This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Hatem A. Alharbi, CSchool of Electronic and Electrical Engineering, University of Leeds, LS2 9JT, United Kingdom;
(2) Taisir E.H. Elgorashi, School of Electronic and Electrical Engineering, University of Leeds, LS2 9JT, United Kingdom;
(3) Jaafar M.H. Elmirghani, School of Electronic and Electrical Engineering, University of Leeds, LS2 9JT, United Kingdom.
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III. REPEALING NET NEUTRALITY
In this paper, we consider the economic concept of PED to study the impact of ISP’s price change on the number of users accessing CPs content. In the following subsections, we present the pricing scheme used in this work, followed by the developed network and pricing MILP model.
A. Pricing scheme:
In economics, the relationship between users’ demand and price is referred to as price elasticity of demand (PED) [40]. PED measures the percentage change in demand resulting from a one percent change in price. To decide the pricing strategy of a product, the seller looks at different sensitivities to various factors that may affect their decision to purchase a product. The dominant factor in determining PED is the users’ ability and willingness at any given price. Many factors have an effect on users’ behavior, such as substitution availability, market competition, frequency of purchase, the necessity of the product, and how much the product price represents in users into income. The PED is calculated as follows:
In telecommunications, it is not an easy task to estimate an exact value of PED for various Internet applications as the factors that affect the elasticity change from area to another e.g. wealth, popularity of an application, quality of service provided by ISPs/CPs or competition between different CPs. However, PED for broadband subscriptions in Organization for Economic Co-operation and Development (OECD) countries has been analyzed in [41] by studying the relationship between price, income and broadband adoption. Additional factors have been included in [42], which are age and education to study PED for broadband subscriptions in Latin America and the Caribbean countries. They found that 1% decrease in price would lead to 0.43% and 2.2% increase in demand, respectively, over the two selected areas.
B. Profit-Driven MILP Model:
We develop a profit-driven MILP model where the objective is to maximize the total profit of an ISP offering core network infrastructure to CPs to deliver content from distributed clouds and/or fog nodes to their users.
We consider a monopolist ISP who owns the network backbone, i.e. CPs have to subscribe to the monopolist ISP to reach their customers. According to the FCC, 40% of total US Internet subscribers only have a single ISP option in their area [43]. The ISP has the power to control the pricing scheme. Under the net neutrality repeal, the ISP can deliver CPs content of different data rate requirements at a varying price per bit rate. We consider three classes to represent different data rate requirements of CPs services:
• Class A for high data rate content (i.e. UHD video service).
• Class B for medium data rate content (i.e. HD video service).
• Class C for low data rate content (i.e. SD video service).
The ISP needs to optimize the price of the three classes to maximize its profit. We consider content with higher data rate, which causes extra burden on the core network, to be priced higher per bit rate than content with a lower data rate. End-users will perceive varied video definitions from CPs based on their CP subscribed class. We assume that CPs will transfer the ISP new prices to their users to maintain their profit margin. Therefore, for the sake of simplicity we consider CPs to offer the same classes to their users. We assume a certain number of users to initially subscribe to each class under net neutrality. As the ISP and consequently the CPs vary the per bit rate charges for the different classes, users can choose to upgrade, downgrade or unsubscribe to the service. The number of users subscribing to each class depends on the PED. We assume that users leaving class A will join class B, users leaving class B will join class C and users leaving class C will unsubscribe to the service.
The ISP needs to optimize the price of the three classes to maximize its profit. We consider content with higher data rate, which causes extra burden on the core network, to be priced higher per bit rate than content with lower data rate. End-users will perceive varied video definitions from CPs based on their CP subscribed class. We assume that CPs will transfer the ISP new prices to their users to maintain their profit margin. Therefore, for the sake of simplicity we consider CPs to offer the same classes to their users. We assume a certain number of users to initially subscribe to each class under net neutrality. As the ISP and consequently the CPs vary the per bit rate charges for the different classes, users can choose to upgrade, downgrade or unsubscribe to the service. The number of users subscribing to each class depends on the price elasticity of demand (PED). We assume that users leaving class A will join class B, users leaving class B will join class C and users leaving class C will unsubscribe to the service.
Before introducing the model, we define the parameters and variables used in the model:
Parameters:
Variables:
Total ISP’s cost and revenue of delivering CP contents are calculated as follows:
Cost of provisioning core, metro and access networks infrastructure (C):
Revenue of delivering networking services to CP users (R):
The model is defined as follows:
The objective:
Maximize total profit given as:
Equation (4) gives the total profit in US dollar.
The total profit is maximized by maximizing the revenue and minimizing the cost of serving users in different classes.
Subject to:
Revenue of each class:
Constraint (6) calculates the number of users located in node d of class i in solution s. The number of users in class A is the number of users subscribing to the class as a result of its PED (from a look up table). In the case of class B, the number of users available to class B includes all users subscribing to the class B as a result of its PED plus any users downgrading their subscription from class A to class B. In the case of class C, the number of users available to class C includes users subscribing to class C as a result of its PED plus any users downgrading their subscription from class B to class C. Constraint (7) gives the price of each class based on the solution selected from the lookup table. Constraint (8) ensures that only one solution is selected. Constraint (9) calculates the number of users of class i in node d. Constraint (10) calculates the revenue the ISP achieves by delivering a service class by multiplying the class price by the total traffic in each class.
Constraints on number of users and prices:
Constraint (11) defines the minimum user percentage the CP service needs to maintain. Constraint (12) ensures that the price of a lower class does not exceed the price of upper classes, i.e. the price of class C does not exceed the price of class B and the price of class B does not exceed the price of class A. Constraint (13) ensures that the ratio of users in different nodes is identical.
Core network traffic:
Constraint (14) ensures that nodes with a fog built in its proximity are not served by a cloud. Constraint (15) calculates the download traffic from CP cloud to users in different nodes. User demands can be used to decide on datacenter locations as follows:
Constraint (18) represents the flow conservation for IP layer in the IP over WDM network. It ensures that the total incoming traffic equal the total outgoing traffic in all node; excluding the source and destination nodes.
Virtual link capacity constraint:
Constraint (18) ensures that the traffic transmitted through a virtual link does not exceed its maximum capacity.
Flow conservation constraint in the optical layer:
Constraint (20) represents the flow conservation for the optical layer. It ensures that the total number of incoming wavelengths in a virtual link is equal to the total number of outgoing wavelengths in all nodes excluding the source and destination nodes of the virtual link.
Physical link capacity:
Constraint (22) represents the physical link capacity limit. It ensures that the number of wavelengths in virtual links traversing a physical link does not exceed the maximum capacity of fibres in the physical link.
Total number of aggregation ports in a core node:
Constraint (22) calculates the total number of router ports in each core node that aggregate the traffic from/to the clouds.
The mathematical model given above maximizes the total profit of an ISP. To calculate the core network power consumption achieved from the profit- driven model, following parameters and variables are introduced;
Parameters:
Under the non-bypass approach [44], the IP over WDM network power consumption is composed of: