Analytical Comparison of Fairness Principles for Resource Sharing in Packet-Based Communication...

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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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Vol. 8, No. 4 , July 2010

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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Vol. 8, No. 4 , July 2010

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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Vol. 8, No. 4 , July 2010

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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Vol. 8, No. 4 , July 2010

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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Vol. 8, No. 4 , July 2010

[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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