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 congestion control algorithms that provide alternatives to Reno 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 acknowledgments (ACKs), Explicit Congestion Notification-Echo (ECN-Echo (ECE)) ACKs [RFC3168], RACK-TLP for TCP [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 algorithm stability while maintaining high network utilization [CEHRX09]. 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 Reno-Friendliness

CUBIC promotes per-flow fairness to Reno. Note that Reno performs well over paths with small BDPs and only experiences problems when attempting to increase bandwidth utilization on paths with large BDPs.¶

A congestion control algorithm designed to be friendly to Reno 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 Reno, CUBIC simply follows the window size of Reno to ensure that CUBIC achieves at least the same throughput as Reno in small-BDP networks. The region where CUBIC behaves like Reno is called the "Reno-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 that is independent of RTTs outside the Reno-friendly region, and thus flows with different RTTs have similar congestion window sizes under steady state when they operate outside the Reno-friendly region.¶

This notion of a linear throughput ratio is similar to that of Reno under an asynchronous loss model, where flows with different RTTs have the same packet loss rate but experience loss events at different times. However, under a synchronous loss model, where flows with different RTTs experience loss events at the same time but have different packet loss rates, the throughput ratio of Reno flows with different RTTs is quadratically proportional to the inverse of their RTT ratio [XHR04].¶

CUBIC always ensures a linear throughput ratio that is independent of the loss environment. This is an improvement over Reno. While there is no consensus on the optimal throughput ratio for different RTT flows, 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 quadratic throughput ratio of Reno in synchronous loss environments).¶

3.4. Principle 4 for the CUBIC Decrease Factor

To achieve a balance between scalability and convergence speed, CUBIC sets the multiplicative window decrease factor to 0.7, whereas Reno 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 independently of statistical multiplexing, thus achieving intra-algorithm fairness. 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 SMSS, and the unit of all times is seconds. Implementations can use bytes to express window sizes, which would require factoring in the SMSS wherever necessary and replacing segments_acked (Figure 4) with the number of acknowledged bytes.¶

4.2. Window Increase Function

CUBIC maintains the ACK clocking of Reno by increasing the congestion window only at the reception of a new 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 as described in Section 3.1, CUBIC uses a window increase function different from Reno.¶

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 t_epoch 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.  K is calculated using the following equation:¶

where cwnd_epoch is the congestion window at the beginning of the current congestion avoidance stage.¶

Upon receiving a new 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 [SXEZ19].¶

The elapsed time t in Figure 1 MUST NOT include periods during which cwnd has not been updated due to application-limited behavior (see Section 5.8).¶

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

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

To summarize, CUBIC computes both W_cubic(t) and W_est (see Section 4.3) on receiving a new ACK in congestion avoidance and chooses the larger of the two values.¶

The next sections describe the exact actions taken by CUBIC in each region.¶

4.3. Reno-Friendly Region

Reno 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 Reno-friendly region to achieve at least the same throughput as Reno.¶

The Reno-friendly region is designed according to the analysis discussed 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.¶

By the same analysis, to achieve an average window size similar to Reno 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 Reno-friendly region with¶

which achieves approximately the same average window size as Reno in many cases. The model used to calculate α_cubic is not absolutely precise, but analysis and simulation as discussed in [AIMD-friendliness], as well as over a decade of experience with CUBIC in the public Internet, show that this approach produces acceptable levels of rate fairness between CUBIC and Reno flows. Also, no significant drawbacks of the model have been reported. However, continued detailed analysis of this approach would be beneficial. When receiving a new 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 Reno-friendly region and cwnd SHOULD be set to W_est at each reception of a new ACK.¶

W_est is set equal to cwnd_epoch at the start of the congestion avoidance stage. After that, on every new ACK, W_est is updated using Figure 4. Note that this equation uses segments_acked and cwnd is measured in segments. An implementation that measures cwnd in bytes should adjust the equation accordingly using the number of acknowledged bytes and the SMSS. 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 a new ACK.¶

Once W_est has grown to reach the cwnd at the time of most recently setting ssthresh -- that is, W_est >= cwnd_prior -- the sender SHOULD set α_cubic to 1 to ensure that it can achieve the same congestion window increment rate as Reno, which uses AIMD(1, 0.5).¶

The next two sections assume that CUBIC is not in the Reno-friendly region and uses the window increase function described in Section 4.2. Although cwnd is incremented in the same way for both concave and convex regions, they are discussed separately to analyze and understand the difference between the two regions.¶

4.4. Concave Region

When receiving a new ACK in congestion avoidance, if CUBIC is not in the Reno-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 new ACK, where target is calculated as described in Section 4.2.¶

4.5. Convex Region

When receiving a new ACK in congestion avoidance, if CUBIC is not in the Reno-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 the cwnd is overridden by the AIMD window increase, CUBIC will behave cautiously when operating 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. This region is also called the "maximum probing phase", since CUBIC is searching for a new W_max.  In this region, cwnd MUST be incremented by¶

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

4.6. Multiplicative Decrease

When a congestion event is detected by the mechanisms described in Section 3.1, CUBIC updates W_max and reduces cwnd and ssthresh immediately, as described below. In the case of packet loss, the sender MUST reduce cwnd and ssthresh immediately upon entering loss recovery, similar to [RFC5681] (and [RFC6675]). Note that other mechanisms, such as Proportional Rate Reduction [RFC6937], can be used to reduce the sending rate during loss recovery more gradually. The parameter β_cubic SHOULD be set to 0.7, which is different from the multiplicative decrease factor used in [RFC5681] (and [RFC6675]) during fast recovery.¶

In Figure 5, flight_size is the amount of outstanding (unacknowledged) data in the network, as defined in [RFC5681]. Note that a rate-limited application with idle periods or periods when unable to send at the full rate permitted by cwnd could easily encounter notable variations in the volume of data sent from one RTT to another, resulting in flight_size that is significantly less than cwnd when there is a congestion event. The congestion response would therefore decrease cwnd to a much lower value than necessary. To avoid such suboptimal performance, the mechanisms described in [RFC7661] can be used. [RFC7661] describes how to manage and use cwnd and ssthresh during a rate-limited interval, and how to update cwnd and ssthresh after congestion has been detected. The mechanisms defined in [RFC7661] are safe to use even when cwnd is greater than the receive window, because they validate cwnd based on the amount of data acknowledged by the network in an RTT, which implicitly accounts for the allowed receive window.¶

Some implementations of CUBIC currently use cwnd instead of flight_size when calculating a new ssthresh.  Implementations that use cwnd MUST use other measures to prevent cwnd from growing when the volume of bytes in flight is smaller than cwnd.  This also effectively prevents cwnd from growing beyond the receive window. Such measures are important for preventing a CUBIC sender from using an arbitrarily high cwnd value when calculating new values for ssthresh and cwnd when congestion is detected. This might not be as robust as the mechanisms described in [RFC7661].¶

A QUIC sender that uses a cwnd value to calculate new values for cwnd and ssthresh after detecting a congestion event is REQUIRED to apply similar mechanisms [RFC9002].¶

A side effect of setting β_cubic to a value bigger than 0.5 is that packet loss can happen for more than one RTT in certain cases, but it can work efficiently in other cases -- for example, when HyStart++ [RFC9406] is used along with CUBIC or when the sending rate is limited by the application. While a more adaptive setting of β_cubic could help limit packet loss to a single round, it would require detailed analyses and large-scale evaluations to validate such algorithms.¶

Note that CUBIC MUST continue to reduce cwnd in response to congestion events detected by ECN-Echo ACKs until it reaches a value of 1 SMSS. If congestion events indicated by ECN-Echo ACKs persist, a sender with a cwnd of 1 SMSS MUST reduce its sending rate even further. This can be achieved by using a retransmission timer with exponential backoff, as described in [RFC3168].¶

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, W_max is updated as follows, before the window reduction described in Section 4.6.¶

During 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. This flow can then 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 the case of a timeout, CUBIC follows Reno to reduce cwnd [RFC5681] but sets ssthresh using β_cubic (same as in Section 4.6) in a way that is different from Reno 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 stage, 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 Reno-friendly region, W_est SHOULD be set to the congestion window size at the beginning of the current congestion avoidance stage.¶

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, it is possible that the missing ACK could 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.¶

For TCP, there are two types of spurious events: spurious timeouts and spurious fast retransmits. In the case of QUIC, there are no spurious timeouts, as the loss is only detected after receiving an ACK.¶

4.10. Slow Start

When cwnd is no more than ssthresh, CUBIC MUST employ a slow start algorithm. In general, CUBIC SHOULD use the HyStart++ slow start algorithm [RFC9406] or MAY use the Reno TCP slow start algorithm [RFC5681] in the rare cases when HyStart++ is not suitable. Experimental alternatives include hybrid slow start [HR11], a predecessor to HyStart++ that some CUBIC implementations have used as the default for the last decade, and limited slow start [RFC3742]. Whichever startup algorithm is used, work might be needed to ensure that the end of slow start and the first multiplicative decrease of congestion avoidance work well together.¶

When CUBIC uses HyStart++ [RFC9406], it may exit the first slow start without incurring any packet loss and thus W_max is undefined. In this special case, CUBIC sets cwnd_prior = cwnd and switches to congestion avoidance. It then increases its congestion window size using Figure 1, where t is the elapsed time since the beginning of the current congestion avoidance stage, 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 Reno

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

Reno performs well in the following two types of networks:¶

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

CUBIC is designed to behave very similarly to Reno in the above two types of networks. The following two tables show the average window sizes of Reno TCP, HSTCP, and CUBIC TCP. The average window sizes of Reno TCP and HSTCP are from [RFC3649]. The average window size of CUBIC is calculated using Figure 7 and the CUBIC Reno-friendly region for three different values of C.¶

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

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

Both tables show that CUBIC with any of these three C values is more friendly to Reno TCP than HSTCP, especially in networks with a short RTT where Reno TCP performs reasonably well. For example, in a network with RTT = 0.01 seconds and p=10^-6, Reno TCP has an average window of 1200 packets. If the packet size is 1500 bytes, then Reno 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 Reno TCP, whereas HSTCP is about ten times more aggressive than Reno TCP.¶

C determines the aggressiveness of CUBIC in competing with other congestion control algorithms for bandwidth. CUBIC is more friendly to Reno TCP if the value of C is lower. However, it is NOT RECOMMENDED to set 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, C=0.4 seems to provide a good balance between Reno-friendliness and aggressiveness of window increase. Therefore, C SHOULD be set to 0.4. With C set to 0.4, Figure 7 is reduced to¶

Figure 8 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 Reno for fast and long-distance networks.¶

Table 3 shows that to achieve the 10 Gbps rate, Reno TCP requires a packet loss rate of 2.0e-10, while CUBIC TCP requires a packet loss rate of 2.9e-8.¶

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

The test results provided in [HLRX07] indicate that, in typical cases with a degree of background traffic, CUBIC uses the spare bandwidth left unused by existing Reno 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 Reno in fast and long-distance networks.¶

5.4. Investigating a Range of Environments

CUBIC has been extensively studied using simulations, testbed emulations, Internet experiments, and Internet measurements, covering a wide range of network environments [HLRX07] [H16] [CEHRX09] [HR11] [BSCLU13] [LBEWK16]. They have convincingly demonstrated that CUBIC delivers substantial benefits over classical Reno congestion control [RFC5681].¶

Same as Reno, 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 Reno in fast and long-distance networks, it can fill large drop-tail buffers more quickly than Reno and increases the risk of a standing queue [RFC8511]. In this case, proper queue sizing and management [RFC7567] could be used to mitigate the risk to some extent and reduce the packet queuing delay. Also, in large-BDP networks after a congestion event, CUBIC, due to its cubic window increase function, recovers quickly to the highest link utilization point. This means that link utilization is less sensitive to an active queue management (AQM) target that is lower than the amplitude of the whole sawtooth.¶

Similar to Reno, the performance of CUBIC as a loss-based congestion control algorithm suffers in networks where packet loss is not a good indication of bandwidth utilization, such as wireless or mobile networks [LIU16].¶

5.5. Protection against Congestion Collapse

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

CUBIC also satisfies the "full backoff" requirement as described in [RFC5033]. After reducing the sending rate to one packet per RTT in response to congestion events detected by ECN-Echo ACKs, CUBIC then exponentially increases the transmission timer for each packet retransmission while congestion persists.¶

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 and is independent of the level of statistical multiplexing on the link. The convergence time depends on the network environments (e.g., bandwidth, RTT) and the level of statistical multiplexing, as mentioned in Section 3.4.¶

5.7. Performance with Misbehaving Nodes and Outside Attackers

CUBIC does not introduce new entities or signals, so its vulnerability to misbehaving nodes or attackers is unchanged from Reno.¶

5.8. Behavior for Application-Limited Flows

A flow is application limited if it is currently sending less than what is allowed by the congestion window. This can happen if the flow is limited by either the sender application or the receiver application (via the receiver's advertised window) and thus sends less data than what is allowed by the sender's congestion window.¶

CUBIC does not increase its congestion window if a flow is application limited. Per Section 4.2, it is required that t in Figure 1 not include application-limited periods, such as idle 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 increase in capacity, e.g., due to variable radio capacity, a routing change, or a mobility event, CUBIC is designed to utilize the newly available capacity more quickly than Reno.¶

On the other hand, if there is a sudden decrease in capacity, CUBIC reduces more slowly than Reno. This remains true regardless of whether CUBIC is in Reno-friendly mode and regardless of whether fast convergence is enabled.¶

5.10. Incremental Deployment

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