Abstract

The web is the largest distributed database deploying time-to-live-based weak consistency. Each object has a lifetime-duration assigned to it by its origin server. A copy of the object fetched from its origin server is received with maximum time-to-live (TTL) that equals its lifetime duration. In contrast a copy obtained through a cache have shorter TTL since the age (elapsed time since fetched from the origin) is deducted from its lifetime duration. A request served by a cache constitutes a hit if the cache has a fresh copy of the object. Otherwise, the request is considered a miss and is propagated to another server. It is evident that the number of cache misses depends on the age of the copies the cache receives. Thus, a cache that sends requests to another cache would suffer more misses than a cache that sends requests directly to an authoritative server.

In this paper, we model and analyze the effect of age on the performance of various cache configurations. We consider a low-level cache that fetches objects either from their origin servers or from other caches and analyze its miss-rate as function of its fetching policy. We distinguish between three basic fetching policies, namely, fetching always from the origin, fetching always from the same high-level cache, and fetching from a “random” high-level cache. We explore the relationships between these policies in terms of the miss-rate achieved by the low-level cache, both on worst-case sequences, and on sequences generated using particular probability distributions.

Guided by web caching practice, we consider two variations of the basic policies. In the first variation the high-level cache uses pre-term refreshes to keep a copy with lower age. In the second variation the low-level cache uses extended lifetime duration. We analyze how these variations affect the miss-rates. Our theoretical results help to understand how age may affect the miss-rate, and imply guidelines for improving performance of web caches.

Keywords: Caching hierarchy; Cache consistency; Time-to-live; Web caching; Miss-rate