cnp3-ebook/principles/sharing — Czech @ Weblate: the node's lookup performance measured in packets per second

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	Fairness in computer networks
	In large networks, fairness is always a compromise. The most widely used definition of fairness is the `max-min fairness`. A bandwidth allocation in a network is said to be `max-min fair` if it is such that it is impossible to allocate more bandwidth to one of the flows without reducing the bandwidth of a flow that already has a smaller allocation than the flow that we want to increase. If the network is completely known, it is possible to derive a `max-min fair` allocation as follows. Initially, all flows have a null bandwidth and they are placed in the candidate set. The bandwidth allocation of all flows in the candidate set is increased until one link becomes congested. At this point, the flows that use the congested link have reached their maximum allocation. They are removed from the candidate set and the process continues until the candidate set becomes empty.
	In the above network, the allocation of all flows would grow until `A1-A2` and `B1-B2` reach 5 Mbps. At this point, link `R1-R2` becomes congested and these two flows have reached their maximum. The allocation for flow `C1-C2` can increase until reaching 15 Mbps. At this point, link `R2-R3` is congested. To increase the bandwidth allocated to `C1-C2`, one would need to reduce the allocation to flow `B1-B2`. Similarly, the only way to increase the allocation to flow `B1-B2` would require a decrease of the allocation to `A1-A2`.
	Network congestion
	In the network above, consider the case where host `A` is transmitting packets to destination `C`. `A` can send one packet per second and its packets will be delivered to `C`. Now, let us explore what happens when host `B` also starts to transmit a packet. Node `R1` will receive two packets that must be forwarded to `R2`. Unfortunately, due to the limited bandwidth on the `R1-R2` link, only one of these two packets can be transmitted. The outcome of the second packet will depend on the available buffers on `R1`. If `R1` has one available buffer, it could store the packet that has not been transmitted on the `R1-R2` link until the link becomes available. If `R1` does not have available buffers, then the packet needs to be discarded.
	Besides the link bandwidth, the buffers on the network nodes are the second type of resource that needs to be shared inside the network. The node buffers play an important role in the operation of the network because that can be used to absorb transient traffic peaks. Consider again the example above. Assume that on average host `A` and host `B` send a group of three packets every ten seconds. Their combined transmission rate (0.6 packets per second) is, on average, lower than the network capacity (1 packet per second). However, if they both start to transmit at the same time, node `R1` will have to absorb a burst of packets. This burst of packets is a small `network congestion`. We will say that a network is congested, when the sum of the traffic demand from the hosts is larger than the network capacity :math:`\sum{demand}>capacity`. This `network congestion` problem is one of the most difficult resource sharing problem in computer networks. `Congestion` occurs in almost all networks. Minimizing the amount of congestion is a key objective for many network operators. In most cases, they will have to accept transient congestion, i.e. congestion lasting a few seconds or perhaps minutes, but will want to prevent congestion that lasts days or months. For this, they can rely on a wide range of solutions. We briefly present some of these in the paragraphs below.
	Congestion collapse on the Internet
	Congestion collapse is unfortunately not only an academic experience. Van Jacobson reports in [Jacobson1988]_ one of these events that affected him while he was working at the Lawrence Berkeley Laboratory (LBL). LBL was two network nodes away from the University of California in Berkeley. At that time, the link between the two sites had a bandwidth of 32 Kbps, but some hosts were already attached to 10 Mbps LANs. "In October 1986, the data throughput from LBL to UC Berkeley ... dropped from 32 Kbps to 40 bps. We were fascinated by this sudden factor-of-thousand drop in bandwidth and embarked on an investigation of why things had gotten so bad." This work lead to the development of various congestion control techniques that have allowed the Internet to continue to grow without experiencing widespread congestion collapse events.
	Packets per second versus bits per second
	the node's capacity measured in bits per second
	the node's lookup performance measured in packets per second
	The node's capacity in bits per second mainly depends on the physical interfaces that it uses and also on the capacity of the internal interconnection (bus, crossbar switch, ...) between the different interfaces inside the node. Many vendors, in particular for low-end devices will use the sum of the bandwidth of the nodes' interfaces as the node capacity in bits per second. Measurements do not always match this maximum theoretical capacity. A well designed network node will usually have a capacity in bits per second larger than the sum of its link capacities. Such nodes will usually reach this maximum capacity when forwarding large packets.
	When a network node forwards small packets, its performance is usually limited by the number of lookup operations that it can perform every second. This lookup performance is measured in packets per second. The performance may depend on the length of the forwarded packets. The key performance factor is the number of minimal size packets that are forwarded by the node every second. This rate can lead to a capacity in bits per second which is much lower than the sum of the bandwidth of the node's links.
	Let us first explore which mechanisms can be used inside a network to control congestion and how these mechanisms can influence the behavior of the end hosts.
	As explained earlier, one of the first manifestation of congestion on network nodes is the saturation of the network links that leads to a growth in the occupancy of the buffers of the node. This growth of the buffer occupancy implies that some packets will spend more time in the buffer and thus in the network. If hosts measure the network delays (e.g. by measuring the round-trip-time between the transmission of a packet and the return of the corresponding acknowledgment) they could start to sense congestion. On low bandwidth links, a growth in the buffer occupancy can lead to an increase of the delays which can be easily measured by the end hosts. On high bandwidth links, a few packets inside the buffer will cause a small variation in the delay which may not necessarily be larger that the natural fluctuations of the delay measurements.
	If the buffer's occupancy continues to grow, it will overflow and packets will need to be discarded. Discarding packets during congestion is the second possible reaction of a network node to congestion. Before looking at how a node can discard packets, it is interesting to discuss qualitatively the impact of the buffer occupancy on the reliable delivery of data through a network. This is illustrated by the figure below, adapted from [Jain1990]_.
	When the network load is low, buffer occupancy and link utilization are low. The buffers on the network nodes are mainly used to absorb very short bursts of packets, but on average the traffic demand is lower than the network capacity. If the demand increases, the average buffer occupancy will increase as well. Measurements have shown that the total throughput increases as well. If the buffer occupancy is zero or very low, transmission opportunities on network links can be missed. This is not the case when the buffer occupancy is small but non zero. However, if the buffer occupancy continues to increase, the buffer becomes overloaded and the throughput does not increase anymore. When the buffer occupancy is close to the maximum, the throughput may decrease. This drop in throughput can be caused by excessive retransmissions of reliable protocols that incorrectly assume that previously sent packets have been lost while they are still waiting in the buffer. The network delay on the other hand increases with the buffer occupancy. In practice, a good operating point for a network buffer is a low occupancy to achieve high link utilization and also low delay for interactive applications.
	Discarding packets is one of the signals that the network nodes can use to inform the hosts of the current level of congestion. Buffers on network nodes are usually used as FIFO queues to preserve packet ordering. Several `packet discard mechanisms` have been proposed for network nodes. These techniques basically answer two different questions :
	`Which packet(s) should be discarded ?` Once the network node has decided to discard packets, it needs to actually discard real packets.
	By combining different answers to these questions, network researchers have developed different packet discard mechanisms.
	Discarding packets is a frequent reaction to network congestion. Unfortunately, discarding packets is not optimal since a packet which is discarded on a network node has already consumed resources on the upstream nodes. There are other ways for the network to inform the end hosts of the current congestion level. A first solution is to mark the packets when a node is congested. Several networking technologies have relied on this kind of packet marking.

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