Comparing Locality of Reference – Some Folk Theorems for the Miss Rates and the Output of Caches

The performance of demand-driven caching is known to depend on the locality of reference exhibited by the stream of requests made to the cache. In spite of numerous efforts, no consensus has been reached on how to formalize this notion, let alone on how to compare streams of requests on the basis of their locality of reference. We take on this issue with an eye towards validating operational expectations associated with the notion of locality of reference. We focus on two “folk theorems,” namely (i) The stronger locality of reference, the smaller the miss rate of the cache; (ii) Good caching is expected to produce an output stream of requests exhibiting less locality of reference than the input stream of requests. We discuss these two folk theorems in the context of a cache operating under a demand-driven replacement policy when document requests are modeled according to the Independent Reference Model (IRM). As we propose to measure strength of locality of reference in a stream of requests through the skewness of its popularity distribution, we introduce the notion of majorization as a mean for capturing this degree of skewness. We show that these folk theorems hold for caches operating under a large class of cache replacement policies, including the optimal policy A0 and the random policy, but may fail under the LRU policy.