Analytic Approach of Internet Pricing Scheme Model Based on function of Bandwidth Diminished with Increasing Bandwidth

Along with the changing times, the internet is becoming essential for everyday life. As the internet service providers, ISPs are required to provide a good service so as to give satisfaction to consumers at a low price. However, ISPs are expected to not only take into account customer satisfaction, but also take into account the advantages gained by considering all the factors that exist. Therefore, ISPs are given the option of pricing schemes, namely flat fee, usagebased, and two part tariff pricing schemes to be applied to the utility function as a function of bandwidth decreases with increasing bandwidth to maximize the benefits ISPs with regard to the level of user satisfaction. This study analyzed the two types of customers, namely homogeneous and heterogeneous consumers. Consumers are divided into heterogeneous consumer of willingness to pay (high end and low end) and with different consumption levels (high demand and low demand). In the case of consumers with homogeneous and heterogeneous consumer of willingness to pay (high end and low end), optimal pricing scheme is obtained if the ISP uses a flat fee and a two-part tariff schemes. As for heterogeneous consumers with different consumption levels (high demand and low demand), the scheme of two part tariff is the optimal scheme to generate maximum profits. Keywords—Pricing scheme; Flat fee; Usage based; Two-part tariff; Optimal solution.


I. INTRODUCTION
Over time, the development of technology with the development of internet services is in balance. Internet Service Provider (ISP) is required to compete to provide maximum service but at minimum cost, because at minimum cost will increase consumer interest to use the service offered. However, as the company's internet service provider, ISPs also have to consider the profits and maintaining the quality of the service with minimum prices for consumers.
ISPs are trying to provide the best service with the best pricing scheme anyway. However, there is now a wide variety of user demand internet and various applications that make the Internet providers must take into account the quality of service (Quality of Service, QoS). Basically, QoS makes it possible to provide better service to a particular request. In demonstrating efficiency in service, it is a must for ISP to show interaction between price and QoS [1].
Not only ISP, there should be a separate consideration for consumers who use the internet service there must be compatibility between the prices given to customer satisfaction. As customer satisfaction can be viewed by using the utility function. Utility function describes the level of customer satisfaction in consuming a product [2]. Internet Service Provider (ISP) is currently handling a high demand to promote good quality information. But a new initiative to develop a new price that involves QoS is only a few [3][4][5]. Therefore, it is important to consider the ISP customer satisfaction in creating a scheme that will make the relationship between user satisfactions with the QoS provided by ISPs.
By taking into account all the factors of the providers and consumers then, three types of pricing schemes are most often used, namely a flat fee, usagebased, and the two-part tariff [6,7] will be further analyzed. Analysis of these strategies is divided into two parts that considers homogeneous and heterogeneous customers. In the case of a homogeneous, all customers have the same utility on the level of consumption per day whereas in the case of heterogeneous, customers have two segments according to willingness to pay (willingness to pay) and the level of consumption (consumption level). Different analysis using different utility function has been introduced to show the variety of utility function applied to obtain new sight on choosing the satisfaction of the user both analytically or iteratively [8,9] Furthermore, in the article, a modification of the other utility function except Cobb-Douglas utility function will be discussed. This research will seek better schemes by using a utility function as a function of bandwidth which decreases with increasing bandwidth since this utility function is the best utility function which deals with the various level of QoS [10][11][12] .

II. RESEARCH METHODOLOGY
The steps undertaken in this study are as follows: 1. Formulate a utility function as a function of bandwidth which decreases with increasing bandwidth (functions of bandwidth diminished with increasing bandwidth) based on three types of pricing schemes which are flat fee, usage-based, and the two-part tariff for two types of customers, namely homogeneous and heterogeneous consumers , 2. Conduct an analysis of the utility function selected in order to obtain a model scheme based on the utility function.
3. Comparing the schematic model derived from the analysis.
4. Make the appropriate conclusions and comparative analysis obtained.

III. RESULT AND DISCUSSIONS
In next steps, we define the parameter and variables involved as follows.

P
: Costs incurred if the following services rendered Px : Price given service provider during peak hours Py : Price given the current service providers off-peak hours ̅ : The highest level of consumer i in using the service during peak hours : The variable i consumer purposes with respect to its participation

Ui(Xi,Yi)
: The utility function of consumer i with Xi is the level of service usage during peak hours and Yi is the level of service usage when not busy hours In this case utility function as a function of bandwidth which decreases with increasing bandwidth of [11] will be applied: Class J is divided into classes at busy times (x) and a class that is not at peak hours (y) thus obtained: This change was made to simplify the calculation when the minimum consumption level, and and the level of consumption during peak hours and off-peak hours respectively, dan can produce a minimum value of 0 rather than making value becomes negative.

A. Homogeneous Consumer
In the case of homogeneous consumers, it was assumed that all consumers have the same level of satisfaction and the maximum the same level of use in peak hours and in off-peak hours, i.e. ̅ and ̅ .
The optimization of consumer problem will be as follows: The optimization of supplier problem will be as follows: , , The selection of the best scheme is determined by analysis of derivatives as follows: ).

Proof of Lemma 1
If the ISP chooses to use a flat fee pricing scheme then PX = 0, PY = 0, dan P > 0 will be set. With the enactment of these provisions, the level of consumer spending will be = ̅ dan = ̅ so Eq. (7) will be as follows. ).

Lemma 2:
If ISPs use usage-based pricing scheme, the optimal price is

Proof of Lemma 2
If ISP choose usage based pricing scheme then PX > 0, PY > 0, dan P = 0. So Eq. (7) will be max , , To maximize Eq. (17), ISP should lower the value of PX and PY. Firstly, to optimize the consumer problem, we derive Eq. (17) to x and y. * +1 The optimization of supplier problem will be: Since X and Y are restricted so X * and Y will be ̅ and ̅ . In other words, PX and PY will be = ̅ +1 and

Proof of Lemma 3
If ISPs chooses two part tariff pricing scheme, then the requirements are PX > 0, PY > 0, and P > 0. Eq. (7) will be max , , We derive the Eq. (21) toward x and y to maximize PX and PY so it will be Eq. (18)-Eq.(19).
The optimization of supplier problem will be as follows.
since X and Y are restricted then, X * and Y * will be ̅ and ̅ . PX and PY will be . So the prices charged according to usage of the consumer will with the maximum profit of ∑ ( 0 + ln +1 +1 + ln +1 +1 ).
Then the type of flat fee and a two-part tariff pricing schemes generate huge profits equally according to maximize profit-making for the ISP (supplier) while the usage-based pricing scheme is different from the two schemes. ).

Proof of Lemma 4
Appling flat fee scheme, then we have PX = 0, PY = 0, dan P > 0. If the consumers choose to join the services, then the maximum level of satisfaction can be determined by choosing the level of consumption of 1 = ̅ , 1 = ̅ or 2 = ̅ , 2 = ̅ . This makes ISP can give the prices for each high-end consumer of no more than 01 + 1 ln 1 +1 +1 + 1 ln 1 +1 +1 and low end consumer of no more than 02 + 2 ln 2 +1 +1 + 2 ln 2 +1

+1
. So, it is easier to assume that 1 < To maximize Eq.(31), ISP should lower the value of PX and PY. Since X1, X2, Y1, dan Y2 are restricted, then 1 * , 2 * , 1 * , and 2 * cannot be more than ̅ and ̅ . For seeking the optimal price, first, we do the analysis on peak hours. The supplier optimization problem will be as follows.
To maximize Eq. (32) the supplier should lower the value of so the best value of cannot be greater than 1 ̅ +1 . In other words, if the supplier gives the price below 2 ̅ +1 than we do not obtain maximum profit since the values of 1 * and 2 * are not greater than ̅ and the consumer demand will increase toward the decrement of the price. So, the best price should be between . When the price is between that interval, high-end consumer demand will stay in ̅ will for lowend consumer will increase proportionally to the decrement of the price. Then, and will be = . When the price is between that interval, high end consumer demand will remain the same in ̅ whereas the low-end consumer demand will stay proportional to decrement of the value. Then, and will be = 2 ).
Then the type of financing schemes of flat fee and a two-part tariff generate huge profits equally in maximizing profit-making for the ISP (supplier) while the usage-based financing scheme obtain different value from the two schemes. ].

Proof of Lemma 7
For flat fee scheme, we set PX = 0, PY = 0, dan P > 0. If consumers choose to join the service then the maximum satisfaction level will be obtained by choosing consumption level 1  ).

Proof of lemma 8
Choosing the usage based scheme means that PX > 0, PY > 0, and P = 0. First order derivative for both consumers are as follows.  then the profit cannot be optimal when 1 * and 2 * are not greater than 1 ̅̅̅ and 2 ̅̅̅ and also the consumer demand cannot increase due to value decrement. So, the best price for should be between . When the price is between that interval, low demand consumer remains in 2 ̅̅̅ and high demand consumer will increase proportionally to price decrement. The, the best price for will be 1 ̅̅̅̅ +1 . Also, for off-peak hour time, the price will be = ).

Proof of Lemma 9
If ISP choose to use two-part tariff scheme, then PX > 0, PY > 0, dan P > 0.
We use first order derivative to obtain Eq. (34)-Eq. (37). Then the supplier optimization problem will be From Eq. (39) it can be seen that to obtain the maximum profit than the value of and should be as low as possible so the value of P remains large. So, 1 , 2 , 1 and 2 are restricted then 1 * , 2 * , 1 * and 2 * will be 1 ̅̅̅ , 2 ̅̅̅ , 1 ̅ and 2 ̅ . will be between .
When the price is between that interval, the demand of low demand consumer will stay in 2 ̅̅̅ and the demand of high demand consumer will increase proportionally to value decrement. Then, the best price for will be 1 ̅̅̅̅ +1 . Then, for the analysis for non = ).
Lastly, from the analysis of high demand and low demand consumers, it can be seen that for each scheme, the maximum profit obtained are different. Due to the differences, we can conclude that two-part tariff achieves maximum(optimal) value.

IV. CONCLUSIONS
Based on the analysis conducted applying utility function as a function of bandwidth which decreases with increasing bandwidth by using three types of existing pricing schemes on homogeneous consumers and heterogeneous consumers we obtained optimal financing scheme on each consumer. Homogeneous consumer pricing schemes if ISPs choose to use flat fee or two-part tariff then ISP can obtain optimal profit. Whereas in the case of heterogeneous customers which have two types, i.e., according to willingness to pay (willingness to pay) and the level of consumption (consumption level). For heterogeneous consumers with a desire to pay (high end and low end) ISP will gain maximum benefit when using flat fee or a two part tariff schemes. For heterogeneous consumers with different consumption levels (high demand and low demand) optimal scheme exists when ISPs choose to use two part tariff scheme of scheme.
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