Serving content with unknown demand: the high-dimensional regime

Abstract

In this paper we look at content placement in the highdimensional regime: there are n servers, and O(n) distinct types of content. Each server can store and serve O(1) types at any given time. Demands for these content types arrive, and have to be served in an online fashion; over time, there are a total of O(n) of these demands. We consider the algorithmic task of content placement: determining which types of content should be on which server at any given time, in the setting where the demand statistics (i.e. the relative popularity of each type of content) are not known a-priori, but have to be inferred from the very demands we are trying to satisfy. This is the high-dimensional regime because this scaling (everything being O(n)) prevents consistent estimation of demand statistics; it models many modern settings where large numbers of users, servers and videos/webpages interact in this way.We characterize the performance of any scheme that separates learning and placement (i.e. which use a portion of the demands to gain some estimate of the demand statistics, and then uses the same for the remaining demands), showing it is order-wise strictly suboptimal. We then study a simple adaptive scheme -which myopically attempts to store the most recently requested content on idle serversand show it outperforms schemes that separate learning and placement. Our results also generalize to the setting where the demand statistics change with time. Overall, our results demonstrate that separating the estimation of demand, and the subsequent use of the same, is strictly suboptimal.

Optimal Content Replication and Request Matching in Large Caching Systems

“…The vector of content popularities is denoted as Λ = (λ c , c ∈ C) and is assumed to be a known constant throughout the paper. Typically, the popularities of news items containing videos or movies vary over periods ranging from few hours to few weeks [11] (and have to be estimated periodically [12]) which are slower than the time scales of interest in the paper. For this reason we do not consider the effect of time-varying popularities and errors in estimation of the popularities in this paper.…”

Resource pooling in large-scale content delivery systems

“…The problem of content replication for the case where each request can only be served by one cache has been widely studied [6]- [10], [14]. In [6]- [8] the focus is on the setting where each request can be served by any one cache and the central server communicates with each user separately.…”

“…In [6]- [8] the focus is on the setting where each request can be served by any one cache and the central server communicates with each user separately. The setting where each user is pre-matched to a server and the central server communicates with the users via an error free broadcast link has been studied in [9], [10], [15]- [17].…”

“…Recent work on content replication strategies in content delivery systems focuses on the setting where each user request is served by only one cache and each cache serves only one request at a time [6]- [10]. In a departure from these works, we explore the benefits of relaxing this constraint by allowing caches to pool their resources, i.e., allowing a request to be served by multiple caches.…”

Impact of Fairness and Heterogeneity on Delays in Large-scale Content Delivery Networks

“…There has been substantial recent interest in understanding basic design questions for these systems including, see e.g. [10,14,20,23] and references therein: How should the number of file copies scale with the demand? What kinds of hierarchical caching policies are most suitable?…”