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Most TCP implementations update the congestion window when they receive an acknowledgment. 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 [#fwrap]_ below. This pseudocode includes the optimization proposed in :rfc:`3042` that allows a sender to send new unsent data upon reception of the first or second duplicate acknowledgment. The reception of each of these acknowledgment indicates that one segment has left the network and thus additional data can be sent without causing more congestion. Note that the congestion window is *not* increased upon reception of these first duplicate acknowledgments.
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.
Initial congestion window
The original TCP congestion control mechanism proposed in [Jacobson1988]_ recommended that each TCP connection should begin by setting :math:`cwnd=MSS`. 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. In 2002, :rfc:`3390` allowed an initial congestion window of about 4 KBytes, which corresponds to 3 segments in many environments. Recently, researchers from Google proposed to further increase the initial window up to 15 KBytes [DRC+2010]_. The measurements that they collected show that this increase would not significantly increase congestion but would significantly reduce the latency of short HTTP responses. Unsurprisingly, the chosen initial window corresponds to the average size of an HTTP response from a search engine. This proposed modification has been adopted in :rfc:`6928` and TCP implementations support it.
Controlling congestion without losing data
In today's Internet, congestion is controlled by regularly sending packets at a higher rate than the network capacity. These packets fill the buffers of the routers and are eventually discarded. But shortly after, TCP senders retransmit packets containing exactly the same data. This is potentially a waste of resources since these successive retransmissions consume resources upstream of the router that discards the packets. Packet losses are not the only signal to detect congestion inside the network. An alternative is to allow routers to explicitly indicate their current level of congestion when forwarding packets. This approach was proposed in the late 1980s [RJ1995]_ and used in some networks. Unfortunately, it took almost a decade before the Internet community agreed to consider this approach. In the mean time, a large number of TCP implementations and routers were deployed on the Internet.
As explained earlier, Explicit Congestion Notification :rfc:`3168` improves the detection of congestion by allowing routers to explicitly mark packets when they are lightly congested. In theory, a single bit in the packet header [RJ1995]_ is sufficient to support this congestion control scheme. When a host receives a marked packet, it returns the congestion information to the source that adapts its transmission rate accordingly. Although the idea is relatively simple, deploying it on the entire Internet has proven to be challenging [KNT2013]_. It is interesting to analyze the different factors that have hindered the deployment of this technique.
The first difficulty in adding Explicit Congestion Notification (ECN) in TCP/IP network was to modify the format of the network packet and transport segment headers to carry the required information. In the network layer, one bit was required to allow the routers to mark the packets they forward during congestion periods. In the IP network layer, this bit is called the `Congestion Experienced` (`CE`) bit and is part of the packet header. However, using a single bit to mark packets is not sufficient. Consider a simple scenario with two sources, one congested router and one destination. Assume that the first sender and the destination support ECN, but not the second sender. If the router is congested it will mark packets from both senders. The first sender will react to the packet markings by reducing its transmission rate. However since the second sender does not support ECN, it will not react to the markings. Furthermore, this sender could continue to increase its transmission rate, which would lead to more packets being marked and the first source would decrease again its transmission rate, ... In the end, the sources that implement ECN are penalized compared to the sources that do not implement it. This unfairness issue is a major hurdle to widely deploy ECN on the public Internet [#fprivate]_. The solution proposed in :rfc:`3168` to deal with this problem is to use a second bit in the network packet header. This bit, called the `ECN-capable transport` (ECT) bit, indicates whether the packet contains a segment produced by a transport protocol that supports ECN or not. Transport protocols that support ECN set the ECT bit in all packets. When a router is congested, it first verifies whether the ECT bit is set. In this case, the CE bit of the packet is set to indicate congestion. Otherwise, the packet is discarded. This eases the deployment of ECN [#fecnnonce]_.
The second difficulty is how to allow the receiver to inform the sender of the reception of network packets marked with the `CE` bit. In reliable transport protocols like TCP and SCTP, the acknowledgments can be used to provide this feedback. For TCP, two options were possible : change some bits in the TCP segment header or define a new TCP option to carry this information. The designers of ECN opted for reusing spare bits in the TCP header. More precisely, two TCP flags have been added in the TCP header to support ECN. The `ECN-Echo` (ECE) is set in the acknowledgments when the `CE` was set in packets received on the forward path.
The TCP flags
The third difficulty is to allow an ECN-capable sender to detect whether the remote host also supports ECN. This is a classical negotiation of extensions to a transport protocol. In TCP, this could have been solved by defining a new TCP option used during the three-way handshake. To avoid wasting space in the TCP options, the designers of ECN opted in :rfc:`3168` for using the `ECN-Echo` and `CWR` bits in the TCP header to perform this negotiation. In the end, the result is the same with fewer bits exchanged.
Thanks to the `ECT`, `CE` and `ECE`, routers can mark packets during congestion and receivers can return the congestion information back to the TCP senders. However, these three bits are not sufficient to allow a server to reliably send the `ECE` bit to a TCP sender. TCP acknowledgments are not sent reliably. A TCP acknowledgment always contains the next expected sequence number. Since TCP acknowledgments are cumulative, the loss of one acknowledgment is recovered by the correct reception of a subsequent acknowledgment.
If TCP acknowledgments are overloaded to carry the `ECE` bit, the situation is different. Consider the example shown in the figure below. A client sends packets to a server through a router. In the example below, the first packet is marked. The server returns an acknowledgment with the `ECE` bit set. Unfortunately, this acknowledgment is lost and never reaches the client. Shortly after, the server sends a data segment that also carries a cumulative acknowledgment. This acknowledgment confirms the reception of the data to the client, but it did not receive the congestion information through the `ECE` bit.
To solve this problem, :rfc:`3168` uses an additional bit in the TCP header : the `Congestion Window Reduced` (CWR) bit.
The `CWR` bit of the TCP header provides some form of acknowledgment for the `ECE` bit. When a TCP receiver detects a packet marked with the `CE` bit, it sets the `ECE` bit in all segments that it returns to the sender. Upon reception of an acknowledgment with the `ECE` bit set, the sender reduces its congestion window to reflect a mild congestion and sets the `CWR` bit. This bit remains set as long as the segments received contained the `ECE` bit set. A sender should only react once per round-trip-time to marked packets.
The last point that needs to be discussed about Explicit Congestion Notification is the algorithm that is used by routers to detect congestion. On a router, congestion manifests itself by the number of packets that are stored inside the router buffers. As explained earlier, we need to distinguish between two types of routers :
routers that have a single FIFO queue
routers that have several queues served by a round-robin scheduler
Routers that use a single queue measure their buffer occupancy as the number of bytes of packets stored in the queue [#fslot]_. A first method to detect congestion is to measure the instantaneous buffer occupancy and consider the router to be congested as soon as this occupancy is above a threshold. Typical values of the threshold could be 40% of the total buffer. Measuring the instantaneous buffer occupancy is simple since it only requires one counter. However, this value is fragile from a control viewpoint since it changes frequently. A better solution is to measure the *average* buffer occupancy and consider the router to be congested when this average occupancy is too high. Random Early Detection (RED) [FJ1993]_ is an algorithm that was designed to support Explicit Congestion Notification. In addition to measuring the average buffer occupancy, it also uses probabilistic marking. When the router is congested, the arriving packets are marked with a probability that increases with the average buffer occupancy. The main advantage of using probabilistic marking instead of marking all arriving packets is that flows will be marked in proportion of the number of packets that they transmit. If the router marks 10% of the arriving packets when congested, then a large flow that sends hundred packets per second will be marked 10 times while a flow that only sends one packet per second will not be marked. This probabilistic marking allows marking packets in proportion of their usage of the network resources.
If the router uses several queues served by a scheduler, the situation is different. If a large and a small flow are competing for bandwidth, the scheduler will already favor the small flow that is not using its fair share of the bandwidth. The queue for the small flow will be almost empty while the queue for the large flow will build up. On routers using such schedulers, a good way of marking the packets is to set a threshold on the occupancy of each queue and mark the packets that arrive in a particular queue as soon as its occupancy is above the configured threshold.
Modeling TCP congestion control
Thanks to its congestion control scheme, TCP adapts its transmission rate to the losses that occur in the network. 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 :math:`p` is the segment loss ratio, then the TCP connection successfully transfers :math:`\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 that the `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.
Evolution of the congestion window with regular losses
As the losses are equally spaced, the congestion window always starts at some value (:math:`\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 :math:`\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 :
:math:`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 :math:`\frac{1}{p}`. Thus, :math:`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 :
:math:`Throughput=\frac{area \times MSS}{time} = \frac{ \frac{3 \times W^2}{8}}{\frac{W}{2} \times rtt}` or, after having eliminated `W`, :math:`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 :math:`Throughput \approx \frac{k \times MSS}{rtt \times \sqrt{p}}`. This 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-times.
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.

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locale/pot/protocols/congestion.pot, string 28