The Caching and Pricing Strategy for Information-Centric Networking with Advertisers’Participation

Zheng Quan ,Yan Wenliang ,Wu Rong,4 ,Tan Xiaobin,,* ,Yang Jian, ,Yuan Liu ,Xu Zhenghuan

1 Laboratory for Future Networks,Department of Automation,University of Science and Technology of China,Hefei 230026,China

2 Institute of Artificial Intelligence,Hefei Comprehensive National Science Center,Hefei 230088,China

3 Institute of Advanced Technology,University of Science and Technology of China,Hefei 230088,China

4 Suzhou Nuclear Power Research Institute,Suzhou 215004,China

5 National Engineering Laboratory for Public Safety Risk Perception and Control by Big Data(NEL-PSRPC),China Academy of Electronics and Information Technology of CETC,Beijing 100041,China

Abstract: As users’ access to the network has evolved into the acquisition of mass contents instead of IP addresses,the IP network architecture based on end-to-end communication cannot meet users’ needs.Therefore,the Information-Centric Networking(ICN)came into being.From a technical point of view,ICN is a promising future network architecture.Researching and customizing a reasonable pricing mechanism plays a positive role in promoting the deployment of ICN.The current research on ICN pricing mechanism is focused on paid content.Therefore,we study an ICN pricing model for free content,which uses game theory based on Nash equilibrium to analysis.In this work,advertisers are considered,and an advertiser model is established to describe the economic interaction between advertisers and ICN entities.This solution can formulate the best pricing strategy for all ICN entities and maximize the benefits of each entity.Our extensive analysis and numerical results show that the proposed pricing framework is significantly better than existing solutions when it comes to free content.

Keywords: advertisers;cache;free content;Information-Centric Networking;pricing strategy

I.INTRODUCTION

Cisco’s reports show that Annual global IP traffic will reach 4.8 ZB per year by 2022,or 396 exabytes(EB)per month[1].Moreover,the vast majority of internet traffic relates to content access.The rapid growth of Internet content delivery shows the need for different network architectures.Consequently,researchers have proposed future Internet architectures.Such architectural schemes are generally referred to as Information-Centric Networking(ICN).In ICN,users are only interested in the content,not where it is,or even how it is delivered[2].An essential feature of ICN is that content can be selectively stored on routers.Through caching within the network,users can access content nearby[3].This approach can improve the efficiency of content distribution.Based on the above characteristics,and as a future network architecture that has attracted much attention,operators have shown stronger enthusiasm for the deployment of ICN in recent years.We know that the development of the Internet not only requires technological advancement,but the charging model and pricing mechanism are equally important.Therefore,it is necessary to establish an appropriate pricing mechanism to motivate all Internet Service Providers(ISPs)to deploy caches.

Much work has been done on the current Internet to study the pricing mechanism[4-9].Generally,for the access ISPs and the transit ISPs,their income mainly comes from the revenue obtained by providing the transmission service.For content providers (CPs),in the pricing mechanism under the IP network,there are two sources of revenue: a small part comes from the content fees paid by the users;most other CPs provide free content but get profit from advertisers.In this case,the number of users’ requirements can be described by the number of content attentions,such as clicking on the content or browsing online ads[7].However,some research in ICN has shown that the traditional Internet pricing mechanism cannot encourage ISPs to deploy caches in future Internet architectures[10-14].Therefore,we need new models to give them economic incentives to cooperate in caching and distributing content.

Some studies have contributed to the pricing mechanism of subscription (paid content) models in ICN[15-19],but so far,no research has been conducted on the pricing mechanism of a large number of free content in the ICN.Considering the above problems,we need to perfect the pricing mechanism on the ICN.In this work,a pricing mechanism with advertisers’participation is proposed.We study how to efficiently add advertisers to the ICN pricing model while deriving mutually beneficial strategies to maximize the revenues for ICN entities.With the participation of advertisers,more users can be greatly attracted,and at the same time,ISPs and CPs will have better revenue.

It is worth noting that we have studied the use of game theory methods based on Nash equilibrium to determine the caching and pricing strategy of ICN.In addition,we studied how advertisers and pricing strategies interact,and how caching costs affects ISP’s caching strategies.Our main contributions are summarized as follows:

• Different from the traditional paid content models in ICN,we add advertisers to the network pricing model and study the interaction between advertisers and other entities.

• We derive effective pricing and caching strategies for all ICN entities from the utility functions,user selection model,and advertiser model.

• We using game theory comprehensively consider the impact of caching and pricing on their revenue and give the solution method and results of the equilibrium point.

• We use Matlab to simulate the impact of changes in pricing and caching parameters on the revenue of various entities in different situations,evaluate the proposed scheme and compare with theContent Acquisition with Retail and Lump-sump(CARL)scheme.

The rest of the paper is organized as follows.Section II introduces and analyzes the research work of related pricing mechanism.The pricing model of free content is proposed in Section III.In Section IV,we analyze advertisers’behavior,and prove the existence of an equilibrium point.The results of the numerical analysis are presented in Section V.Finally,we summarize our work and further research direction in Section VI.

II.RELATED WORK

In the current Internet,much researchs have been done to increase the ISPs’revenue worldwide[5-9].In the traditional IP network,the typical models of pricing and charging have been researched.G.Kesidis [8]studied a simple bilateral market model of ISP and CP based on users’ demand,and proved that advertising revenue could stimulate users’demand.Altmanet al.[7]studied two charging modes of CP in the IP network,and explained how to set a reasonable charging mechanism.However,it only considered that each role has only one single entity.Eitan Hanawalet al.[9]explored the payment relationship between multiple ISPs and one CP in traditional networks.Douroset al.[5] studied the game between multiple ISPs and multiple CPs,explored whether ISPs had an incentive to cache content created by CPs,and finally proved that fair and effective profit-sharing could be achieved.In the current network,there are still some scholars dedicated to studying the security in mobile edge caching with reinforcement learning[20].

However,due to the differences in the characteristics between IP networks and ICN,none of these pricing mechanisms applied to IP networks is applicable to ICN[13,14].As early researchers on economic incentives in ICN,Rajahalmeet al.found that access ISP and transit ISP are reluctant to cooperate with other entities due to lack of income [10].Agyapong PKet al.[13] found that without some explicit monetary compensation from publishers,networks will fail to deploy the socially optimal number of caches.F.Kocaket al.[21] considered a two-sided market with multiclass demand and based on the delay-sensitive applications.The work in [15] compared the differences in pricing between CDN and ICN and proposed a simple pricing scheme for ICN.In [19],based on the unilateral payment model of traditional networks,a non-cooperative game model between ISP and CP in ICN was proposed.Mohammadet al.[16] proposed a cooperative cache pricing strategy that focuses more on popular content.Hajimirsadeghi Met al.[17]evaluated joint caching and pricing strategies among access networks,transit networks,and content providers in an Information-Centric Network.J.Duanet al.[18]proposed a collaborative pricing strategy,which considered two charging methods: retail and lump-sum.

However,the above studies only focus on the paid content in the ICN.There is currently no research on the pricing mechanism of the free content in ICN.According to the inspiration of traditional network development,most of the content on the network is free[10].Therefore,for researching the pricing mechanisms comprehensively,we should also pay attention to the free content in the network and the essential participant: advertisers.

III.SYSTEM MODEL

In this section,we present the free content pricing model and formulate the economic interactions among all entities including advertisers in the ICN.Eventually,the utility functions for all ICN entities to maximize their revenues are characterized.

3.1 Basic Framework

The hierarchical network model we adopted is shown in Figure 1.It contains two access ISPs(A and B),one transit ISP (C),one CP,any number of users and advertisers.The role of the access ISP is to connect the users to the network,and users can switch from one access ISP to another.The transit ISP provides widearea transport for access ISP,that is,through transit ISP,access ISP can interact with other entities in ICN.The CP distributes the content to users through the ISP and it can caches content to the ISP.Furthermore,Figure 1 shows the data flow and monetary flow between entities.

Figure 1.Simplified payment model between different entities in ICN.

Different from the models based on paid content in ICN,advertisers are added to our model.When users request content,the advertisers should pay the corresponding fees to the entity which stores the content.We study the impact of caching and pricing strategies on the revenue of ICN entities and obtain the best strategy to maximize their benefits.The scheme can guide different entities to adopt appropriate caching and pricing strategies to achieve the purpose of motivating ISPs to deploy in-network caches.

3.2 Cost Model

Based on the above analysis,we can usePAas the pricing strategy of ISP A.Similarly,the pricing strategies of ISP B and ISP C can be expressed asPBandPC.Content provider also has storage priceAnd when ISPs choose to cache content from CP,CP will charge them a one-time content feePO.Besides,CP determines the advertising feePADthat advertisers should pay for users’request.Therefore,CP’s pricing strategy includesPOandPAD.In this network,if users’ request content from access ISP A and ISP B,ISP A and ISP B charge themPAandPB.The transit ISP C charges access ISPs with pricePC,if it stores or forwards their requested content.Furthermore,each ICN entity will obtain advertising profits when they satisfy users’requests.

In order to reflect the price how to effect users’demand,we assume that the number of users at ISP A and ISP B has a linear relationship with their price.σAandσBrepresent the proportion of the actual users accessing ISP A and ISP B to the total users.The expressions are as follows:

In Eq.(1),ρAandρBrepresent the influence factors of price on the number of users.It can be seen that the prices of ISP A and ISP B can directly affect the number of users.When the price of ISP A rises,users will switch from ISP A to ISP B,so the number of users at ISP A will decrease,and the number of users at ISP B will increase.Conversely,when the number of users in ISP B decreases,the number of users in ISP A will increase.In addition to those symbols mentioned above,more notations are presented in Table 1.

Table 1.Notations.

Through analysis,it can be found that when ISPs and CP adopt strategies to maximize their profits,the strategies of different entities will inevitably conflict.In the following sections,we will use the knowledge of game theory to analyze the impact of caching and pricing strategies on the benefits of various entities.

3.3 Advertiser Model

Pareto’s law tells us that the vast majority of content provided by CP is free.In the IP network,CP can get additional income from advertisers.At the same time,in order to attract more users to request the content,CP will make a specific investment in the content.In the advertising model,users’demand can be expressed by the attention,such as users’requests.In ICN,ISP can distribute content instead of CP.Therefore,ISP can also get corresponding benefits from advertisers.This will promote content caching by the ISP.And within a certain range,the free contents attract more users,which increases the revenue of both ISP and CP.We will describe the economic interactions between advertisers and ICN entities.

Suppose there areNadvertisers in the network,and each advertiser has a fixed budgetEfor a given period of time[7].The investment willingness of each advertiser isv ∈[0,],wherevobeys a certain probability distribution.Its probability density function(PDF)is recorded asx(v),and the cumulative distribution function (CDF) is recorded asX(v).Only when the advertising feePADformulated by CP is less than or equal to the advertiser’s investment willingnessv,the advertisers will invest.

According to the nature of the cumulative distribution function,we can getP {X ≥v}=1-X(v).Therefore,the investment probabilityProb(v ≥PAD) of an advertiser can be expressed by 1-X(PAD).Then the advertisers’ total investment can be presented asN·E·Prob(v ≥PAD)=N·E·[1-X(PAD)].

3.4 Utility Function

In order to use mathematical methods to describe the revenue of entities,reasonable assumptions should be made on the model.The relevant assumptions of this model are as follows:

1) The one-time content fee paid by the ISPs to the CP is proportional to the amount of cached content.

2) The proportion of ISP cached content is equal to the proportion of users’ requests here.The content cache ratioαK,Mmeans that the requests arriving at K(K∈A,B)are in the entity M(M∈A,B,C,O)to be satisfied.

We model each part as:

The utility function of access ISP A is as follows:

EA1in Eq.(2)indicates the part of the users’request of ISP A that is satisfied at ISP A.EA2represents that the users’ request of ISP A are forwarded to another entities.EA3denotes the part of ISP B’s users’request satisfied at ISP A.EA4represents the advertising revenue of ISP A.EA5is the one-time content fee paid by ISP A to the CP.Access ISP A can control caching and pricing parametersαA,A,,PA.Access ISP B is the same as access ISP A,and we model each part as:

The utility function of access ISP B is as follows:

EB1in Eq.(4)indicates the part of the users’request of ISP B that is satisfied at ISP B.EB2represents the part of ISP B’s user’request forwarded.EB3denotes the part of ISP A’s users’ request satisfied at ISP B.EB4represents the advertising revenue of ISP B.EB5is the one-time content fee paid by ISP B to the CP.Access ISP B can control caching and pricing parametersαB,B,,PB.We model the parts of ISP C as:

The utility function of transit ISP C can be written as:

EC1in Eq.(6)indicates the part of the users’request of ISP A and B satisfied at ISP C.EC2represents the part of ISP A’s users’request satisfied at ISP B and CP.EC3denotes the part of ISP B’s users’request satisfied at ISP A and CP.EC4is the one-time content fee paid by ISP C to the CP.Transit ISP C can control caching and pricing parametersαA,B,αA,C,αA,O,αB,A,αB,C,αB,OandPC.The utility function of CP is given as:

The first term in Eq.(8) represents the part of the ISP A and ISP B request satisfied at the CP,and the second term is the revenue from selling content to the ISPs.CP can control pricing parametersPADand

IV.FREE CONTENT PRICING STRATEGY

4.1 Maximum Response Function

In order to obtain the equilibrium point in the game,it is necessary to write the maximum response function of each entity’s utility.The maximum response function of access ISP A is:

ISP B is similar to ISP A,and its maximum response function is:

The maximum response function for the transit ISP C is given as:

And the maximum response function for CP is:

4.2 Analysis of Equilibrium

To solve the above problems,we need to derive utility functions and solve the following equations:

Theorem 1.The value of the caching parameter at the equilibrium point can only be 0 or 1.[17]

Proof.The solution of a maximization(minimization)problem with an objective function that has a linear relationship with the variable is the boundary point of the feasible interval.Therefore,since the relationship between utility function and caching parameters are linear,then for maximizing the utility functions,they just take on the boundary values.As theαK,M ∈[0,1],then their values can be either 0 or 1.

Theorem 2.The amount of content cached by ISPs is affected by the caching cost and the cost of obtaining content from others.

Details of the proof for Theorem 2 is given in Appendix A.

Based on Theorem 1 and Theorem 2,the game in ICN is divided into nine results,and the classification details are shown in Table 2.

Table 2.Caching strategies.

4.3 Advertisers and CP’s Behavior Analysis

In advertising mode,we useDAD(σA+σB) to denote the number of users in advertising mode.According to the Section 3.3,we can obtain:

When the users obtain content from the CP,the users’ demands satisfied at the CP isDAD(σAαA,O+σBαB,O).Since the users’ demands of the CP come from ISP A and ISP B,so it is limited by ISP A and ISP B,that is,the users’demands at the CP should be:

Then,the benefit maximum response function of CP is:

According to Eq.(16)and Eq.(17),plot theEOalone withPAD,as shown in Figure 2.

Figure 2.Utility function of CP in advertising mode.

Under this premise,D(C)=DADis satisfied in any case of Table 2.For the convenience of description,the following usesD(C)as the user’s overall demands.

4.4 Results

Table 2 divides the situation of game equilibrium points into 9 cases: in case 1,the cost of accessing ISP A and ISP B to cache content is less than the cost of forwarding users’requests,so each one chooses to cache all content.This situation causes transmission ISP C useless.In cases 2-4,the cost of cached content by ISP A is small,but the cost of cached content by ISP B is higher than the cost of forwarding users’requests.Cases 5-7 are exactly the opposite of cases 2-4.Cases 8-9 indicate that the cost of caching the content of ISP A and ISP B is higher than the cost of forwarding the users’ request.Therefore,neither ISP A nor ISP B will cache any content.Under the assumption ofρA=ρB=ρ,βA=βB=βandcA=cB=c,we solved the best strategy and best benefit of each entity for the nine situations.We show the calculation results of Case 1 in Table 2.The calculation results are shown in Table 3.

Table 3.The equilibrium of case 1.

V.NUMERICAL RESULTS

In this section,we simulate and evaluate our scheme based on the network structure shown in Figure 1.We useαK,Mto represent the proportion of requests arriving atKthat are satisfied atM.Unless otherwise specified,the access ISP A’s cache parameters in the experiment are as follows:αA,A=0.5,αA,C=αA,B=0.1,αA,O=0.3.Caching parameters of access ISP B are set asαB,B=0.4,αB,C=0.2,αB,O=αB,A=0.2.For each unit of data,the caching costs of different ISPs and CPs are:cA=cB=0.5,cC=cO=0.4.The ratio of the traffic price and cache price is set as:β=7.The impact factor of price on number of users is set as:ρ=0.1.The initial number of users of ISP A and B is set to 10000.

5.1 THE IMPACT OF ADVERTISER FEES ON ACCESS ISPs’PRICE

According to the previous analysis,it is known that the strategies adopted by entities in the network model are closely related.After one player adjusts the strategy,other players will make corresponding adjustments.Figure 3 shows the impact of advertising fees set by the CP on the pricing of access ISPs.With the increase ofPAD,in order to achieve the best revenue,access ISPs will appropriately reduce the price to the user in exchange for more users’ clicks.Increased users’clicks will lead to increased advertising revenue.In this model,access ISP’s price is linearly related to advertisers’fees.

Figure 3.Impact of advertisers fees on access ISPs’price.

5.2 THE IMPACT OF TRANSIT ISP’s PRICE

The revenue of the transit ISP consists of two parts,one from transmitting the users’ request out and the other from charging advertising fees when users’ request local content.Accordingly,when the content stored in the transit ISP cannot satisfy the users’ requests,the pricing of the access ISPs will affect the pricing of the transit ISP.Figure 4 shows a linear relationship between the two prices.When the price of transit ISP increases,access ISPs’price will increase.However,this will reduce the number of users at access ISPs,which will affect the advertising revenue of the transit ISP eventually.

Figure 4.Impact of ISP C’s price on access ISPs’price.

5.3 THE IMPACT OF THE ACCESS ISP’s PRICE AND TRANSIT ISP’s PRICE

Figure 5 shows the impact of the price of access ISP A and the price of transit ISP C on the revenue of access ISP A.It can be seen from the figure that as the price of transit ISP C increases,the overall revenue of ISP A decreases.When transit ISP C to forward users’demand for free,ISP A has the best revenue.Meanwhile,When the price of ISP C is determined,there is an extreme point in the revenue function of ISP A,that is the best pricing strategy for ISP A.When ISP A’s price exceeds the extreme point,its revenue will decline,because the high price will lead to the number of users decrease.

Figure 5.Impact of ISP A’s and ISP C’s price on ISP A’s utility.

5.4 THE IMPACT OF THE ACCESS ISP’s PRICE AND ADVERTISER FEES

Figure 6 describes the impact of ISP A’s price and advertising fees determined by CP on the revenue of ISP A and CP.One can see that when the advertising fees are low,the revenue of CP will increase as the advertising fees increase.When the advertising fees are larger than the optimal value,the investment willingness of advertisers will decrease,which will cause the advertising revenue to decline.The revenue of ISP A will increase as the advertising fees increase.However,The revenue of CP will decrease as ISP A’s price increase.ISP A will only determine the price based on its benefits.In this case,CP and ISP A will restrain each other to achieve a balanced situation.

Figure 6.Impact of ISP A’s price and advertiser fees on the utility function.

5.5 THE IMPACT OF THE ACCESS ISP’s PRICE AND CP’s ONE-TIME CHARGES

Figure 7 describes the impact of ISP A’s price and CP’s one-time content fees on their benefits.We can see that the revenue of CP will increase with the one-time content fees rise;in contrast,the revenue of ISP A will decrease.If the one-time content fees are too high,ISP A will be reluctant to purchase content from CP.In this case,the ISP will be unwilling to deploy caches.Therefore,the CP must set an appropriate price for one-time content fees,which not only guarantees its revenue but also stimulate the ISP to deploy caches.

Figure 7.Impact of ISP A’s price and CP’s one-time content fees on the utility function.

5.6 COMPARISON BETWEEN FCPS AND CARL

Figure 8 compares the performance of free content pricing strategy proposed in this paper(FCPS)model with the latestCARLmodel based on paid content in[18].CARL is a predecessor’s research on the pricing mechanism of paid content.All other parameters of the two models in the experiment take the same value.The simulations show that theCARLmodel cannot be well applied to the actual situation where free content exists.In Figure 8,the red curve simulates the revenue of theCARLmodel with content fee of 0,3,and 6,while the blue curve simulates the revenue of theFCPSmodel with advertising price of 0,3,and 6.

Figure 8.Comparison between FCPS and CARL.

To simulate free content in the subscription model,we set the content fee to 0.The simulation results in Figure 8a and Figure 8b show that when the price of ISP is low,theCARLmodel’s revenue is negative.If the content is free,the expenditure of ISP A and ISP C is more than their income.This situation will not occur in theFCPSmodel.Even if the fees charged by ISP A and ISP C are zero,due to the presence of advertisers,ISPs can still guarantee good revenue,which will be beneficial to encourage ISPs to deploy caches.However,it can also be seen from the figure that when the advertising cost is zero,the revenue of the ISP are unsatisfactory.The actual situation shows that when the ISP’s fees are relatively low,it will get more users.In order to improve the situation where the revenue is negative under theCARLmodel,we also simulate the situation where the content fee is 3 and 6.The simulation results show that within a specific range,increasing the content fee will increase the revenue of the ISPs.However,excessive content fees will reduce the number of users,leading to a decline in revenue.Figure 8c shows the impact of ISP A’s price on CP’s revenue.When the content is free,the CP under theCARLmodel has only one-time revenue from selling content,without retail revenue.In this case,theCARLmodel cannot show the effect of the price of ISP A on CP’s revenue,which is not applicable.Because the price of ISP A will affect the number of users,thus affecting the revenue of CP.Besides,even ifCARLincreases content costs,it can be seen that in theFCPSmodel,the revenue of CP are still more advantageous.It can be seen from the figure that when the advertising cost is zero,the utility of CP is not ideal.Therefore,reasonable advertisers are required to participate in the game to obtain better results.

In summary,in networks with free content,the existing models such asCARLare no longer applicable.Therefore,a new model is needed to describe the economic interaction of entities in ICN.TheFCPSmodel in this paper is based on free content,which is more practical and applicable.Meanwhile,it can be seen from the comparison results that theFCPSmodel will bring higher benefits to each entity in the ICN.

VI.CONCLUSION

In this paper,we have presented the pricing and caching strategies based on free content in ICN for the first time.For the free content,we have added advertisers to the ICN pricing model while considering the interaction between pricing strategies and advertiser behaviors.Advertising fees determined by ICN entities affect the investment willingness of advertisers.For example,advertisers will give up investing with high fees.Based on the advertiser investment model and free content,the utility function for each entity is derived,and the mutually beneficial pricing and caching strategies for different entities are developed.Further,for the case of symmetric access ISPs,we have figure out that the equilibrium point exists.Our extensive simulation results have shown that the pricing and caching strategies based on free content with the advertisers’ participation model can maximize the revenue for all entities and significantly surpasses the existingCARLmodel.

In future work,we will further improve and develop our model.We will gradually study the impact of CP’s investment strategy on the income of ICN entities,analyze the situation of advertisers’ investment willingness under different probability distributions,and comprehensively consider economic models with charing and free content.

ACKNOWLEDGEMENT

This work was supported by the Key R&D Program of Anhui Province in 2020 under Grant No.202004a05020078 and China Environment for Network Innovations (CENI) under Grant No.2016-000052-73-01-000515.

APPENDIX

Proof.Proof of Theorem 2(Through ISP A)

The expression in brackets in Eq.(19) is the total cost paid by ISP A when it chooses to cache the content,which is recorded as the equivalent caching costWhenPC-＞0,it means that the cost of ISP A to obtain content from others is higher than the cost to cache content.In this case,ISP A will choose to cache the content locally.Conversely,whenPC-＜0,it means that the cost of ISP A to obtain content from others is less than the cost to cache content,so ISP A will choose to forward the user’s requests.