TTL model for an LRU-based similarity caching policy

Similarity caching allows requests for an item to be served by a similar item. Applications include recommendation systems, multimedia retrieval, and machine learning. Recently, many similarity caching policies have been proposed, like SIM-LRU and its generalization RND-LRU, but the performance analysis of their hit ratio is still wanting. In this paper, we show how to extend the popular time-to-live approximation in classic caching to similarity caching. In particular, we propose a method to estimate the hit ratio of the similarity caching policy RND-LRU. Our method, the RND-TTL approximation, introduces the RND-TTL cache model and then tunes its parameters in such a way as to mimic the behavior of RND-LRU. The parameter tuning involves solving a fixed point system of equations for which we provide an algorithm for numerical resolution and sufficient conditions for its convergence. Our approach for approximating the hit ratio of RND-LRU is evaluated on both synthetic and real-world traces.