistake in W_max calculation in the fast convergence section. (#51)¶
clarity on setting ssthresh and cwnd_start during multiplicative decrease. (#53)¶

B.6. Since draft-eggert-tcpm-rfc8312bis-01

rename TCP-Friendly to AIMD-Friendly and rename Standard TCP to AIMD TCP to avoid confusion as CUBIC has been widely used on the Internet. (#38)¶
change introductory text to reflect the significant broader deployment of CUBIC on the Internet. (#39)¶
rephrase introduction to avoid referring to variables that have not been defined yet.¶

B.7. Since draft-eggert-tcpm-rfc8312bis-00

acknowledge former co-authors (#15)¶
prevent cwnd from becoming less than two (#7)¶
add list of variables and constants (#5, #6)¶
update K's definition and add bounds for CUBIC target cwnd [SXEZ19] (#1, #14)¶
update W_est to use AIMD approach (#20)¶

set alpha_aimd to 1 once W_est reaches W_max (#2)¶
add Vidhi as co-author (#17)¶
note for Fast Recovery during cwnd decrease due to congestion event (#11)¶
add section for spurious congestion events (#23)¶
initialize W_est after timeout and remove variable W_{last_max} (#28)¶

B.8. Since RFC8312

converted to Markdown and xml2rfc v3¶
updated references (as part of the conversion)¶
updated author information¶
various formatting changes¶
move to Standards Track¶

B.9. Since the Original Paper

CUBIC has gone through a few changes since the initial release [HRX08] of its algorithm and implementation. Below we highlight the differences between its original paper and [RFC8312].¶

The original paper [HRX08] includes the pseudocode of CUBIC implementation using Linux's pluggable congestion control framework, which excludes system-specific optimizations. The simplified pseudocode might be a good source to start with and understand CUBIC.¶
[HRX08] also includes experimental results showing its performance and fairness.¶

The definition of beta_cubic constant was changed in [RFC8312]. For example, beta_cubic in the original paper was the window decrease constant while [RFC8312] changed it to CUBIC multiplication decrease factor. With this change, the current congestion window size after a congestion event in [RFC8312] was beta_cubic * W_max while it was (1-beta_cubic) * W_max in the original paper.¶
Its pseudocode used W_{last_max} while [RFC8312] used W_max.¶
Its AIMD-friendly window was W_tcp while [RFC8312] used W_est.¶