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Joint Caching and Pricing Strategies for Popular Content in Information Centric Networks
Mohammad Hajimirsadeghi, Narayan B. Mandayam, Alex Reznik
TL;DR
The paper asks how ICNs can coordinate caching and pricing as popular content is distributed among access networks, a transit network, and a content provider. It models their strategic interaction using generalized Zipf popularity and shows that equilibrium caching is all-or-nothing, with a unique popularity threshold in the symmetric-access case.
Problem
ICNs need pricing policies that incentivize cooperation in caching and distributing content with different popularities.
Source: §I · p. 1Method
The paper models access ICNs, a transit ICN, and a content provider as game-theoretic players choosing joint caching and pricing strategies under generalized Zipf demand.
Source: §I · p. 1Results
At Nash equilibrium, caching is 0-1, and symmetric access ICNs have a unique equilibrium policy determined by a threshold on content popularity.
Source: §VIII · p. 11Takeaways & Limitations
In the symmetric-access case, content above the popularity threshold is cached, yielding a threshold-based caching policy.
Source: §VIII · p. 11The general mixed-integer, multi-objective problem does not admit a characterized unique Nash equilibrium in pricing and caching strategies.
Source: B. Characterization of Nash Strategies · p. 6
Abstract
from arXiv · showhide
We develop an analytical framework for distribution of popular content in an Information Centric Network (ICN) that comprises of Access ICNs, a Transit ICN and a Content Provider. Using a generalized Zipf distribution to model content popularity, we devise a game theoretic approach to jointly determine caching and pricing strategies in such an ICN. Under the assumption that the caching cost of the access and transit ICNs is inversely proportional to popularity, we show that the Nash caching strategies in the ICN are 0-1 (all or nothing) strategies. Further, for the case of symmetric Access ICNs, we show that the Nash equilibrium is unique and the caching policy (0 or 1) is determined by a threshold on the popularity of the content (reflected by the Zipf probability metric), i.e., all content more popular than the threshold value is cached. We also show that the resulting threshold of the Access and Transit ICNs, as well as all prices can be obtained by a decomposition of the joint caching and pricing problem into two independent caching only and pricing only problems.
I. INTRODUCTION
The paper motivates ICN caching and pricing as a response to growing content traffic and the need for cooperation among network entities. It models popularity with a generalized Zipf distribution and studies joint caching and pricing in a hierarchical ICN.
I. INTRODUCTION
- In-network caching is presented as a way to serve popular content near users, improving response time and reducing congestion and access latency.The paper notes that request rates may follow a generalized Zipf distribution, with the rate for content ranked i proportional to 1/i^γ for positive γ below one.Source: §I · p. 1
- Because ICNs must cooperate to cache and distribute content, pricing policies are needed to provide monetary incentives to network participants.The paper argues that contemporary pricing policies may not incentivize lower-tier ISPs to cooperate in future network architectures.Source: §I · p. 1
- The paper studies joint caching and pricing among access ICNs, a transit ICN, and a content provider, with strategies shaped by content popularity.Its model uses generalized Zipf request probabilities and popularity-varying caching costs for ICNs, while the content provider's unit cost is fixed across content types.Source: §I · p. 1
II. RELATED WORK
- Prior work considers caching and pricing in network settings, but the cited studies do not address joint caching and pricing in an ICN with content of differing popularity.The paper contrasts its popularity-aware setting with earlier work on joint strategies that treated ICNs as agnostic to content type.Source: §II · p. 2
A. Content Popularity
- The model assumes users across the network share the same generalized Zipf popularity distribution, while differing per-user popularity profiles remain an open problem.The paper motivates Zipf modeling by reported empirical fit and analytical tractability, and notes that demand-model changes and learning could extend the framework.Source: A. Content Popularity · p. 3
B. Cost Model
The cost model makes access and transit caching costs depend inversely on content popularity, while the provider incurs a fixed cost per unit of any content.
B. Cost Model
- Access and transit ICN caching costs are defined to be inversely proportional to content popularity.The model uses a fixed initial caching cost for each ICN.Source: B. Cost Model · p. 3
- As the Zipf factor γ changes, caching costs decrease for more popular content and increase for less popular content.For fixed content rank, the direction of the cost change depends on whether the content is relatively popular or less popular.Source: B. Cost Model · p. 3
- Unlike access and transit ICNs, the content provider has no content-type caching priority and incurs the same cost cO for every unit of data it serves.The model describes the provider as caching all content types.Source: B. Cost Model · p. 3
C. Access and Demand Model
The model places two access ICNs between users and a transit ICN, with a content provider supplying requested data. It specifies usage-based service prices and makes user demand depend linearly on prices.
C. Access and Demand Model
- Two access ICNs connect users to the content network, a transit ICN provides wide-area transport, and a content provider supplies content.Users may switch between access ICNs, and each network entity can cache content or obtain it from another source.Source: C. Access and Demand Model · p. 3
- Access ICNs set network and storage prices, while the transit ICN and content provider charge for their respective transport, storage, or content services.The model uses usage-based prices per unit of data and assumes a linear relationship between an access ICN's network and storage prices, with storage price lower.Source: C. Access and Demand Model · pp. 3–4
- User demand is modeled as a linear function of prices, with positive reflective coefficients for price influence.Demand decreases as the content price rises, and users may switch to another access ICN when one access ICN raises its price.Source: C. Access and Demand Model · p. 4
- The network model frames caching and pricing as competing decisions among entities seeking to maximize revenue.The paper uses a game-theoretic approach to analyze their joint strategies.Source: C. Access and Demand Model · p. 4
A. Utility Function
Each network player earns utility by providing services, with caching and forwarding choices affecting how requests are served. The paper represents these choices and prices in a non-cooperative game in which players maximize their own utility.
A. Utility Function
- Each ICN may cache content or forward requests to other ICNs or the content provider according to the utility it gains.The utility functions depend on prices, popularity-sensitive caching costs, demand, and the fractions of content stored.Source: A. Utility Function · p. 4
- An access ICN's utility accounts for serving its own users from cache, forwarding its users' demand, and serving demand forwarded from the other access ICN.The access ICN controls its caching fraction and prices; the passage defines the terms of its payoff using demand and revenue from serving content.Source: A. Utility Function · pp. 4–5
- The transit ICN's utility includes serving access-ICN requests from its cache or forwarding them, while the provider serves requests not handled by either network tier.The provider has all content available and incurs the same cost across content types.Source: A. Utility Function · p. 5
- The non-cooperative game assigns each player a joint caching-and-pricing strategy and utility, with each player seeking to maximize its own utility.A Nash equilibrium is an operating point at which no player benefits from a unilateral strategy deviation.Source: A. Utility Function · p. 5
B. Characterization of Nash Strategies
The four network entities choose caching and pricing strategies in a non-cooperative game, with each optimizing its utility against the other players’ strategies. At equilibrium, caching is binary, while pricing can remain continuous, so uniqueness of the joint equilibrium cannot generally be characterized.
B. Characterization of Nash Strategies
- Access ICNs A and B, transit ICN C, and content provider O each maximize utility; the access ICNs adjust caching and pricing strategies while other players’ strategies are unknown.Source: B. Characterization of Nash Strategies · pp. 5–6
- Caching variables take only 0 or 1 at equilibrium because utility is linear in each caching parameter over its feasible interval.A linear objective reaches an endpoint of the interval [0, 1].Source: B. Characterization of Nash Strategies · p. 6
- If the transit price for content i exceeds access ICN A’s local caching cost, A caches that content rather than transferring its request to the transit ICN.The condition is PC > cAi.Source: B. Characterization of Nash Strategies · p. 6
- Pricing parameters may be continuous, so the joint problem is a mixed-integer program and general uniqueness of the Nash equilibrium in pricing and caching cannot be characterized.Source: B. Characterization of Nash Strategies · p. 6
V. GENERALIZATION TO K ACCESS ICNS
The model extends from two access ICNs to K access ICNs connected to one transit ICN and one content provider. In this generalized game, caching variables remain binary, producing all-or-nothing strategies.
V. GENERALIZATION TO K ACCESS ICNS
- The access ICN set comprises A1 through AK, connected to transit ICN C, and α denotes the set of all caching variables.Source: §V · p. 6
- The demand of content type i at access ICN Aj is σAj qM(i).Source: §V · p. 6
- The generalized model formulates utility-maximization problems for each access ICN, the transit ICN, and the content provider.Source: §V · p. 6
- For K access ICNs connected to one transit ICN and one content provider, all caching variables take binary 0–1 values.The generalized joint caching and pricing game is therefore a mixed-integer program.Source: §V · p. 6
VI. SYMMETRIC ACCESS ICNS SCENARIO ANALYSIS
In the symmetric scenario, access ICNs do not serve one another’s users, and caching choices reduce to popularity-based thresholds. The caching problem can be separated from pricing, yielding a unique Nash equilibrium.
VI. SYMMETRIC ACCESS ICNS SCENARIO ANALYSIS
- For each content type, symmetric access ICNs do not cache requests for one another’s users; this result is specific to symmetry.In the asymmetric setup, access ICNs can cache requests for users of other access ICNs.Source: §VI · pp. 6–7
- With symmetric access ICNs, monotonically increasing caching costs and binary caching choices imply that each access ICN caches content up to a popularity threshold.The transit ICN likewise uses a threshold to choose which less-popular content to cache, forwarding content beyond its threshold to the provider.Source: §VI · p. 8
- The symmetric joint problem is decomposed into independent caching and pricing optimization problems.The caching problem yields a four-tuple that is substituted into the pricing problem.Source: §VI · p. 8
- The caching problem is a two-player matrix game between the transit ICN and content provider, with discrete actions based on their prices and caching thresholds.The transit ICN’s and provider’s feasible actions are discrete, while access ICNs follow the transit ICN’s actions.Source: §VI · p. 9
- Theorem 4 establishes a unique Nash equilibrium for the symmetric joint caching and pricing game.The analysis derives the caching thresholds first and then obtains the prices from them.Source: §VI · p. 9
VII. NUMERICAL RESULTS
The numerical results show how caching thresholds and prices vary with Zipf skew, content-provider cost, and the transit-to-access caching-cost ratio. As popularity becomes more skewed, access ICNs favor popular content, while transit and provider caching and pricing respond to their costs.
VII. NUMERICAL RESULTS
- The numerical scenario uses two symmetric access ICNs, one transit ICN, one provider, and M = 100 content types requested according to a generalized Zipf distribution.The demand-price sensitivity parameters are set to 0.1, and the storage-to-network price scaling parameters are set to 10.Source: §VII · p. 10
- At R = 0.7, caching thresholds vary with Zipf factor γ and provider cost cO; as γ rises, access ICNs favor popular content while transit caching declines.For small γ the transit ICN caches most content; at higher γ it may stop caching and forward requests to the provider.Source: Figure 4 · p. 10, §VII · p. 10
- At R = 0.5, the transit ICN caching cost is half the access ICN cost, and the transit ICN caches more requested content.The results compare caching thresholds across provider costs and Zipf factors.Source: Figure 5 · p. 10, §VII · pp. 10–11
- Access price PA decreases with γ when provider cost cO is relatively low, while higher cO raises access prices and can produce bimodal variation with γ.The reported explanation links the price changes to caching costs, transit and provider prices, and access-cache choices.Source: Figure 6 · p. 11, §VII · p. 11
- As γ increases, the transit price and content-provider storage price increase with the caching costs of less-popular content.The figure reports transit price and provider storage price against γ for different provider costs at R = 0.7.Source: §VII · p. 11, Figure 7 · p. 11
VIII. CONCLUSION
The conclusion reports all-or-nothing Nash caching and, for symmetric access ICNs, a unique popularity-threshold equilibrium whose thresholds and prices can be found by decomposition. Numerical results describe how caching roles shift as popularity becomes more skewed, while identifying broader network settings and learned popularity as future directions.
VIII. CONCLUSION
- At Nash equilibrium, caching strategies are 0-1; for symmetric access ICNs, the equilibrium is unique and caches content above a popularity threshold.The threshold is expressed using the Zipf probability metric.Source: §VIII · p. 11
- The joint caching-and-pricing problem decomposes into independent caching-only and pricing-only problems for obtaining the thresholds and prices.Source: §VIII · p. 11
- As γ increases and popularity becomes more skewed, access ICNs cache popular content, the provider serves less-popular requests, and the transit ICN forwards demands without caching.Source: §VIII · p. 11
- The analysis leaves asymmetric access ICNs and learned content popularity for further investigation; interconnected multiple transit ICNs and multiple providers are also future work.Source: §VIII · pp. 11–12
APPENDIX A PROOF OF PROPOSITION 1
The appendix proves concavity of the sequences used in Proposition 1 by checking discrete second differences and the monotonicity of the Zipf probability sequence. It establishes concavity over the stated content-count and Zipf-factor ranges.
APPENDIX A PROOF OF PROPOSITION 1
- The proof uses that the sum of two concave sequences is concave to establish concavity of g from its component sequences.Source: Appendix A · p. 12
- The proof sets qM(i) = 0 for i > M and treats ε tending to zero as zero when defining the sequences.Source: Appendix A · p. 12
- For every M and 0 ≤ γ ≤ 1, sequence f is concave, as shown by the sign of its discrete second difference.The proof treats the limiting small ε as zero and uses ϕγ(Th) to establish the inequality.Source: Appendix A · p. 12
- For g, the proof reduces the remaining concavity check to qM(i), which is strictly decreasing across the stated threshold-index range.The resulting inequality is qM(ThC) > qM(ThC + 1) for ThC = 1, ..., M−1.Source: Appendix A · p. 12