On the Convergence of the TTL Approximation for an LRU Cache under Independent Stationary Request Processes

Bo Jiang 1 Philippe Nain 2 Don Towsley 1
2 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : The modeling and analysis of an LRU cache is extremely challenging as exact results for the main performance metrics (e.g. hit rate) are either lacking or cannot be used because of their high computational complexity for large caches. Recently a TTL-based approximation has been developed for requests described by various workload models and numerically demonstrated to be accurate. The theory for such an approximation, however, is not yet fully developed. In this paper we provide theoretical justification for the approximation in the case where distinct contents are described by independent stationary and ergodic processes. We show that this approximation is exact as the cache size and the number of contents go to infinity. This extends earlier results for the independent reference model. Moreover, we establish results not only for the aggregate cache hit probability but also for every individual content. Last, we obtain bounds on the rate of convergence.
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Submitted on : Tuesday, July 10, 2018 - 3:26:09 PM
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Bo Jiang, Philippe Nain, Don Towsley. On the Convergence of the TTL Approximation for an LRU Cache under Independent Stationary Request Processes. ACM Transactions on Modeling and Performance Evaluation of Computing Systems, ACM, 2018, 3 (4). ⟨hal-01673272v4⟩

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