3.1.Principle 1 for the CUBIC Increase Function

For better network utilization and stability, CUBIC[HRX08] uses acubic window increase function in terms of the elapsed time from thelast congestion event. While most congestion controlalgorithms that provide alternatives to Reno increase the congestion window using convexfunctions, CUBIC uses both the concave and convex profiles of a cubicfunction for window growth.¶

After a window reduction in response to a congestion event detected byduplicate 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 itreceived the congestion event and performs a multiplicative decrease ofthe congestion window. When CUBIC enters into congestion avoidance, itstarts to increase the congestion window using the concave profile ofthe cubic function. The cubic function is set to have its plateau atthe remembered congestion window size, so that the concave windowincrease continues until then. After that, the cubic function turnsinto a convex profile and the convex window increase begins.¶

This style of window adjustment (concave and then convex) improvesalgorithm 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 thelast congestion event, where network utilization is deemed highest.Under steady state, most window size samples of CUBIC are close tothat remembered congestion window size, thus promoting high networkutilization and stability.¶

Note that congestion control algorithms that only use convex functionsto increase the congestion window size have their maximum incrementsaround the remembered congestion window size of the last congestionevent and thus introduce many packet bursts around thesaturation point of the network, likely causing frequent global losssynchronizations.¶

3.2.Principle 2 for Reno-Friendliness

CUBIC promotes per-flow fairness to Reno. Note that Renoperforms well over paths with small BDPs and onlyexperiences problems when attempting to increase bandwidth utilizationon paths with large BDPs.¶

A congestion control algorithm designed to be friendly to Reno ona per-flow basis must increase its congestion window less aggressivelyin small-BDP networks than in large-BDP networks.¶

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

Furthermore, in cases when the cubic function of CUBIC would increasethe congestion window less aggressively than Reno, CUBIC simplyfollows the window size of Reno to ensure that CUBIC achieves atleast the same throughput as Reno in small-BDP networks. The regionwhere CUBIC behaves like Reno is called the "Reno-friendlyregion".¶

3.3.Principle 3 for RTT-Fairness

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

Specifically, CUBIC maintains a window increase rate that is independent of RTTs outside the Reno-friendly region, and thus flows withdifferent RTTs have similar congestion window sizes under steady statewhen they operate outside the Reno-friendly region.¶

This notion of a linear throughput ratio is similar to that of Renounder an asynchronous loss model, where flows with different RTTshave the same packet loss rate but experience loss events at differenttimes. However, under a synchronous loss model, where flows with differentRTTs experience loss events at the same time but have different packet lossrates, the throughput ratio of Reno flows with different RTTs is quadraticallyproportional 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 fordifferent RTT flows, over wired Internet paths, use ofa linear throughput ratio seems more reasonable than equal throughputs(i.e., the same throughput for flows with different RTTs) or ahigher-order throughput ratio (e.g., a quadratic throughput ratio ofReno in synchronous loss environments).¶

3.4.Principle 4 for the CUBIC Decrease Factor

To achieve a balance between scalability and convergence speed, CUBIC sets themultiplicative window decrease factor to 0.7, whereas Reno uses0.5.¶

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

In such environments, even strict Multiplicative-IncreaseMultiplicative-Decrease (MIMD) can converge. CUBIC flows with the sameRTT always converge to the same throughput independently of statisticalmultiplexing, thus achieving intra-algorithm fairness.In environments with sufficient statistical multiplexing, theconvergence speed of CUBIC is reasonable.¶

4.1.Definitions

The unit of all window sizes in this document is segments of theSMSS, and the unit of all times is seconds.Implementations can use bytes to express window sizes, which wouldrequire factoring in the SMSS wherever necessaryand replacingsegments_acked (Figure 4) with the number of acknowledged bytes.¶

4.2.Window Increase Function

CUBIC maintains the ACK clocking of Reno byincreasing the congestion window only at the reception of a new ACK. Itdoes not make any changes to the TCP Fast Recovery and Fast Retransmitalgorithms[RFC6582][RFC6675].¶

During congestion avoidance, after a congestion event is detectedas described inSection 3.1, CUBIC uses a windowincrease function different from Reno.¶

CUBIC uses the following window increase function:¶

wheret is the elapsed time in seconds from the beginning of thecurrent congestion avoidance stage -- that is,¶

and wheret_epoch is the time at which the currentcongestion avoidance stage starts.  K is the time period that theabove function takes to increase the congestion window size at thebeginning of the current congestion avoidance stage toW_max if there are no further congestion events.  K iscalculated using the following equation:¶

wherecwnd_epoch is the congestion window at the beginningof the current congestion avoidance stage.¶

Upon receiving a new ACK during congestion avoidance, CUBIC computes thetarget congestion window size after the nextRTT usingFigure 1 asfollows, whereRTT is the smoothed round-trip time. The lower andupper bounds below ensure that CUBIC's congestion window increase rateis non-decreasing and is less than the increase rate of slow start[SXEZ19].¶

The elapsed timet inFigure 1MUST NOT include periods duringwhichcwnd has not been updated due to application-limited behavior(seeSection 5.8).¶

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

1. The Reno-friendly region, which ensures that CUBIC achieves atleast the same throughput as Reno.¶
2. The concave region, if CUBIC is not in the Reno-friendly regionandcwnd is less thanW_max.¶
3. The convex region, if CUBIC is not in the Reno-friendly region andcwnd is greater thanW_max.¶

To summarize, CUBIC computes both W_cubic(t) andW_est (seeSection 4.3) on receiving a new ACKin 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 thesenetworks, CUBIC remains in the Reno-friendly region to achieve atleast 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 anadditive factor of α (segments perRTT) anda multiplicative factor of β, denoted byAIMD(α, β).  p is the packet loss rate.Specifically, the average congestion window size ofAIMD(α, β) can becalculated usingFigure 3.¶

By the same analysis, to achieve an average window size similar to Renothat uses AIMD(1, 0.5), α must be equal to¶

Thus, CUBIC usesFigure 4 to estimate the windowsizeW_est in the Reno-friendly region with¶

which achieves approximately the same average window size as Reno inmany cases. The model used to calculate α_cubic is notabsolutely precise, but analysis and simulation as discussed in[AIMD-friendliness],as well as over a decade of experience with CUBIC in the publicInternet, show that this approach produces acceptable levels ofrate fairness between CUBIC and Reno flows. Also, no significantdrawbacks of the model have been reported. However, continued detailedanalysis of this approach would be beneficial. Whenreceiving a new ACK in congestion avoidance (wherecwnd could begreater than or less thanW_max), CUBIC checks whetherW_cubic(t) is less thanW_est.  If so, CUBIC isin the Reno-friendly region andcwndSHOULD be set toW_est at each reception of a new ACK.¶

W_est is set equal tocwnd_epoch at the startof the congestion avoidance stage. After that, on every new ACK,W_est is updated usingFigure 4. Note that this equationusessegments_acked andcwnd is measured in segments. An implementationthat measurescwnd in bytes should adjust the equation accordingly usingthe number of acknowledged bytes and the SMSS. Also note that this equation works forconnections with enabled or disabled delayed ACKs[RFC5681], assegments_acked will be different based on the segments actuallyacknowledged by a new ACK.¶

OnceW_est has grown to reach thecwnd at the time ofmost recently settingssthresh -- that is,W_est >=cwnd_prior --the senderSHOULD set α_cubic to 1 to ensure thatit 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 anduses the window increase function described inSection 4.2. Althoughcwnd is incremented in the same way for both concave and convex regions,they are discussed separately to analyze and understand the differencebetween the two regions.¶

4.4.Concave Region

When receiving a new ACK in congestion avoidance, if CUBIC is not in theReno-friendly region andcwnd is less thanW_max, thenCUBIC is in the concave region. In this region,cwndMUST beincremented by¶

for each received new ACK, wheretarget is calculated as described inSection 4.2.¶

4.5.Convex Region

When receiving a new ACK in congestion avoidance, if CUBIC is not in theReno-friendly region andcwnd is larger than or equal toW_max, then CUBIC is in the convex region.¶

The convex region indicates that the network conditions might havechanged since the last congestion event, possibly implying moreavailable bandwidth after some flow departures. Since the Internet ishighly asynchronous, some amount of perturbation is always possiblewithout 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 toincrease the window very slowly at the beginning whencwnd isaroundW_max and then gradually increases its rate of increase.This region is also called the "maximum probing phase", since CUBIC issearching for a newW_max.  In this region,cwndMUST beincremented by¶

for each received new ACK, wheretarget is calculated as described inSection 4.2.¶

4.6.Multiplicative Decrease

When a congestion event is detected by the mechanisms described inSection 3.1, CUBIC updatesW_max and reducescwndandssthresh immediately, as described below.In the case of packet loss, the senderMUST reducecwndandssthresh immediately upon entering loss recovery, similar to[RFC5681] (and[RFC6675]). Note that other mechanisms,such as Proportional Rate Reduction[RFC6937], can be usedto reduce the sending rate during loss recovery more gradually.The parameter β_cubicSHOULD be set to 0.7, whichis different from the multiplicative decrease factor used in[RFC5681](and[RFC6675]) during fast recovery.¶

InFigure 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 periodsor periods when unable to send at the full rate permitted bycwndcould easily encounter notable variations in the volume of data sentfrom one RTT to another, resulting inflight_size that issignificantly less thancwnd when there is a congestion event. Thecongestion response would therefore decreasecwnd to a much lowervalue than necessary. To avoid such suboptimal performance, themechanisms described in[RFC7661] can be used.[RFC7661] describes how to manage and usecwnd andssthresh during a rate-limited interval,and how to updatecwnd andssthresh after congestion has been detected. Themechanisms defined in[RFC7661] are safe to use even whencwnd isgreater than the receive window, because they validatecwnd based onthe amount of data acknowledged by the network in an RTT, whichimplicitly accounts for the allowed receive window.¶

Some implementations of CUBIC currently usecwnd instead offlight_size when calculating a newssthresh.  Implementations thatusecwndMUST use other measures to preventcwnd from growing whenthe volume of bytes in flight is smaller thancwnd.  This alsoeffectively preventscwnd from growing beyond the receive window. Suchmeasures are important for preventing a CUBIC sender from using anarbitrarily high cwndvalue when calculating new values forssthresh andcwnd when congestion is detected. This might not be asrobust as the mechanisms described in[RFC7661].¶

A QUIC sender that uses acwndvalue to calculate new values forcwnd andssthresh after detecting a congestion event isREQUIRED to applysimilar mechanisms[RFC9002].¶

A side effect of setting β_cubic to a value biggerthan 0.5 is that packet loss can happen for more than one RTT in certaincases, 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_cubiccould help limit packet loss to a single round, it would require detailedanalyses and large-scale evaluations to validate such algorithms.¶

Note that CUBICMUST continue to reducecwnd in response to congestionevents 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 acwnd of 1 SMSSMUST reduce its sending rate even further. This can be achievedby using a retransmission timer with exponential backoff, asdescribed in[RFC3168].¶

4.7.Fast Convergence

To improve convergence speed, CUBIC uses a heuristic. When a new flowjoins the network, existing flows need to give up some of theirbandwidth to allow the new flow some room for growth if the existingflows have been using all the network bandwidth. To speed up thisbandwidth release by existing flows, the following fast convergencemechanismSHOULD be implemented.¶

With fast convergence, when a congestion event occurs,W_maxis updated as follows, before the window reduction describedinSection 4.6.¶

During a congestion event, if the currentcwnd is less thanW_max, this indicates that the saturation pointexperienced by this flow is getting reduced because of a change inavailable bandwidth. This flow can then release more bandwidthby reducingW_max further. This action effectivelylengthens the time for this flow to increase its congestion window,because the reducedW_max forces the flow to plateauearlier. This allows more time for the new flow to catch up to itscongestion window size.¶

Fast convergence is designed for network environments with multipleCUBIC flows. In network environments with only a single CUBIC flow andwithout any other traffic, fast convergenceSHOULD be disabled.¶

4.8.Timeout

In the case of a timeout, CUBIC follows Reno to reducecwnd[RFC5681] but setsssthresh using β_cubic(same as inSection 4.6) in a way that is different from Reno TCP[RFC5681].¶

During the first congestion avoidance stage after a timeout, CUBICincreases its congestion window size usingFigure 1, wheret is theelapsed time since the beginning of the current congestion avoidance stage,K is set to 0, andW_max is set to the congestion windowsize at the beginning of the current congestion avoidance stage. Inaddition, for the Reno-friendly region,W_estSHOULD beset to the congestion window size at the beginning of the currentcongestion avoidance stage.¶

4.9.Spurious Congestion Events

In cases where CUBIC reduces its congestion window in response tohaving detected packet loss via duplicate ACKs or timeouts, it ispossible that the missing ACK could arrive after the congestionwindow reduction and a corresponding packet retransmission. Forexample, packet reordering could trigger this behavior. A high degreeof packet reordering could cause multiple congestion window reductionevents, where spurious losses are incorrectly interpreted ascongestion signals, thus degrading CUBIC's performance significantly.¶

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

4.10.Slow Start

Whencwnd is no more thanssthresh, CUBICMUST employ a slow start algorithm. In general, CUBICSHOULD use the HyStart++ slow startalgorithm[RFC9406] orMAY use the Reno TCPslow start algorithm[RFC5681] in the rare cases whenHyStart++ is not suitable. Experimental alternatives includehybrid slow start[HR11], a predecessor to HyStart++ that some CUBICimplementations have used as the default for the last decade, andlimited slow start[RFC3742]. Whichever startup algorithm is used,work might be needed to ensure that the end of slow start and the firstmultiplicative decrease of congestion avoidance work well together.¶

When CUBIC uses HyStart++[RFC9406], it mayexit the first slow start without incurring any packet loss andthusW_max is undefined. In this special case, CUBICsetscwnd_prior = cwnd and switches to congestion avoidance.It then increases its congestion windowsize usingFigure 1, wheret is the elapsed time since the beginningof the current congestion avoidance stage,K is set to 0,andW_max is set to the congestion window size at thebeginning of the current congestion avoidance stage.¶

5.1.Fairness to Reno

In environments where Reno is able to make reasonable use of theavailable 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 abovetwo types of networks. The following two tables show the averagewindow sizes of Reno TCP, HSTCP, and CUBIC TCP. The average window sizesof Reno TCP and HSTCP are from[RFC3649]. The average window sizeof CUBIC is calculated usingFigure 7 and the CUBIC Reno-friendlyregion for three different values ofC.¶

Table 1 describes the response function of Reno TCP, HSTCP, and CUBICin networks withRTT = 0.1 seconds. The average window size is inSMSS-sized segments.¶

Table 2 describes the response function of Reno TCP, HSTCP, and CUBICin networks withRTT = 0.01 seconds. The average window size is inSMSS-sized segments.¶

Both tables show that CUBIC with any of these threeC values is morefriendly to Reno TCP than HSTCP, especially in networks with a shortRTT where Reno TCP performs reasonably well. For example, in anetwork withRTT = 0.01 seconds and p=10^-6, Reno TCP has an averagewindow of 1200 packets. If the packet size is 1500 bytes, then RenoTCP can achieve an average rate of 1.44 Gbps. In this case, CUBIC withC=0.04 orC=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 incompeting with other congestion control algorithms for bandwidth.CUBIC is more friendly to Reno TCP if the value ofC is lower.However, it isNOT RECOMMENDED to setC to a very low value like0.04, since CUBIC with a lowC cannot efficiently use the bandwidthin fast and long-distance networks. Based on these observations andextensive deployment experience,C=0.4 seems to provide a good balancebetween Reno-friendliness and aggressiveness of window increase.Therefore,CSHOULD be set to 0.4. WithC set to 0.4,Figure 7 isreduced to¶

Figure 8 is then used in the next subsection to show the scalability ofCUBIC.¶

5.2.Using Spare Capacity

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

Table 3 shows that to achieve the 10 Gbps rate, Reno TCPrequires a packet loss rate of 2.0e-10, while CUBIC TCP requires a packetloss 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 packetsand anRTT of 0.1 seconds.¶

The test results provided in[HLRX07] indicate that, in typical cases with adegree of background traffic, CUBIC uses the sparebandwidth left unused by existing Reno TCP flows in the samebottleneck link without taking away much bandwidth from the existingflows.¶

5.3.Difficult Environments

CUBIC is designed to remedy the poor performance of Reno in fastand long-distance networks.¶

5.4.Investigating a Range of Environments

CUBIC has been extensively studied using simulations,testbed emulations, Internet experiments, and Internetmeasurements, covering a wide range of network environments[HLRX07][H16][CEHRX09][HR11][BSCLU13][LBEWK16].They have convincingly demonstratedthat CUBIC delivers substantial benefits overclassical 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 fasterwindow increase function and bigger multiplicative decrease factor)than Reno in fast and long-distance networks, it can fill largedrop-tail buffers more quickly than Reno and increases the risk of astanding queue[RFC8511]. In this case, proper queue sizing andmanagement[RFC7567] could be used to mitigate the risk to someextent and reduce the packet queuing delay. Also, in large-BDPnetworks after a congestion event, CUBIC, due to its cubic windowincrease function, recovers quickly to the highest link utilizationpoint. This means that link utilization is less sensitive to an activequeue management (AQM) target that is lower than the amplitude of thewhole sawtooth.¶

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

5.5.Protection against Congestion Collapse

With regard to the potential of causing congestion collapse, CUBICbehaves like Reno, since CUBIC modifies only the window adjustmentalgorithm of Reno. Thus, it does not modify the ACK clocking andtimeout behaviors of Reno.¶

CUBIC also satisfies the "full backoff" requirement as described in[RFC5033]. After reducing the sending rate to one packet perRTT in response to congestion events detected by ECN-Echo ACKs, CUBICthen exponentially increases the transmissiontimer 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 RTTin the same bottleneck links to an equal throughput. When competingflows have different RTT values, their throughput ratio is linearlyproportional to the inverse of their RTT ratios. This is true and isindependent 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 inSection 3.4.¶

5.7.Performance with Misbehaving Nodes and Outside Attackers

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

5.8.Behavior for Application-Limited Flows

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

CUBIC does not increase its congestion window if a flow is application limited.PerSection 4.2, it is required thatt inFigure 1 not includeapplication-limited periods, such as idle periods; otherwise,W_cubic(t) might be very high after restarting from theseperiods.¶

5.9.Responses to Sudden or Transient Events

If there is a sudden increase in capacity, e.g., due to variable radiocapacity, a routing change, or a mobility event, CUBIC is designed toutilize the newly available capacity more quickly than Reno.¶

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

5.10.Incremental Deployment

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