Optimizing TTL Caches under Heavy-Tailed Demands

Abstract

In this paper we analyze the hit performance of cache systems that receive file requests with general arrival distributions and different popularities. We consider timer-based (TTL) policies, with differentiated timers over which we optimize. The optimal policy is shown to be related to the monotonicity of the hazard rate function of the inter-arrival distribution. In particular for decreasing hazard rates, timer policies outperform the static policy of caching the most popular contents. We provide explicit solutions for the optimal policy in the case of Pareto-distributed inter-request times and a Zipf distribution of file popularities, including a compact fluid characterization in the limit of a large number of files. We compare it through simulation with classical policies, such as least-recently-used and discuss its performance. Finally, we analyze extensions of the optimization framework to a line network of caches.