DYNAMIC SERVICE DISCRIMINATION STRATEGY

DEVELOPMENT USING GAME THEORY

Kwang Sup Shin, Suk-Ho Kang

Department of Industrial Engineering, Seoul National University, Korea

Jae-Yoon Jung

Department of Industrial and Management Systems Engineering, Kyung Hee University, Korea

Doug Young Suh

Department of Electronic and Radio Engineering, Kyung Hee University, Korea

Keywords: Multimedia resource allocation, Service discrimination, Game theory, Bargaining solution.

Abstract: This research proposes a dynamic service discrimination strategy for wireless multimedia services. In

particular, bargaining solutions in the game theory are applied to allocate the limited resources to users for

the purpose of proportional fairness. We assume that users can choose one of discriminated media services

and multimedia resources are then allocated to users according to their service selections. In the mechanism,

an efficiency function for the network manager and a utility function for users are devised to reflect quality

of service and cost. The optimized service discrimination and resource allocation policy have been

developed not only from user’s standpoint, but also from network manager’s. We illustrated experimental

results with synthesis multimedia data and analyzed the effect of the proposed service differentiation and

resource allocation algorithms.

1 INTRODUCTION

As the real-time wireless multimedia service

requires pretty much resource, it has been the major

issues to utilize the limited resources in the wireless

network. There are lots of researches how to utilize

the limited resources, especially using the game

theoretic approaches. Game theory has been already

applied and shown the advances to improve the

performance of resource allocation in the various

research areas including wireless multimedia

networks.

The most intuitive way to allocate resources is to

equally allocate resources to the participating users.

But an important disadvantage of this policy is that it

does not consider characteristics of users and

systems. Alternatively, the notion of proportional

fairness was introduced to allocate resources based

on the user’s requirements (Kelly, Maulloo, & Tan,

1998). In the point of proportional fairness, KSBS

(Kalai-Smorodinsky Bargaining Solution) was

compared with the NBS. Park and Schaar (2007)

analyzed the optimality conditions of both solutions

and differences between the quantitative

proportional fairness of NBS and the qualitative one

of KSBS. Although this proportional fairness policy

was successfully implemented in several works

(Kelly, Maulloo & Tan, 1998), it is not suitable for

content aware multimedia applications since it does

not consider explicitly the resulting impact on the

quality of the service (Park & Schaar, 2007).

In this research, the concept of cost, to model the

efforts which users invest to achieve their own goals,

is additionally considered to express user’s

satisfaction. Although there are a lot of researches

related to the costing or pricing (Courcoubetis, Siris

& Stamoulis, 1996; Shenker, 1995), it is general to

charge according to the amount of allocated

resources (Avriel, 1976). And the most important

thing is that pricing mechanism and resource

allocation policy should be able to maximize the

282

Sup Shin K., Kang S., Jung J. and Young Suh D. (2010).

DYNAMIC SERVICE DISCRIMINATION STRATEGY DEVELOPMENT USING GAME THEORY.

In Proceedings of the 2nd International Conference on Agents and Artiﬁcial Intelligence - Agents, pages 282-286

DOI: 10.5220/0002714902820286

 SciTePress

profit or revenue of each participants of the game

(Ya¨ıche, Mazumdar,& Rosenberg, 2003).

2 BASIC ASSUMPTIONS

The salient concepts and the basic assumptions for

service discrimination and the resource allocation

game are presented. Parameters and descriptions are

summarized in Table 1.

Table 1: Parameters and descriptions.

Parameters Descriptions

total available resource

maximum requirement of user

minimum requirement user

amount of resource allocated to user

unit price for resource of jth service type

decision variable of user

bargaining power of user

bargaining power of

j th service type

()

⋅

utility function of user

utility of user

resource usage efficiency of jth service type

weight value for the linear combination of

service discrimination strategies

In this research, following wireless communication

network is assumed.

There are

users who compete

for the available network resources. A user

has its

own utility function

()()

which can be derived

from the allocated resource

(

)

and it has also a

minimum desired utility

(

)

(

)

, called a

disagreement point. The disagreement point is the

minimum requirement that each user expects by

joining the game. There are m different service

types. Users who want to stay in this network should

select one of the service types and pay for allocated

resource according to the selected service type. The

network manager can discriminate service levels by

adjusting the bargaining power of each service

type

(

)

(, , )

ββ β

= "

. However, the network

manager does not announce the adjusted bargaining

power because it is internal decision of the network

manager. The bargaining power

of user i (

) is

determined when the user selects a service type.

3 SERVICE DISCRIMINATION

STRATEGIES

In this section, the procedure network manager to

discriminate services with bargaining power.

Adjusting the bargaining power is conducted based

on the result of service selection of users.

3.1 Efficiency based Strategy

Based on the result of service type selection, the net-

work manager adjusts its service discrimination

policy. The bargaining power is the only one that the

network manager can change. The efficiency, the

performance measure of the system, can be

calculated with the ratio between actual profit and

service selection and expected profit. The expected

profit can be derived from the bargaining power of

each service type because it can be said that the

network manager already planned to allocate a

certain amount of resources,

, to the

service type. Therefore, considering the system

performance with the resource allocation results,

utility function of network manager can be defined

as following equation (1):

()

min min

1, 1,

ijij iij

MAX MAX

jj j

Cx Rx

RC R

ββ

⎛⎞⎛⎞

⎜⎟⎜⎟

⎝⎠⎝⎠

∑∑

(1)

Hence the network manager should adjust the

resource allocation policy to maximize the system

efficiency. The optimization problem of the network

manager can be expressed as follows:

()

{}

max

. 1, 0< , 1,...,

EF EF

tjm

ββ

=∀∈

∏

∑

(2)

3.2 Stepwise Service Discrimination

The optimal solution of problem (2) can be found by

using Algorithm 1. Algorithm 1 guarantees the

optimal solution of problem (2) and it can be proved

as follows. First, as

iij

∑

and

have nothing

to do with the decision variable

, the optimization

problem (2) can be simplified to (3). At this time, it

is assumed that

≤

∑

and

≤

{}

max

. ,0< , 1,...,

MAX

tbR bj m

=∀∈

∏

∑

(3)

DYNAMIC SERVICE DISCRIMINATION STRATEGY DEVELOPMENT USING GAME THEORY

283

Algorithm 1. Stepwise Service Discrimination.

1) Calculate amount of the allocated resources for the

each service type

{}

, 1,...,

iij

xj m

⎛⎞

∀=

⎜⎟

⎝⎠

∑

2) Set the order vector of service types (

SEQ

) based

on the amount of allocated resources

3) if

[1] [ 1]SEQ j SEQ m≤≤ −

iij

MAX

∑

4) else

AX t MAX

MAX

−

∑

The optimal solution of the problem is that

,1 1

ba jm=≤≤−

and

MAX

bR b

−

=−

∑

Let

()

,...,

bb b=

be a feasible solution. If

(

)

(

)

zb zb≤

is established, then it can be said that

always becomes the optimal solution. First of all, it

can be assumed that

{

}

,1,...,1

baj m≥∈ −

and there

exists at least one

meet

{

}

, 1,..., 1

baj m>∈ −

from

the Lemma 1.

Lemma 1.

ab<

and

ab<

are established,

bb≤

can be assumed without loss of generality.

Let

ab→

and

ij j i

bb a b+−→

, the following

equation becomes true.

()

()()

ij i j j j

ji j i ji j j

bb b b a a

bb b a ab b a

−+−

=+−−+−>

(4)

In order to make the proof simple and readers

easily understood, let the number of service types be

two. Then it can be said that

MAX

Rbb=+

and

aa R+<

. If

ab<

, following inequality (5)

should be true.

()

1212

121

min ,1 min ,1

MAX

aaaa

bba

⎧⎫ ⎧⎫

×<

⎨⎬ ⎨⎬

−

⎩⎭ ⎩⎭

(5)

And assuming

ab≥

makes the following

inequality true.

()()

11212

121

min ,1 min ,1

MAX MAX

aaaaa

baa

Ra Ra

⎧⎫ ⎧⎫

⎨⎬ ⎨⎬

⎩⎭ ⎩⎭

=×= <

−−

(6)

It is the reason that Lemma 1 makes the

following equation (7) established.

()()

()

22 11

1221

MAX MAX

MAX

aa R aa

Raaaa

−− −

=−− −>

(7)

And then, assuming

ab<

and

ab<

become

established from the condition,

aa<

. As with the

case of

ab≥

, the following equation is established

from Lemma 1.

()

12 1 2 1 2

12 1 1

min ,1 min ,1

MAX

aa a a a a

bb b a

⎧⎫ ⎧⎫

⎨⎬ ⎨⎬

⎩⎭ ⎩⎭

=×=× <

−

(8)

Therefore, it is proved that the following solution

is the optimal solution of problem (3).

MAX

ajm

Rbjm

−

≤≤ −

⎧

⎪

⎨

−=

⎪

⎩

∑

(9)

3.3 Profitability based Strategy

Along with the efficiency of resource allocation

policy, the network manager should also consider

the unit price of each service type. Generally it is

more beneficial to adjust bargaining power in order

to induce users to get together in the more expensive

service type. Therefore, the price ratio of each

service type

(

)

CC C

∑

should be considered

to adjust the bargaining power.

Combining these two service discrimination

strategies can be the overall strategy as following

equation (3). And weight factor, (

), means the

weight of profitability compared to the efficiency.

(1 ) , 0 1

jjj

βζ ζβζ

←

⋅+− ≤≤

(10)

4 RESOURCE ALLOCATION

In this section utility function of users and resource

allocation algorithm will be explained.

4.1 Utility Function for Users

The utility function of each user,

, can be defined

by summing noise ratio and the cost factor.

(

)

()

(()) (())

iii iii i ii

iii i

ii i jij

iii i i

xNoiseRatioRx COSTRx

kRx R

Rx Cx

DRx R

πτ

== +

−

−+

∑

(11)

The parameter

is a term to adjust the scale of

cost factor to distortion rate factor. Since it means

the degree of cost-sensitivity, it has negative value.

The first part of the function,

NoiseRatio, is

designed based on the distortion rate model

(Stuhlmüller

et al., 2000), which is well suited for

ICAART 2010 - 2nd International Conference on Agents and Artificial Intelligence

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the multimedia network (Andreopoulos

et al., 2004).

In addition, the cost factor added to the noise ratio

part.

4.2 Resource Allocation: KSBS

The criteria for bargaining solution to allocate

resources to users are needed. Multiple bargaining

solutions which have different properties can be

found in prior researches dealing with resource

management problems. And they provide

consideration of optimality and fairness (Monderer

& Shapley, 1996; Andreopoulos

et al., 2004).

Specifically KSBS guarantees the same quality drop

from each user’s maximum achievable utility (Kalai

& Smorodinsky, 1975). The generalized KSBS can

be obtained by the following equation (12).

AX MAX

αα

==="

(12)

However, this equation is generally an

degree polynomial of

. Hence, efficient and

simple numerical methods like the bisection method

is required (Boyd & Vandenberghe, 2004). Because

the upper and lower bounds are already known, the

bisection method can be applied. After finding the

optimal utility of the first user, it is easy to calculate

the others’ optimal utilities.

It can be said that finding the optimal resource

allocation plan using KSBS means finding the

maximum value of

. It is possible to obtain the

optimal resource allocation plan with the reverse

function of the utility function.

()

*1*1*

MAX

iiii i jij

RX X x

ππδ β

−−

⎛⎞

=⋅

⎜⎟

⎝⎠

∑

(13)

As described earlier, the optimal solution should

meet three different constraints

iMAX

≤

∑

ijiji

Cx b

≤

∑

and

(

)

iii

RRR≤≤

4.3 Utility based Service Selection

Decision problems of users, which service type

should be selected, is absolutely based on the utility.

If all users try to change service type at the same

time, the resource allocation plan cannot be ensured.

Therefore it should be assumed that only one user

can change the service type at time and implement

the

Elementary Stepwise System (ESS), where each

user decides their service type sequentially. It has

already proved that the ESS converges to Nash

Equilibrium in polynomial time (Park & Schaar,

2007-2). The order to change the service type is

determined based on the utility status, the difference

between maximum required utility and current

derived utility.

5 CONCLUSIONS

Different from current related researches, this paper

assumed multiple service types and presented

service discrimination algorithm which can be

actively determined by the network manager.

Moreover, users’ utility function includes both

concepts of quality and cost of service. Also, this

paper suggested an efficient resource allocation

algorithm which considers both the network manger

and users.

Considering the concept of “traffic classes”, it

seems that discriminated services can be released

over the short haul when the number of users rapidly

increases, although a flat sum system is the most

general way in the multi-media services such as

Wibro, DMB, and IPTV. Likewise, the proposed

approach can be applied when there are multiple

multimedia servers and cost factor of utility function

can be substituted with channel status according to

the distance.

ACKNOWLEDGEMENTS

This work was supported by the IT R&D program of

MKE/IITA. [2008-F-005-02, Game Theoretic

Approach for Cross-layer Design in Wireless

Communications]

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