Fairness measure
Fairness measures or metrics
Metric (mathematics)
In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric...

 are used in network engineering
Network engineering
In telecommunications, network engineering may refer to:*The field concerned with internetworking service requirements for switched telephone networks and developing the required hardware and software...

 to determine whether users or applications are receiving a fair share of system resources. There are several mathematical and conceptual definitions of fairness.

TCP fairness

Congestion control mechanisms for new network transmission protocols or peer-to-peer
Peer-to-peer computing or networking is a distributed application architecture that partitions tasks or workloads among peers. Peers are equally privileged, equipotent participants in the application...

 applications must interact well with TCP
Transmission Control Protocol
The Transmission Control Protocol is one of the core protocols of the Internet Protocol Suite. TCP is one of the two original components of the suite, complementing the Internet Protocol , and therefore the entire suite is commonly referred to as TCP/IP...

. TCP fairness requires that a new protocol receive no larger share of the network than a comparable TCP flow. This is important as TCP is the dominant transport protocol on the Internet, and if new protocols acquire unfair capacity they tend to cause problems such as congestion collapse. This was the case with the first versions of RealMedia's
RealMedia is a proprietary multimedia container format created by RealNetworks. Its extension is ".rm". It is typically used in conjunction with RealVideo and RealAudio and is used for streaming content over the Internet....

 streaming protocol
Streaming media
Streaming media is multimedia that is constantly received by and presented to an end-user while being delivered by a streaming provider.The term "presented" is used in this article in a general sense that includes audio or video playback. The name refers to the delivery method of the medium rather...

: it was based on UDP
User Datagram Protocol
The User Datagram Protocol is one of the core members of the Internet Protocol Suite, the set of network protocols used for the Internet. With UDP, computer applications can send messages, in this case referred to as datagrams, to other hosts on an Internet Protocol network without requiring...

 and was widely blocked at organizational firewalls until a TCP-based version was developed.

Jain's fairness index

Raj Jain
Raj Jain
Raj Jain is a professor of Computer Science and Engineering in the Washington University School of Engineering and Applied Science at Washington University in St. Louis, Missouri.-Affiliations:...

's equation,

rates the fairness of a set of values where there are users and is the throughput for the th connection. The result ranges from (worst case) to 1 (best case), and it is maximum when all users receive the same allocation. This index is when users equally share the resource, and the other users receive zero allocation.

This metric identifies underutilized channels and is not unduly sensitive to atypical network flow patterns.

Max-min fairness

Max-min fairness is said to be achieved by an allocation if and only if the allocation is feasible and an attempt to increase the allocation of any flow necessarily results in the decrease in the allocation of some other flow with an equal or smaller allocation. A max-min fair allocation is achieved when bandwidth is allocated equally and in infinitesimal increments to all flows until one is satisfied, then amongst the remainder of the flows and so on until all flows are satisfied or the bandwidth is exhausted.

Fairly shared spectrum efficiency

In packet radio
Packet radio
Packet radio is a form of packet switching technology used to transmit digital data via radio or wireless communications links. It uses the same concepts of data transmission via Datagram that are fundamental to communications via the Internet, as opposed to the older techniques used by dedicated...

 wireless network
Wireless network
Wireless network refers to any type of computer network that is not connected by cables of any kind. It is a method by which homes, telecommunications networks and enterprise installations avoid the costly process of introducing cables into a building, or as a connection between various equipment...

s, The fairly shared spectrum efficiency (FSSE) can be used as a combined measure of fairness and system spectrum efficiency. The system spectral efficiency is the aggregate throughput in the network divided by the utilized radio bandwidth in hertz. The FSSE is the portion of the system spectral efficiency that is shared equally among all active users (with at least one backlogged data packet in queue or under transmission). In case of scheduling starvation, the FSSE would be zero during certain time intervals. In case of equally shared resources, the FSSE would be equal to the system spectrum efficiency. To achieve max-min fairness
Max-min fairness
In communication networks and multiplexing, a division of the bandwidth resources is said to be max-min fair when: firstly, the minimum data rate that a dataflow achieves is maximized; secondly, the second lowest data rate that a dataflow achieves is maximized, etc.In best-effort statistical...

, the FSSE should be maximized.

FSSE is useful especially when analyzing advanced radio resource management
Radio resource management
Radio resource management is the system level control of co-channel interference and other radio transmission characteristics in wireless communication systems, for example cellular networks, wireless networks and broadcasting systems...

 (RRM) schemes, for example channel adaptive scheduling, for cellular networks with best-effort packet data service. In such system it may be tempting to optimize the spectrum efficiency (i.e. the throughput). However, that might result in scheduling starvation of "expensive" users at far distance from the access point, whenever another active user is closer to the same or an adjacent access point. Thus the users would experience unstable service, perhaps resulting in a reduced number of happy customers. Optimizing the FSSE results in a compromise between fairness (especially avoiding scheduling starvation) and achieving high spectral efficiency.

If the cost of each user is known, in terms of consumed resources per transferred information bit, the FSSE measure may be redefined to reflect proportional fairness. In a proportional fair system, this "proportionally fair shared spectrum efficiency" (or "fairly shared radio resource cost") is maximized. This policy is less fair since "expensive" users are given lower throughput than others, but still scheduling starvation is avoided.

Further reading

  • Almeida, A.; Casetti, C.; Oueslati, S.; Avratchenkov, K. & Johansson, M. A Taxonomy of Congestion Control (in deliverable No: D.WP.JR.2.1.1) EuroNGI, 2004
  • http://www.ecse.rpi.edu/Homepages/shivkuma/teaching/sp2001/readings/mo-walrand.pdf - Mo, J. & Walrand, J. Fair End-to-End Window-Based Congestion Control IEEE/ACM transactions on Networking, 2000, 8, 556-567
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