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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.
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The second possible physical organization, which is also used inside computers to connect different extension cards, is the bus. In a bus network, all hosts are attached to a shared medium, usually a cable through a single interface. When one host sends an electrical signal on the bus, the signal is received by all hosts attached to the bus. A drawback of bus-based networks is that if the bus is physically cut, then the network is split into two isolated networks. For this reason, bus-based networks are sometimes considered to be difficult to operate and maintain, especially when the cable is long and there are many places where it can break. Such a bus-based topology was used in early Ethernet networks.
A third organization of a computer network is a star topology. In such networks, hosts have a single physical interface and there is one physical link between each host and the center of the star. The node at the center of the star can be either a piece of equipment that amplifies an electrical signal, or an active device, such as a piece of equipment that understands the format of the messages exchanged through the network. Of course, the failure of the central node implies the failure of the network. However, if one physical link fails (e.g. because the cable has been cut), then only one node is disconnected from the network. In practice, star-shaped networks are easier to operate and maintain than bus-shaped networks. Many network administrators also appreciate the fact that they can control the network from a central point. Administered from a Web interface, or through a console-like connection, the center of the star is a useful point of control (enabling or disabling devices) and an excellent observation point (usage statistics).
A fourth physical organization of a network is the ring topology. Like the bus organization, each host has a single physical interface connecting it to the ring. Any signal sent by a host on the ring will be received by all hosts attached to the ring. From a redundancy point of view, a single ring is not the best solution, as the signal only travels in one direction on the ring; thus if one of the links composing the ring is cut, the entire network fails. In practice, such rings have been used in local area networks, but are now often replaced by star-shaped networks. In metropolitan networks, rings are often used to interconnect multiple locations. In this case, two parallel links, composed of different cables, are often used for redundancy. With such a dual ring, when one ring fails all the traffic can be quickly switched to the other ring.
A fifth physical organization of a network is the tree. Such networks are typically used when a large number of customers must be connected in a very cost-effective manner. Cable TV networks are often organized as trees.
Sharing bandwidth
In all these networks, except the full-mesh, the link bandwidth is shared among all connected hosts. Various algorithms have been proposed and are used to efficiently share the access to this resource. We explain several of them in the Medium Access Control section below.
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.

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locale/cs/LC_MESSAGES/principles/sharing.po, string 19