Paging with Multiple Caches

TL;DR

This paper introduces the Multiple Cache Paging (MCP) problem, extending classical paging to multiple caches, and analyzes its complexity, showing unbounded competitive ratios for online algorithms, while proposing near-optimal stochastic policies.

Contribution

It formalizes the MCP problem, proves the unbounded competitive ratio for online algorithms, and develops simple stochastic policies that perform near-optimally without cache coordination.

Findings

Competitive ratio is unbounded for arbitrary inputs.

Simple stochastic policies achieve near-optimal performance.

MCP differs fundamentally from classical paging problem.

Abstract

Modern content delivery networks consist of one or more back-end servers which store the entire content catalog, assisted by multiple front-end servers with limited storage and service capacities located near the end-users. Appropriate replication of content on the front-end servers is key to maximize the fraction of requests served by the front-end servers. Motivated by this, a multiple cache variant of the classical single cache paging problem is studied, which is referred to as the Multiple Cache Paging (MCP) problem. In each time-slot, a batch of content requests arrive that have to be served by a bank of caches, and each cache can serve exactly one request. If a content is not found in the bank, it is fetched from the back-end server, and one currently stored content is ejected, and counted as fault. As in the classical paging problem, the goal is to minimize the total number of faults. The competitive ratio of any online algorithm for the MCP problem is shown to be unbounded for arbitrary input, thus concluding that the MCP problem is fundamentally different from the classical paging problem. Consequently, stochastic arrivals setting is considered, where requests arrive according to a known/unknown stochastic process. It is shown that near optimal performance can be achieved with simple policies that require no co-ordination across the caches.