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.

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

“…Note that the TTL approximation for general independent stationary and ergodic processes takes the same form as for renewal processes [18], which is not surprising in view of Theorem 2 in [19].…”

“…It immediately follows that (53) holds. 19 The next proposition provides a faster rate of convergence under a different condition, (R6), which says the change in the value of a cdf is bounded by a constant multiple of the relative change in its argument. In fact, we only need (25) to hold with t = T n .…”

Analytical characterization of cache replacement policy impact on content delivery time in information‐centric networks

“…Also, it is proved that a constant time‐to‐live (TTL) policy minimizes/maximizes the hit probability if the requests' renewal function is convex/concave. TTL approximations were introduced in Gast and Houdt to determine the cache hit probability of two classes of cache replacement algorithms: h‐LRU and LRU(m). Also, the presence of invalidation events with LRU has been taken into account by authors in Detti et al They used these approximations to compare the performance of the mentioned policies mostly regarding cache miss/hit probability.…”

“…24 There are many papers evaluating the performance of cache replacement policies. [25][26][27][28][29][30][31] The characterization of the miss sequence of the LRU cache was fulfilled in Jelenković and Kang. 26 They discovered that the missing stream from one single cache is approximated well by the superposition of some asymptotically independent renewal processes.…”

A Decomposition Framework for Optimal Edge-Cache Leasing

“…An important body of work concerns the joint edge-cache placement and wireless user association problem. One can identify two different content placement approaches: dynamic caching [6], [8], [12]- [18], and prefetching [4], [5], [7], [10], [11], [19]- [21]. This work falls into the second category.…”