TTL Approximations of the Cache Replacement Algorithms LRU(m) and h-LRU

Abstract : Computer system and network performance can be significantly improved by caching frequently used information. When the cache size is limited, the cache replacement algorithm has an important impact on the effectiveness of caching. In this paper we introduce time-to-live (TTL) approximations to determine the cache hit probability of two classes of cache replacement algorithms: h-LRU and LRU(m). These approximations only require the requests to be generated according to a general Markovian arrival process (MAP). This includes phase-type renewal processes and the IRM model as special cases. We provide both numerical and theoretical support for the claim that the proposed TTL approximations are asymptotically exact. In particular, we show that the transient hit probability converges to the solution of a set of ODEs (under the IRM model), where the fixed point of the set of ODEs corresponds to the TTL approximation. We use this approximation and trace-based simulation to compare the performance of h-LRU and LRU(m). First, we show that they perform alike, while the latter requires less work when a hit/miss occurs. Second, we show that as opposed to LRU, h-LRU and LRU(m) are sensitive to the correlation between consecutive inter-request times. Last, we study cache partitioning. In all tested cases, the hit probability improved by partitioning the cache into different parts—each being dedicated to a particular content provider. However, the gain is limited and the optimal partition sizes are very sensitive to the problem's parameters.
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Nicolas Gast, Benny van Houdt. TTL Approximations of the Cache Replacement Algorithms LRU(m) and h-LRU. Performance Evaluation, Elsevier, 2017, ⟨10.1016/j.peva.2017.09.002⟩. ⟨hal-01622059⟩

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