Fundamentals of Caching Layered Data objects

The effective management of the vast amounts of data processed or required by modern cloud and edge computing systems remains a fundamental challenge. This paper focuses on cache management for applications where data objects can be stored in layered representations. In such representations, each additional data layer enhances the 'quality' of the object's version, albeit at the cost of increased memory usage. This layered approach is advantageous in various scenarios, including the delivery of zoomable maps, video coding, future virtual reality gaming, and layered neural network models, where additional data layers improve quality/inference accuracy. In systems where users or devices request different versions of a data object, layered representations provide the flexibility needed for caching policies to achieve improved hit rates, i.e., delivering the specific representations required by users. This paper investigates the performance of the Least Recently Used (LRU) caching policy in the context of layered representation for data, referred to as Layered LRU (LLRU). To this end, we develop an asymptotically accurate analytical model for LLRU. We analyze how LLRU's performance is influenced by factors such as the number of layers, as well as the popularity and size of an object's layers. For example, our results demonstrate that, in the case of LLRU, adding more layers does not always enhance performance. Instead, the effectiveness of LLRU depends intricately on the popularity distribution and size characteristics of the layers.