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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 4 , July 2010
Analytical Comparison of Fairness Principles for
Resource Sharing in Packet-Based Communication
Networks Yaser Miaji and Suhaidi Hassan
InterNetWorks Research Group, UUM College of Arts and Sciences
Universiti Utara Malaysia, 06010 UUM Sintok, MALAYSIA
[email protected] [email protected]
ABSTRACT
Current Internet users are enormously increased and
application that they are using is magnificently bandwidth
devoured. With this manner, Internet is no longer a fair and
protective environment. The diversity in the Internet
applications required a reconsideration of the mechanisms
used to deliver each packet pass through a router in order to
provide better fairness and more protective place.
Furthermore, the observer of the Internet packet could easily
identify the purpose of the delay which is indeed caused by
the queuing in the output buffer of the router.
Therefore, to reduce such delay for those sensitive
applications such as real-time applications, scholars develop
many fairness principle which by turn could improve the
QoS and hence the fairness and the protection aspect. This
study highlight most famous fairness principles used in the
literature and some other novel ideas in the concept of
fairness. The analytical comparison of these principles shows
the weakness and the strength of each principle.Furthermore, it illuminates which fairness principle is more
appropriate in which environment.
Keywords-components; Fairness, max-min, proportional
fairness, balanced, max-min charge
1. INTRODUCTION
Internet utilization in public and private sector is
magnificently growing with extraordinary manner. The
occupation of the World Wide Web is unpredictable over
time frame. Daily usage of the Internet resources with
current scrambles in network access is hard to be estimatedand hence the distribution of these resources is dynamic.
This dynamic behavior leads to vagueness in constructing
the essential principle of fairness for resource utilization.
Furthermore, not only the dynamic attitude of the
resource utilization is an issue, the behavior and the
characteristics of the application itself also, play a
potential responsibility in structuring the fairness principle.
Some applications require more sensitive pamper and care
such as voice and interactive application such as video
conversation and so forth. The sensitivity of these
applications significantly involved in fairness principle.
Moreover, providing Quality of Service (QoS) is one
big dimension which should be achieved if not fully at
least to the large extent. QoS requirements rhyme heavily
with user and application requirements. Even though,
Service Providers (SP) is one potential dimension which
tighten fairness principle, their requirements is highly
depend on financial matters.
Fairness principle is indeed, applied in routers or to
be more specific in the process of scheduling the
transmission of the packets over a shared link. Fairness
principle should provide three primary function selection,
promptness, and QoS consideration. Selection is thebasically which packet deserves to be transmitted.
Promptness means when the selected packet will be
transmitted. QoS requires considering the delay, loss and
error of overall network performance.
Scholars, since the discovery of the sensitive and
bandwidth hanger applications, dedicate their research in
providing superior fairness and larger protection for these
applications over others less sensitive. This paper
demonstrates most available and used fairness principles in
scheduling packets depending on application sensitivity
and user usage. The rest of the paper is organized as
following. Next section gives the state diagram of theliterature and brief information about the evolution of the
fairness principle. This is followed by thorough conceptual
and analytical illustration of five fairness definition
namely; max-min fairness, proportional fairness, utility
fairness, balanced fairness, and max-min charge fairness.
Section four compares and contrasts all six principles and
finally the conclusion and future works are drawn.
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2. MIND-MAP OF FAIRNESS LITERATURE
In this section, related works to the fairness is presented in
state diagram or min-map diagram to correlate and track
the evolution of fairness principle. Exhibit 2.1 shows the
mind-map diagram which explains the evolution of
fairness principle. In 1967, Kleinrock [1] published hisarticle in sharing one common resource. Although the
article is primarily designed for addressing this specific
issue from processor sharing prospective, it opened sites in
discussing fairness in networks since process sharing
environment shares some similarity with resource sharing
in the Internet or networks. Kleinrock then wrote his book
which consists of two volume in queuing systems [2, 3]. In
this book the essential ideas and explanation of max-min
fairness principle is been demonstrated with the aid of
mathematic. Jaffe [4] incorporates the max-min fairness
principle explicitly in network resource sharing. This
concept is been presented in data networks book written by
Bertsekas et al. [5].
Nevertheless, the concept and regulations which rule
max-min fairness and lead to its result are not convenience
and does not provide the efficient fairness from Kelly
point of view [6, 7]. Consequently, he proposed an
alternative fairness principle named as proportional
fairness. This concepts is further developed by Massoulie
and Roberts [8]. Bothe principles; max-min and
proportional are further compared and thoroughly
analyzed by Denda et al. [9]. However, the advocates of
proportional fairness has comprehensively illustrate the
principle in [10].
Despite the success of the most famous principles;
max-min and proportional, they have some weaknesses
which are discovered by Bonald and Proutiere [11].
Balanced fairness is their proposal which is inspired by
Erlang [12] ideas, has different approaches. All three
principles; max-min, proportional and balanced fairness
are presented in Bonland et al. paper [13]. Bonland has
provided some comparison using analytical demonstration.
Another fairness view is called utility fairness introduced
by Cao and Zegura [14]. Utility fairness has adopted the
concept of utility proposed in [15]. All the above
mentioned fairness definition have been presented in [16]
by Hosaagrahara.
However, these four principles; max-min,
proportional, balanced and utility fairness are in principle
correlated and based on bandwidth allocation with
different approaches in determining the proper algorithm
to chose the next packet in line. The entire principle of
bandwidth allocation has been criticized in Briscoe article
[17]. Therefore, Miaji and Hassan in [18] proposed a new
vision of fairness by providing the principle of charge
allocation rather than bandwidth allocation and it named as
max-min charge. Max-min charge is a new fairness
principle based on charge allocation instead of
conventional bandwidth allocation. Next section
presents all the above mentioned five fairness principles
conceptually and analytically.
Exhibit 2.1: Mind-map literature of fairness
principles
3. PRINCIPLES OF FAIRNESS
Approaching an optimum fairness in shared elasticenvironment such as the Internet is complicated and
frustrated. As a consequence, different proposals have
been drawn to accomplish the mission in several
prospective. This section provides rigorous knowledge in
the most five adopted fairness notions. This
comprehensive illustration will reach the conceptual and
analytical approach of each o these five notions. Next
section compares and contrasts these five principles.
Before the explanation of the five notions mentioned
earlier, a scenario of shared resource is been assumed. So,
let consider the following scenario. Consider a contended
user n with demands variesfrom one user to another. Those users are sharing the one
resource R. Additionally, each user is allocated a specific
portion of the
resource R according to a policy P. There are two main
stipulations for such allocation;
a.The resource which is allocated is finite and limited.
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b.There is no resource feedback from users’ side.
Consequently, any policy abides by these two
conditions is said to be active and defined as follows
[61] :
Definition 3.1: The policy P is said to be active if, for all possible demands D, it results in an allocation A such
that:
1.
2.
Now, let establish the investigation in the five fairness
principles.
3.1 Max-min Fairness
Let first simplify the principle of ma-min fairness be thefollowing example. Let assume that there are buckets
which are corresponding to the demand of the users.
Moreover, let assume that all buckets share the same tab
which corresponds to the resource R. Therefore, since the
resource is limited and the buckets cannot, indeed, provide
any resource enhancement which there is no other resource
except the one which is shared as seen in exhibit 3.1.
Exhibit 3.1: Users Share the same resource
According to max-min principle no user will obtain
more than its demand and also, all not fully served users
will be equally allocated in term of the resource.
Therefore, user 1, 2, and 3 will take exactly what they
demand since their demands is the lowest. In comparison,
user 4 and 5 will take equal resource allocation no matter
what they demand for.
Additionally, any user attempts to increase its
allocation will result in decrease in the resource allocated
to another. Furthermore, it could be obviously seen that the
attempts to increase the demand will not influence thedecision of allocation [16].
Exhibit 3.1 provides us with much information which
has not been illustrated yet. The essential inspiration of
max-min fairness is the Pareto superiority as well as Pareto
efficiency which were suggested by Pareto [19, 20]. In fact,
Pareto proposed his notion in political economic and it has
two main concept; superiority and efficiency for two
active allocation. Firstly, if we have to allocate
to two different resources , is considered
as Pareto superior with respect to if expands the
allocation of at least one entity while not reducing the
allocation of any other entity; for instance, at least one userprefers over . In the case of exhibit 3.1, user 4
prefers to obtain 40 units over 50 units and no other user
request it. This preference will affect other users [21].
Secondly, an allocation is considered as Pareto
optimal if it is active and Pareto superior to all other active
allocations. Indeed, Max-Min fairness shows its Pareto
optimality and hence it is unique since it is the only notion
which meets the conditions of the Pareto optimality [22].
Now, let take the analytical vision of the notion of
Max-Min fairness. So, let presume that is the
allocation dedicated for with demand in flow and is the allocation specified for with demand .
If we assume the then the following theorem
could be deduced;
Theorem 3.1:
The Max-Min fairness is unique.
Proof:
Let and two users with demands and
respectively and the resource allocated for them is respectively as well. So, if then the
allocation results could be;
Only first one is possible since the remaining two are
not Max-Min fair.
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Moreover, consider is the service received by ,
then if that means this allocation is not Max-Min
fair because in Max-Min fair the following should be true:
. Hence the following definition is true for
Max-Min fair:
Definition 3.1:
A policy is considered Max-Min fair if and only if
satisfies the following conditions [22, 23]:
1- A is active;
2- Any attempts to increase and allocation for
specific user result in a decrease in another user with
equal or less value.
Therefore, Max-Min policy should have the following
properties;
Property 3.1: No user gets resource allocation than
what it have been requested.
Property 3.2: users with same demands will be
allocated similar resource.
Property 3.3: Any increase in the demand will not
affect the allocation procedure.
3.2 PROPORTIONAL FAIRNESS
The idea of the proportional fairness is, indeed, proposed
after the discovery of some gap in the fairness of Max-Min. We will simplify this concept by illustrating a
wireless node example [10].
It well known that the fairness goal is not to
maximize the overall throughout or the bit rate or increase
the efficiency, it rather to be fair in allocating the
bandwidth in accordance to the current network status.
From this sense, consider a constant1
wireless network
where there are two status of a node either good or bad.
Therefore, in order to achieve high throughput and hence
to maximize the bit rate or increase the efficiency, it is
better to allocate more bandwidth, transmission power and
so on to those good nodes since the bad one willexperience more loss and required more bandwidth with
1 This situation is likely to be impossibleespecially in the case of mobile wirelessenvironment.
less throughput [13].
Exhibit 3.2 a: Max-Min fairness
Exhibit 3.2 b: Proportional fairness2
Nevertheless, this maximization will not be fair since
those nodes with bad radio channel will suffer from
starvation. In Max-Min concept as shown in exhibit 3.2a,
those nodes with bad radio channel will be allocated more
bandwidth since the main aim of such principle is to
maximize the minimum. However, from proportional
fairness point of view, this solution is not the optimum.
Therefore, there is a trade of between efficiency and
fairness. Proportional fairness is trying to solve and hence
minimize this trade of by proposing the concept of
allocating bandwidth in proportion to charge [6, 7].
2 The width of the wireless communicationlink corresponds to the bandwidth allocated to thisspecific user.
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Logarithmic approach has been dedicated to such
approach. So, proportional fairness concept proposed the
notion of price per unit used or shared (see exhibit 3.2b). If
we assume that user is charge of an amount of
for unit shared. Therefore, in proportion to this user
will be allocated . As a consequence the problem of
maximization could be formed as following;
Maximize
So, the allocation for each user is depend on the
amount it is charged. This gives some restriction in the
utilization of such concept which will be discussed later in
the analysis and comparison section.
3.3 Utility Fairness
The concept of utility fairness is easily to be inferred from
its name. This notion is based on the utility or the
application. It basically, derives the bandwidth allocationin accordance to the characteristic of the application to be
transmitted through the link. Therefore, packets which has
elastic or more tolerance in term of delay or loss or any
other specified criterion, are allocated bandwidth
depending on its specifications, behavior, and
characteristics [14].
Therefore, in the case of the identical utility or packet
specification or in other words applications, packets will
be treated as in Max-Min fairness. On the other hand, as
the application or packets diverse in its characteristics or
manners, the allocation scheme will also, changed and is
highly depends on the utility.
To simplify the idea of utility life example is been
provided. Now, consider an apple which needs to be
divided among three people fairly as in exhibit 3.3. The
simple and basic way is to allocate one third of this apple
to each person equally as shown in exhibit 3.3a. However,
this sort of division is considered unfair if the
circumstances of the people are not equal.
So, now consider the first person is a child how will
any way, cannot eat more than a quarter of the apple. The
second person is in diet and he also, cannot eat more than a
quarter of the apple and the third is very hungry energeticyouth. Consequently, according to the utility as one half is
allocated to the youth, quarter for the child and the last
quarter portion is allocated for the person in diet (see
exhibit 3.3b).
(a) (b)
Exhibit 3.3: example of utility fairness
Cao [14] in his article proposed and proof the
following theorem;
If is the allocated bandwidth for session, is
the link capacity, the real utility function for session is
, is the error in the advertised bandwidth and isthe difference between the utility achieved by session
and the allocation deserved by the same session then;
A quantitative measure of the error in utility
allocation is given by such theorem which resulted from
the inaccurate information. Moreover, it reveals that there
is a strong relationship between the error of utility
allocated to an individual source and the accuracy of
advertised utility functions; nevertheless, it is not affected
by the number of sources sharing the same bottleneck link
and hence no harms from any exponential increase in theusers side.
3.4 Balanced fairness
The proper definition of balanced fairness is the unique
balanced allocation such that belongs to the
boundary f the capacity set in any state If Φ
corresponds to the balance function, the following
equation is true in any state
(3.1)
Therefore, is recursively defined as the
minimum positive constant β such that the vector
belongs to .
Balanced fairness is a new notion of bandwidth
allocation with the very gratifying property that flow level
performance metrics are insensitive to detailed traffic
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characteristics [24]. This is particularly important for data
network engineering since performance can be predicted
from an estimate of overall traffic volume alone and is
independent of changes in the mix of user applications
[13].
3.5 Max-Min charge
Max-Min charge has taken new different vision of fairness
in packet switching networks. The authors claim that to
provide better fairness and proper protection to any user in
a common shared resource, some aggressive penalty
should applied for those who are maliciously use the
sharing procedure [18].
Let take the analogy of multiple buckets sharing one
fountain or resource as in exhibit 3.4. So, let consider
that greedily attempts to gain more bandwidth by
initiating several session with multiple connation and
hence reserves more bandwidth than the others. Suchmanner could breaches both the protection of other users
who indeed fairly be using the resource and the fairness
by making get double service than the others.
Exhibit 3.4: analogy of max-min charge
Nevertheless, Max-Min fairness has nothing to do
regarding such issue since it concern about fairness among
flows and not users. However, Max-Min charge assigns a
specific values and parameters to each user. Thefollowing equation has been deducted to improve the
protection level:
(3.2)
By this notion, the only user who will suffer from any
increase in the demand or in queue number is the
misbehaved user. Some charges will be applied to such
users and hence minimize the allocation.
4. COMPARISON OF FAIRNESS PRINCIPLES
The current status of the Internet provides only best-effort
service. Consequently, providing enhancement for trafficflows for bandwidth reservation purposes is almost absent,
or to be more precise bounding delay and jitter is not up to
the expectation level or even not met. Moreover, any
further modification in the protocols to be able to adopt the
concept of reservation high efficiency of Quality of
Service (QoS) required a crucial modification in the core
of the Internet which is unachievable. These boundaries
rigorously reduce the ability of flows to demand
guarantees from the Internet, and the capability of the
Internet to put forward and accomplish such guarantees.
If these constraints taken in account, the most
appropriate notion to be considered is max-min fairness.The principle of proportional fairness necessitates flows to
transmit information about their bandwidth requirements
and reservations to each router along their rout. The
principle of utility fairness is unclear in term of the
specification of the utility function and it rather demands
flows to convey their utility.
Nevertheless, minimum information about the flows
among all notions is required by the principle of max-min
fairness; a flow has a demand of unity if it has a packet
enqueued and has a demand of zero otherwise. This
information is, indeed, promptly available to each router
and therefore the max-min principle of fairness is the mostamenable to implementation. Likewise, max-min fairness
is presently the most accepted principle of fairness in the
research community.
5. CONCLUSION
The nature of the Internet traffics is random and dynamic;
therefore, such behaviors should be taken in account once
the issue of resource allocation is investigated. It has
proven that max-min fairness, proportional fairness and
balanced fairness provide stability to the network
particularly when the vector of traffic intensities depends
on the interior of the capacity set. It is also, proven thatbalance property have not been met by max-min fairness
notion with the exception of the trivial case where the
network condenses to a set of independent links. This
justifies the limitation of the analytical results for this
allocation and strengthens the assumption that such results
should not be excluded. Proportional fairness is not
balanced either except in some specific cases.
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[20] V. Pareto, R. Marchionatti, and F. Mornati,
Considerations on the fundamental principles of pure
political economy: Routledge, 2007.
[21] E. Karipidis, N. D. Sidiropoulos, and Z. Q. Luo,
"Quality of service and max-min fair transmit
beamforming to multiple cochannel multicast
groups," IEEE Transactions on Signal Processing,vol. 56, pp. 1268-1279, 2008.
[22] D. Chakrabarty, J. Chuzhoy, and S. Khanna, "On
allocating goods to maximize fairness," 2009, pp.
107-116.
[23] A. Sridharan and B. Krishnamachari, "Maximizing
network utilization with max – min fairness in
wireless sensor networks," Wireless Networks, vol.
15, pp. 585-600, 2009.
[24] T. Bonald, A. Proutiere, J. Roberts, and J. Virtamo,
"Computational aspects of balanced fairness," 2003,
pp. 801 – 810.
AUTHORS PROFILE
Yaser Miaji received the B.E.
form Riyadh College of Technology, Saudi Arabia and M.E.degrees, from University of New South Wales, Australia. in 1997and 2007, respectively. He is [16]currently a doctoral
researcher in Computer Science in the University Utara Malaysia.Previously, he works as a lecturer in the College of
Telecommunication and Electronic in Jeddah from 1998-2206.His research interest includes digital electronics, computernetwork, distributed system and genetic algorithm. He is amember of InternetWorks research group, IEEE, ACM ISOC and
STMPE.
Suhaidi Hassan PhD SMIEEE is an
associate professor in computer systems and
communication networks and the Assistant ViceChancellor of the Universiti Utara Malaysia’s College of
Arts and Sciences. He received his PhD in Computingfrom University of Leeds in United Kingdom, MS in
Information Science from University of Pittsburgh, PA and
BS in Computer Science from Binghamton University,
NY. He currently heads the InterNetWorks Research
Group at the Universiti Utara Malaysia and chairs SIG
InterNetWorks of the Internet Society Malaysia Chapter.
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