Joint Pricing and Proactive Caching for Data Services: Global and User-centric Approaches

CTN Issue: September 2014

Authors: John Tadrous, AtillaEryilmaz, and Hesham El Gamal (The Ohio State University, USA)
Title: “Joint Pricing and Proactive Caching for Data Services: Global and User-centric Approaches”
Publication: 2014 IEEE INFOCOM Workshop on Smart Data Pricing

A vexing problem for the service provider is the (typically) high ratio of  daily peak demand to average demand, especially in the context of streaming media.  The service provider must provision sufficient resources in order to handle the peak demand (at potentially significant cost), but these resources then sit idle during off peak times (with corresponding reduced profits).   An appealing solution to lower this ratio is for the service provider to prefetch content during off peak times in order to reduce the network load during peak times.  In order for this prefetching to be effective, the provider must either have a very good characterization of user streaming preferences in each time period, or must be able to incentivize the user to view the cached material.  These two options are by no means exclusive: the provider can prefetch content based on user preference profiles, as well as set prices for streaming to incentivize users to view cached content.  This paper studies the optimal caching and pricing policies in this setting.

As a simplifying but inessential condition, the authors focus on the case of a single user and a single service provider, with a fixed collection of items (streaming content).  The user’s “demand profile” is characterized by a probability that user will select each item to watch in each time period; the user then selects at most one item to watch in each time period, in accordance with the governing probabilities.  These probabilities that the user will select each item are influenced by the prices the service provider sets on each item in each time step. 

In the proactive architecture, the provider selects items to prefetch for the user in advance, as well as a price on each item in the collection.  This leads to a natural “joint pricing and proactive download profit maximization problem” (Equation 3) over the proactive downloads and prices.  By leveraging the assumed cyclostationarity of the user demand profile (i.e., a user’s demand varies over the course of a day, but has the same daily variation across days), the authors are able to focus in on a single “cycle” (day).  Unfortunately, the associated optimization problem has a non-concave objective, making it difficult to obtain a general explicit solution.  Nonetheless, the optimization can be tackled in an iterative manner, by first fixing the proactive downloads and optimizing over prices, then fixing the prices and optimizing over the proactive downloads, etc.  In this iterative manner, increasingly accurate approximations to the optimal solution may be obtained.

The authors next consider a slightly different problem formulation, where the user controls the proactive download decisions and the ISP sets the price on the media content.  The user wishes to minimize the costs its requests incur at the ISP, and the ISP wishes to maximize profit. This scenario is an instance of a coordination game, and due to the convexity of the profit function, the (Nash) equilibrium of this game is obtained by the two players (the user and the ISP) iteratively optimizing the objective over its control, holding the previous player’s control fixed.  Under this scenario, the authors establish (Theorems 3 and 4) that (optimized) proactive downloads (with suitably optimized prices) yields lower user payments and increased ISP profits compared with a system without proactive downloads.

In summary, the paper studies a natural scenario where users and service providers help each other in a distributed manner.  Users select items for proactive download based on set prices and user viewing preference, and the ISP selects prices on content in response to their cached state and the corresponding profit.

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