CUBIC for Fast and Long-Distance Networks

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 is detected by duplicate ACKs or Explicit Congestion Notification-Echo (ECN-Echo, ECE) ACKs [RFC3168], CUBIC remembers the congestion window size where 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 a large number of 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 of 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.¶

4.1. 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.¶

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 where a packet loss is detected by duplicate ACKs or by receiving packets carrying ECE flags [RFC3168], CUBIC changes the window increase function of AIMD TCP.¶

CUBIC uses the following window increase function:¶

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:¶

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:¶

1. The AIMD-friendly region, which ensures that CUBIC achieves at least the same throughput as AIMD TCP.¶
2. The concave region, if CUBIC is not in the AIMD-friendly region and cwnd is less than W_max.¶
3. 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_aimd (segments per RTT) and a multiplicative factor of β_aimd, denoted by AIMD(α_aimd, β_aimd). Specifically, the average congestion window size of AIMD(α_aimd, β_aimd) can be calculated using Figure 3. The analysis shows that AIMD(α_aimd, β_aimd) with¶

achieves the same average window size as AIMD TCP that uses AIMD(1, 0.5).¶

Based on the above analysis, CUBIC uses Figure 4 to estimate the window size W_est of AIMD(α_aimd, β_aimd) 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 once W_est reaches W_max, that is, W_est >= W_max, α_aimd SHOULD be set to 1 to 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.¶

In this region, CUBIC is very careful. The convex profile ensures that the window increases very slowly at the beginning and gradually increases its increase rate. 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 packet loss is detected by duplicate ACKs or by receiving packets carrying ECE flags, 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.¶

5.1. 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:¶

1. networks with a small bandwidth-delay product (BDP)¶
2. 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 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 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 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 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

CUBIC has 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]. Additionally, there is decade-long deployment experience with CUBIC on the Internet.¶

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.¶

B.1. Since draft-eggert-tcpm-rfc8312bis-03

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

B.2. 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.3. 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 in the Internet. (#38)¶
• change introductory text to reflect the significant broader deployment of CUBIC in the Internet. (#39)¶
• rephrase introduction to avoid referring to variables that have not been defined yet.¶

B.4. 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.5. 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.6. 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.¶