Fairness measures or
metrics
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathema ...
are used in
network engineering 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
Network congestion in data networking and queueing theory is the reduced quality of service that occurs when a network node or link is carrying more data than it can handle. Typical effects include queueing delay, packet loss or the blocking of ...
mechanisms for new network transmission protocols or
peer-to-peer applications must interact well with
TCP. TCP fairness requires that a new protocol receive a 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 streaming protocol: it was based on
UDP and was widely blocked at organizational firewalls until a TCP-based version was developed. TCP throughput unfairness over WiFi is a critical problem and needs further investigations.
Jain's fairness index
Raj Jain
Raj Jain (born 17 August 1951) 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.
Education
Dr. Jain obtained a Ph.D. in ...
's equation,
:
rates the fairness of a set of values where there are
users,
is the throughput for the
th connection, and
is the sample
coefficient of variation
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed a ...
. 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.
To achieve a given fairness level
, one approximate method is to let
, where
:
and ''A'' is an arbitrary factor, typically used for normalization. This gives an allocation with a fairness close to ''F'', and the allocation can then be refined to get even closer. Note this also allows for a prioritization of allocation, as the
s will be sorted.
An exact method is to let
, where
solves
:
.
A simple way to calculate
is to use
Newton's Method on
, which converges consistently and fairly quickly.
Both of these methods give non-integer allocations, generally, and sometimes integer allocations are required. This can be done by using one of the above allocation methods, rounding down each allocation to the nearest integer (
), and then iteratively allocating one unit to a user, with the probability that user k receives it is proportional to
.
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
In digital radio, packet radio is the application of packet switching techniques to digital radio communications. Packet radio uses a packet switching protocol as opposed to circuit switching or message switching protocols to transmit digital da ...
wireless networks, ''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
A schedule or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are i ...
, 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, the FSSE should be maximized.
FSSE is useful especially when analyzing advanced
radio resource management Radio resource management (RRM) is the system level management of co-channel interference, radio resources, and other radio transmission characteristics in wireless communication systems, for example cellular networks, wireless local area networks, ...
(RRM) schemes, for example
channel adaptive scheduling, for cellular networks with
best-effort
Best-effort delivery describes a network service in which the network does ''not'' provide any guarantee that data is delivered or that delivery meets any quality of service. In a best-effort network, all users obtain best-effort service. Under b ...
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.
QoE fairness
The idea of QoE fairness is to quantify fairness among users by considering the
Quality of Experience (QoE) as perceived by the end user. This is especially of importance in
network management where operators want to keep their users sufficiently satisfied (i.e. high QoE) in a fair manner, see
QoE management. Several approaches have been proposed to ensure network-wide QoE fairness especially for adaptive video streaming.
In contrast to network related measures like throughput, QoE is typically not measured on
ratio scales. Hence, fairness measures like
Jain's fairness index cannot be applied, as the measurement scale requires to be a ratio scale with a clearly defined zero point (see
examples of misuse for coefficients of variation). QoE may be measure on
interval scales. A typical example is a 5-point
mean opinion score (MOS) scale, with 1 indicating lowest quality and 5 indicating highest quality. While the
coefficient of variation
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed a ...
is meaningless, the
standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, whil ...
provides a measure of the dispersion of QoE among users.
Hossfeld et al. have proposed a QoE Fairness index which considers the lower bound
and the higher bound
of the rating scale.
:
The QoE fairness index
has some desired properties like scale and metric independence. The unit of measurement does not matter. Any linear transformation of the QoE values does not change the value of the fairness index. The fairness index is bounded in the interval