## TCP Congestion Control

TCP's congestion control is one of its best performance control features. This section explains this feature and how it improves performance in the transport layer.

TCP congestion control

In the previous sections, we have explained the mechanisms that TCP uses to deal with transmission errors and segment losses. In a heterogeneous network such as the Internet or enterprise IP networks, endsystems have very different levels of performance. Some endsystems are high-end servers attached to 10 Gbps links while others are mobile devices attached to a very low bandwidth wireless link. Despite these huge differences in performance, a mobile device should be able to efficiently exchange segments with a high-end server.

To understand this problem better, let us consider the scenario shown in the figure below, where a server (A) Attached to a 10 Mbps link is sending TCP segments to another computer (C) through a path that contains a Mbps link.

Figure 4.51: TCP over heterogeneous links

In this network, the TCP segments sent by the server reach router R1. R1 forwards the segments towards router R2. Router R2 can potentially receive segments at 10 Mbps, but it can only forward them at 2 Mbps to router R2 and then to host C. Router R2 contains buffers that allow it to store the packets that cannot immediately be forwarded to their destination. To understand the operation of TCP in this environment, let us consider a simplified model of this network where host A is attached to a 10 Mbps link to a queue that represents the buffers of router R2. This queue is emptied at a rate of 2 Mbps.

Figure 4.52: TCP self clocking

Let us consider that host A uses a window of three segments. It thus sends three back-to-back segments at 10 Mbps and then waits for an acknowledgement. Host A stops sending segments when its window is full. These segments reach the buffers of router R2. The first segment stored in this buffer is sent by router R2 at a rate of Mbps to the destination host. Upon reception of this segment, the destination sends an acknowledgement. This acknowledgement allows host A to transmit a new segment. This segment is stored in the buffers of router R2 while it is transmitting the second segment that was sent by host A... Thus, after the transmission of the first window of segments, TCP sends one data segment after the reception of each acknowledgement returned by the destination 24. In practice, the acknowledgements sent by the destination serve as a kind of clock that allows the sending host to adapt its transmission rate to the rate at which segments are received by the destination. This TCP self-clocking is the first mechanism that allows TCP to adapt to heterogeneous networks [Jacobson1988]. It depends on the availability of buffers to store the segments that have been sent by the sender but have not yet been transmitted to the destination.

However, TCP is not always used in this environment. In the global Internet, TCP is used in networks where a large number of hosts send segments to a large number of receivers. For example, let us consider the network depicted below which is similar to the one discussed in [Jacobson1988] and RFC 896. In this network, we assume that the buffers of the router are infinite to ensure that no packet is lost.

Figure 4.53: The congestion collapse problem

If many TCP senders are attached to the left part of the network above, they all send a window full of segments. These segments are stored in the buffers of the router before being transmitted towards their destination. If there are many senders on the left part of the network, the occupancy of the buffers quickly grows. A consequence of the buffer occupancy is that the round-trip-time, measured by TCP, between the sender and the receiver increases. Consider a network where 10,000 bits segments are sent. When the buffer is empty, such a segment requires 1 millisecond to be transmitted on the 10 Mbps link and 5 milliseconds to be the transmitted on the 2 Mbps link. Thus, the round-trip-time measured by TCP is roughly 6 milliseconds if we ignore the propagation delay on the links. Most routers manage their buffers as a FIFO queue 25. If the buffer contains 100 segments, the round-trip-time becomes 1 + 100 × 5 + 5 milliseconds as new segments are only transmitted on the 2 Mbps link once all previous segments have been transmitted. Unfortunately, TCP uses a retransmission timer and performs go-back-n to recover from transmission errors. If the buffer occupancy is high, TCP assumes that some segments have been lost and retransmits a full window of segments. This increases the occupancy of the buffer and the delay through the buffer... Furthermore, the buffer may store and send on the low bandwidth links several retransmissions of the same segment. This problem is called congestion collapse. It occurred several times in the late 1980s. For example, [Jacobson1988] notes that in 1986, the usable bandwidth of a 32 Kbits link dropped to 40 bits per second due to congestion collapse 26 !

The congestion collapse is a problem that all heterogeneous networks face. Different mechanisms have been proposed in the scientific literature to avoid or control network congestion. Some of them have been implemented and deployed in real networks. To understand this problem in more detail, let us first consider a simple network with two hosts attached to a high bandwidth link that are sending segments to destination C attached to a low bandwidth link as depicted below.

Figure 4.54: The congestion problem

To avoid congestion collapse, the hosts must regulate their transmission rate 27 by using a congestion control mechanism. Such a mechanism can be implemented in the transport layer or in the network layer. In TCP/IP networks, it is implemented in the transport layer, but other technologies such as Asynchronous Transfer Mode (ATM) or Frame Relay include congestion control mechanisms in lower layers.

Let us first consider the simple problem of a set of i hosts that share a single bottleneck link as shown in the example above. In this network, the congestion control scheme must achieve the following objectives [CJ1989]:

1. The congestion control scheme must avoid congestion. In practice, this means that the bottle- neck link cannot be overloaded. If ri(t) is the transmission rate allocated to host i at time t and R the bandwidth of the bottleneck link, then the congestion control scheme should ensure that, on average, $\forall t \sum r_i (t) \leq R$.
2. The congestion control scheme must be efficient. The bottleneck link is usually both a shared and an expensive resource. Usually, bottleneck links are wide area links that are much more expensive to upgrade than the local area networks. The congestion control scheme should ensure that such links are efficiently used. Mathematically, the control scheme should ensure that $\forall t \sum r_i (t) \approx R$.
3. The congestion control scheme should be fair. Most congestion schemes aim at achieving max- min fairness. An allocation of transmission rates to sources is said to be max-min fair if:
• no link in the network is congested
• the rate allocated to source j cannot be increased without decreasing the rate allocated to a source i whose allocation is smaller than the rate allocated to source j [Leboudec2008].

Depending on the network, a max-min fair allocation may not always exist. In practice, max-min fairness is an ideal objective that cannot necessarily be achieved. When there is a single bottleneck link as in the example above, max-min fairness implies that each source should be allocated the same transmission rate.

To visualise the different rate allocations, it is useful to consider the graph shown below. In this graph, we plot on the x-axis (resp. y-axis) the rate allocated to host B (resp. A). A point in the graph (rB, rA) corresponds to a possible allocation of the transmission rates. Since there is a 2 Mbps bottleneck link in this network, the graph can be divided into two regions. The lower left part of the graph contains all allocations (rB, rA) such that the bottleneck link is not congested (rA+ rB< 2). The right border of this region is the efficiency line, i.e. the set of allocations that completely utilise the bottleneck link (rA+ rB= 2). Finally, the fairness line is the set of fair allocations.

Figure 4.55: Possible allocated transmission rates

As shown in the graph above, a rate allocation may be fair but not efficient (e.g. rA= 0.7, rB= 0.7), fair and efficient ( e.g. rA= 1, rB= 1) or efficient but not fair (e.g. rA= 1.5, rB= 0.5). Ideally, the allocation should be both fair and efficient. Unfortunately, maintaining such an allocation with fluctuations in the number of flows that use the network is a challenging problem. Furthermore, there might be several thousands of TCP connections or more that pass through the same link 28.

To deal with these fluctuations in demand, which result in fluctuations in the available bandwidth, computer networks use a congestion control scheme. This congestion control scheme should achieve the three objectives listed above. Some congestion control schemes rely on a close cooperation between the endhosts and the routers, while others are mainly implemented on the endhosts with limited support from the routers.

A congestion control scheme can be modelled as an algorithm that adapts the transmission rate (ri(t)) of host i based on the feedback received from the network. Different types of feedbacks are possible. The simplest scheme is a binary feedback [CJ1989] [Jacobson1988] where the hosts simply learn whether the network is congested or not. Some congestion control schemes allow the network to regularly send an allocated transmission rate in Mbps to each host [BF1995].

Let us focus on the binary feedback scheme which is the most widely used today. Intuitively, the congestion control scheme should decrease the transmission rate of a host when congestion has been detected in the network, in order to avoid congestion collapse. Furthermore, the hosts should increase their transmission rate when the network is not congested. Otherwise, the hosts would not be able to efficiently utilise the network. The rate allocated to each host fluctuates with time, depending on the feedback received from the network. The figure below illustrates the evolution of the transmission rates allocated to two hosts in our simple network. Initially, two hosts have a low allocation, but this is not efficient. The allocations increase until the network becomes congested. At this point, the hosts decrease their transmission rate to avoid congestion collapse. If the congestion control scheme works well, after some time the allocations should become both fair and efficient.

Figure 4.56: Evolution of the transmission rates

Various types of rate adaption algorithms are possible. Dah Ming Chiu and Raj Jain have analysed, in [CJ1989], different types of algorithms that can be used by a source to adapt its transmission rate to the feedback received from the network. Intuitively, such a rate adaptation algorithm increases the transmission rate when the network is not congested (ensure that the network is efficiently used) and decrease the transmission rate when the network is congested (to avoid congestion collapse).

The simplest form of feedback that the network can send to a source is a binary feedback (the network is congested or not congested). In this case, a linear rate adaptation algorithm can be expressed as:

• rate(t + 1) = αC+ βCrate(t) when the network is congested
• rate(t + 1) = αN+ βNrate(t) when the network is not congested

With a linear adaption algorithm, αC, αN, βCand βNare constants. The analysis of [CJ1989] shows that to be fair and efficient, such a binary rate adaption mechanism must rely on Additive Increase and Multiplicative Decrease. When the network is not congested, the hosts should slowly increase their transmission rate (βN= 1 and αN> 0). When the network is congested, the hosts must multiplicatively decrease their transmission rate (βC< 1 and αC= 0). Such an AIMD rate adaptation algorithm can be implemented by the pseudo-code below

# Additive Increase Multiplicative Decreaseif congestion: rate=rate*betaC # multiplicative decrease, betaC<1else rate=rate+alphaN # additive increase, v0>0

Note: Which binary feedback?

Two types of binary feedback are possible in computer networks. A first solution is to rely on implicit feedback. This is the solution chosen for TCP. TCP’s congestion control scheme [Jacobson1988] does not require any coop- eration from the router. It only assumes that they use buffers and that they discard packets when there is congestion.

TCP uses the segment losses as an indication of congestion. When there are no losses, the network is assumed to be not congested. This implies that congestion is the main cause of packet losses. This is true in wired networks, but unfortunately not always true in wireless networks. Another solution is to rely on explicit feedback. This is the solution proposed in the DECBit congestion control scheme [RJ1995] and used in Frame Relay and ATM networks. This explicit feedback can be implemented in two ways. A first solution would be to define a special message that could be sent by routers to hosts when they are congested. Unfortunately, generating such messages may increase the amount of congestion in the network. Such a congestion indication packet is thus discouraged RFC 1812. A better approach is to allow the intermediate routers to indicate, in the packets that they forward, their current congestion status. Binary feedback can be encoded by using one bit in the packet header. With such a scheme, congested routers set a special bit in the packets that they forward while non-congested routers leave this bit unmodified. The destination host returns the congestion status of the network in the acknowledgements that it sends. Details about such a solution in IP networks may be found in RFC 3168. Unfortunately, as of this writing, this solution is still not deployed despite its potential benefits.

The TCP congestion control scheme was initially proposed by Van Jacobson in [Jacobson1988]. The current specification may be found in RFC 5681. TCP relies on Additive Increase and Multiplicative Decrease (AIMD). To implement AIMD, a TCP host must be able to control its transmission rate. A first approach would be to use timers and adjust their expiration times in function of the rate imposed by AIMD. Unfortunately, maintaining such timers for a large number of TCP connections can be difficult. Instead, Van Jacobson noted that the rate of TCP congestion can be artificially controlled by constraining its sending window. A TCP connection cannot send data faster than $\frac{window}{rtt}$ where window is the maximum between the host’s sending window and the window advertised by the receiver.

TCP’s congestion control scheme is based on a congestion window. The current value of the congestion window (cwnd) is stored in the TCB of each TCP connection and the window that can be used by the sender is constrained by min(cwnd, rwin, swin) where swin is the current sending window and rwin the last received receive win- dow. The Additive Increase part of the TCP congestion control increments the congestion window by MSS bytes every round-trip-time. In the TCP literature, this phase is often called the congestion avoidance phase. The Multiplicative Decrease part of the TCP congestion control divides the current value of the congestion window once congestion has been detected.

When a TCP connection begins, the sending host does not know whether the part of the network that it uses to reach the destination is congested or not. To avoid causing too much congestion, it must start with a small congestion window. [Jacobson1988] recommends an initial window of MSS bytes. As the additive increase part of the TCP congestion control scheme increments the congestion window by MSS bytes every round-trip-time, the TCP connection may have to wait many round-trip-times before being able to efficiently use the available bandwidth. This is especially important in environments where the bandwidth × rtt product is high. To avoid waiting too many round-trip-times before reaching a congestion window that is large enough to efficiently utilise the network, the TCP congestion control scheme includes the slow-start algorithm. The objective of the TCP slow-start is to quickly reach an acceptable value for the cwnd. During slow-start, the congestion window is doubled every round-trip-time. The slow-start algorithm uses an additional variable in the TCB: sshtresh (slow- start threshold). The ssthresh is an estimation of the last value of the cwnd that did not cause congestion. It is initialised at the sending window and is updated after each congestion event.

In practice, a TCP implementation considers the network to be congested once its needs to retransmit a segment. The TCP congestion control scheme distinguishes between two types of congestion:

• mild congestion. TCP considers that the network is lightly congested if it receives three duplicate acknowl- edgements and performs a fast retransmit. If the fast retransmit is successful, this implies that only one segment has been lost. In this case, TCP performs multiplicative decrease and the congestion window is divided by 2. The slow-start threshold is set to the new value of the congestion window.
• severe congestion. TCP considers that the network is severely congested when its retransmission timer expires. In this case, TCP retransmits the first segment, sets the slow-start threshold to 50% of the congestion window. The congestion window is reset to its initial value and TCP performs a slow-start.

The figure below illustrates the evolution of the congestion window when there is severe congestion. At the beginning of the connection, the sender performs slow-start until the first segments are lost and the retransmission timer expires. At this time, the ssthresh is set to half of the current congestion window and the congestion window is reset at one segment. The lost segments are retransmitted as the sender again performs slow-start until the congestion window reaches the sshtresh. It then switches to congestion avoidance and the congestion window increases linearly until segments are lost and the retransmission timer expires...

Figure 4.57: Evaluation of the TCP congestion window with severe congestion

The figure below illustrates the evolution of the congestion window when the network is lightly congested and all lost segments can be retransmitted using fast retransmit. The sender begins with a slow-start. A segment is lost but successfully retransmitted by a fast retransmit. The congestion window is divided by 2 and the sender immediately enters congestion avoidance as this was a mild congestion.

Figure 4.58: Evaluation of the TCP congestion window when the network is lightly congested

Most TCP implementations update the congestion window when they receive an acknowledgement. If we assume that the receiver acknowledges each received segment and the sender only sends MSS sized segments, the TCP congestion control scheme can be implemented using the simplified pseudo-code 29 below

# Initialisationcwnd = MSS;ssthresh= swin; # Ack arrivalif tcp.ack > snd.una: # new ack, no congestion  if cwnd < ssthresh:    # slow-start: increase quickly cwnd    # double cwnd every rtt    cwnd = cwnd + MSS  else:    # congestion avoidance: increase slowly cwnd    # increase cwnd by one mss every rtt    cwnd = cwnd+ mss*(mss/cwnd)else: # duplicate or old ack  if tcp.ack==snd.una:                 # duplicate acknowledgement    dupacks++    if dupacks==3:      retransmitsegment(snd.una)      ssthresh=max(cwnd/2,2*MSS)      cwnd=ssthresh    else:      dupacks=0      # ack for old segment, ignored Expiration of the retransmission timer:  send(snd.una)                       # retransmit first lost segment   sshtresh=max(cwnd/2,2*MSS)  cwnd=MSS

Furthermore when a TCP connection has been idle for more than its current retransmission timer, it should reset its congestion window to the congestion window size that it uses when the connection begins, as it no longer knows the current congestion state of the network.

Note: Initial congestion window

The original TCP congestion control mechanism proposed in [Jacobson1988] recommended that each TCP con- nection should begin by setting cwnd = M SS. However, in today’s higher bandwidth networks, using such a small initial congestion window severely affects the performance for short TCP connections, such as those used by web servers. Since the publication of RFC 3390, TCP hosts are allowed to use an initial congestion window of about 4 KBytes, which corresponds to 3 segments in many environments.

Thanks to its congestion control scheme, TCP adapts its transmission rate to the losses that occur in the net- work. Intuitively, the TCP transmission rate decreases when the percentage of losses increases. Researchers have proposed detailed models that allow the prediction of the throughput of a TCP connection when losses occur [MSMO1997]. To have some intuition about the factors that affect the performance of TCP, let us consider a very simple model. Its assumptions are not completely realistic, but it gives us good intuition without requiring complex mathematics.

This model considers a hypothetical TCP connection that suffers from equally spaced segment losses. If p is the segment loss ratio, then the TCP connection successfully transfers $\frac{1}{p} - 1$ segments and the next segment is lost. If we ignore the slow-start at the beginning of the connection, TCP in this environment is always in congestion avoidance as there are only isolated losses that can be recovered by using fast retransmit. The evolution of the congestion window is thus as shown in the figure below. Note the that x-axis of this figure represents time measured in units of one round-trip-time, which is supposed to be constant in the model, and the y-axis represents the size of the congestion window measured in MSS-sized segments.

Figure 4.59: Evolution of the congestion window with regular losses

As the losses are equally spaced, the congestion window always starts at some value ( $\frac{W}{2}$ ), and is incremented by one MSS every round-trip-time until it reaches twice this value (W ). At this point, a segment is retransmitted and the cycle starts again. If the congestion window is measured in MSS-sized segments, a cycle lasts $\frac{W}{2}$ round-trip-times. The bandwidth of the TCP connection is the number of bytes that have been transmitted during a given period of time. During a cycle, the number of segments that are sent on the TCP connection is equal to the area of the yellow trapeze in the figure. Its area is thus:

$area = ( \frac{W}{2} )^2 + \frac{1}{2} \times ( \frac{W}{2} )^2 = \frac{3\times W^2}{8}$

However, given the regular losses that we consider, the number of segments that are sent between two losses (i.e. during a cycle) is by definition equal to $\frac{1}{p}$. Thus, $W = \sqrt{\frac{8}{3\times p}} = \frac{k}{\sqrt{p}}$. The throughput (in bytes per second) of the TCP connection is equal to the number of segments transmitted divided by the duration of the cycle:

$Throughput = \frac{area \times MSS}{time} = \frac{\frac{3\times W^2}{8}}{\frac{W}{2}\times rtt}$ or, after having eliminated W$Throughput = \sqrt{\frac{3}{2}} \times \frac{MSS}{rtt \times \sqrt{p}}$

More detailed models and the analysis of simulations have shown that a first order model of the TCP throughput when losses occur was $Throughput \approx \frac{k \times MSS}{rtt \times \sqrt{p}}$. T his is an important result which shows that:

• TCP connections with a small round-trip-time can achieve a higher throughput than TCP connections having a longer round-trip-time when losses occur. This implies that the TCP congestion control scheme is not completely fair since it favors the connections that have the shorter round-trip-time
• TCP connections that use a large MSS can achieve a higher throughput that the TCP connections that use a shorter MSS. This creates another source of unfairness between TCP connections. However, it should be noted that today most hosts are using almost the same MSS, roughly 1460 bytes.

In general, the maximum throughput that can be achieved by a TCP connection depends on its maximum window size and the round-trip-time if there are no losses. If there are losses, it depends on the MSS, the round-trip-time and the loss ratio.

$Throughput < min ( \frac{window}{rtt}, \frac{k \times MSS}{rtt \times \sqrt{p}} )$

Note: The TCP congestion control zoo

The first TCP congestion control scheme was proposed by Van Jacobson in [Jacobson1988]. In addition to writing the scientific paper, Van Jacobson also implemented the slow-start and congestion avoidance schemes in release 4.3 Tahoe of the BSD Unix distributed by the University of Berkeley. Later, he improved the congestion control by adding the fast retransmit and the fast recovery mechanisms in the Reno release of 4.3 BSD Unix. Since then, many researchers have proposed, simulated and implemented modifications to the TCP congestion control scheme. Some of these modifications are still used today, e.g.:

• NewReno ( RFC 3782), which was proposed as an improvement of the fast recovery mechanism in the Reno implementation
• TCP Vegas, which uses changes in the round-trip-time to estimate congestion in order to avoid it [BOP1994]
• CUBIC, which was designed for high bandwidth links and is the default congestion control scheme in the Linux 2.6.19 kernel [HRX2008]
• Compound TCP, which was designed for high bandwidth links is the default congestion control scheme in several Microsoft operating systems [STBT2009]

A search of the scientific literature will probably reveal more than 100 different variants of the TCP congestion control scheme. Most of them have only been evaluated by simulations. However, the TCP implementation in the recent Linux kernels supports several congestion control schemes and new ones can be easily added. We can expect that new TCP congestion control schemes will always continue to appear.