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Evolution of the transmission rates
Various types of rate adaption algorithms are possible. `Dah Ming Chiu`_ and `Raj Jain`_ have analyzed, 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 :
:math:`rate(t+1)=\alpha_C + \beta_C rate(t)` when the network is congested
:math:`rate(t+1)=\alpha_N + \beta_N rate(t)` when the network is *not* congested
With a linear adaption algorithm, :math:`\alpha_C,\alpha_N, \beta_C` and :math:`\beta_N` are 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 (:math:`\beta_N=1~and~\alpha_N>0`). When the network is congested, the hosts must multiplicatively decrease their transmission rate (:math:`\beta_C < 1~and~\alpha_C = 0`). Such an AIMD rate adaptation algorithm can be implemented by the pseudo-code below.
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 cooperation 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 acknowledgments 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.
Congestion control with a window-based transport protocol
AIMD controls congestion by adjusting the transmission rate of the sources in reaction to the current congestion level. If the network is not congested, the transmission rate increases. If congestion is detected, the transmission rate is multiplicatively decreased. In practice, directly adjusting the transmission rate can be difficult since it requires the utilization of fine grained timers. In reliable transport protocols, an alternative is to dynamically adjust the sending window. This is the solution chosen for protocols like TCP and SCTP that will be described in more details later. To understand how window-based protocols can adjust their transmission rate, let us consider the very simple scenario of a reliable transport protocol that uses `go-back-n`. Consider the very simple scenario shown in the figure below.
The links between the hosts and the routers have a bandwidth of 1 Mbps while the link between the two routers has a bandwidth of 500 Kbps. There is no significant propagation delay in this network. For simplicity, assume that hosts `A` and `B` send 1000 bits packets. The transmission of such a packet on a `host-router` (resp. `router-router` ) link requires 1 msec (resp. 2 msec). If there is no traffic in the network, the round-trip-time measured by host `A` to reach `D` is slightly larger than 4 msec. Let us observe the flow of packets with different window sizes to understand the relationship between sending window and transmission rate.
Consider first a window of one segment. This segment takes 4 msec to reach host `D`. The destination replies with an acknowledgment and the next segment can be transmitted. With such a sending window, the transmission rate is roughly 250 segments per second or 250 Kbps. This is illustrated in the figure below where each square of the grid corresponds to one millisecond.
Consider now a window of two segments. Host `A` can send two segments within 2 msec on its 1 Mbps link. If the first segment is sent at time :math:`t_{0}`, it reaches host `D` at :math:`t_{0}+4`. Host `D` replies with an acknowledgment that opens the sending window on host `A` and enables it to transmit a new segment. In the meantime, the second segment was buffered by router `R1`. It reaches host `D` at :math:`t_{0}+6` and an acknowledgment is returned. With a window of two segments, host `A` transmits at roughly 500 Kbps, i.e. the transmission rate of the bottleneck link.
Our last example is a window of four segments. These segments are sent at :math:`t_{0}`, :math:`t_{0}+1`, :math:`t_{0}+2` and :math:`t_{0}+3`. The first segment reaches host `D` at :math:`t_{0}+4`. Host `D` replies to this segment by sending an acknowledgment that enables host `A` to transmit its fifth segment. This segment reaches router `R1` at :math:`t_{0}+5`. At that time, router `R1` is transmitting the third segment to router `R2` and the fourth segment is still in its buffers. At time :math:`t_{0}+6`, host `D` receives the second segment and returns the corresponding acknowledgment. This acknowledgment enables host `A` to send its sixth segment. This segment reaches router `R1` at roughly :math:`t_{0}+7`. At that time, the router starts to transmit the fourth segment to router `R2`. Since link `R1-R2` can only sustain 500 Kbps, packets will accumulate in the buffers of `R1`. On average, there will be two packets waiting in the buffers of `R1`. The presence of these two packets will induce an increase of the round-trip-time as measured by the transport protocol. While the first segment was acknowledged within 4 msec, the fifth segment (`data(4)`) that was transmitted at time :math:`t_{0}+4` is only acknowledged at time :math:`t_{0}+11`. On average, the sender transmits at 500 Kbps, but the utilization of a large window induces a longer delay through the network.
From the above example, we can adjust the transmission rate by adjusting the sending window of a reliable transport protocol. A reliable transport protocol cannot send data faster than :math:`\frac{window}{rtt}` segments per second where :math:`window` is the current sending window. To control the transmission rate, we introduce a `congestion window`. This congestion window limits the sending window. At any time, the sending window is restricted to :math:`\min(swin,cwin)`, where `swin` is the sending window and `cwin` the current `congestion window`. Of course, the window is further constrained by the receive window advertised by the remote peer. With the utilization of a congestion window, a simple reliable transport protocol that uses fixed size segments could implement `AIMD` as follows.
For the `Additive Increase` part our simple protocol would simply increase its `congestion window` by one segment every round-trip-time. The `Multiplicative Decrease` part of `AIMD` could be implemented by halving the congestion window when congestion is detected. For simplicity, we assume that congestion is detected thanks to a binary feedback and that no segments are lost. We will discuss in more details how losses affect a real transport protocol like TCP in later sections.
A congestion control scheme for our simple transport protocol could be implemented as follows.
In the above pseudocode, `cwin` contains the congestion window stored as a real number of segments. This congestion window is updated upon the arrival of each acknowledgment and when congestion is detected. For simplicity, we assume that `cwin` is stored as a floating point number but only full segments can be transmitted.
As an illustration, let us consider the network scenario above and assume that the router implements the DECBit binary feedback scheme [RJ1995]_. This scheme uses a form of Forward Explicit Congestion Notification and a router marks the congestion bit in arriving packets when its buffer contains one or more packets. In the figure below, we use a `*` to indicate a marked packet.
When the connection starts, its congestion window is set to one segment. Segment `S0` is sent an acknowledgment at roughly :math:`t_{0}+4`. The congestion window is increased by one segment and `S1` and `S2` are transmitted at time :math:`t_{0}+4` and :math:`t_{0}+5`. The corresponding acknowledgments are received at times :math:`t_{0}+8` and :math:`t_{0}+10`. Upon reception of this last acknowledgment, the congestion window reaches `3` and segments can be sent (`S4` and `S5`). When segment `S6` reaches router `R1`, its buffers already contain `S5`. The packet containing `S6` is thus marked to inform the sender of the congestion. Note that the sender will only notice the congestion once it receives the corresponding acknowledgment at :math:`t_{0}+18`. In the meantime, the congestion window continues to increase. At :math:`t_{0}+16`, upon reception of the acknowledgment for `S5`, it reaches `4`. When congestion is detected, the congestion window is decreased down to `2`. This explains the idle time between the reception of the acknowledgment for `S*6` and the transmission of `S10`.
In practice, a router is connected to multiple input links. The figure below shows an example with two hosts.
In general, the links have a non-zero delay. This is illustrated in the figure below where a delay has been added on the link between `R` and `C`.
Footnotes
There are still some vendors that try to put as many buffers as possible on their routers. A recent example is the buffer bloat problem that plagues some low-end Internet routers [GN2011]_.
Some examples of the performance of various types of commercial networks nodes (routers and switches) may be found in http://www.cisco.com/web/partners/downloads/765/tools/quickreference/routerperformance.pdf and http://www.cisco.com/web/partners/downloads/765/tools/quickreference/switchperformance.pdf
Some networking technologies allow to adjust dynamically the bandwidth of links. For example, some devices can reduce their bandwidth to preserve energy. We ignore these technologies in this basic course and assume that all links used inside the network have a fixed bandwidth.
This name should not be confused with the duration of a transmission slot in slotted ALOHA. In CSMA/CD networks, the slot time is the time during which a collision can occur at the beginning of the transmission of a frame. In slotted ALOHA, the duration of a slot is the transmission time of an entire fixed-size frame.
In this section, we focus on congestion control mechanisms that regulate the transmission rate of the hosts. Other types of mechanisms have been proposed in the literature. For example, `credit-based` flow-control has been proposed to avoid congestion in ATM networks [KR1995]_. With a credit-based mechanism, hosts can only send packets once they have received credits from the routers and the credits depend on the occupancy of the router's buffers.
For example, the measurements performed in the Sprint network in 2004 reported more than 10k active TCP connections on a link, see https://research.sprintlabs.com/packstat/packetoverview.php. More recent information about backbone links may be obtained from caida_ 's real-time measurements, see e.g. http://www.caida.org/data/realtime/passive/

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For the `Additive Increase` part our simple protocol would simply increase its `congestion window` by one segment every round-trip-time. The `Multiplicative Decrease` part of `AIMD` could be implemented by halving the congestion window when congestion is detected. For simplicity, we assume that congestion is detected thanks to a binary feedback and that no segments are lost. We will discuss in more details how losses affect a real transport protocol like TCP in later sections.
For the `Additive Increase` part our simple protocol would simply increase its `congestion window` by one segment every round-trip-time. The `Multiplicative Decrease` part of `AIMD` could be implemented by halving the congestion window when congestion is detected. For simplicity, we assume that congestion is detected thanks to a binary feedback and that no segments are lost. We will discuss in more details how losses affect a real transport protocol like TCP in later sections.
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