Performance evaluation of the random replacement policy for networks of caches

Abstract

The overall performance of content distribution networks as well as recently proposed information-centric networks rely on both memory and bandwidth capacities. In this framework, the hit ratio is the key performance indicator which captures the bandwidth / memory tradeoff for a given global performance. This paper focuses on the estimation of the hit ratio in a network of caches that employ the Random replacement policy. Assuming that requests are independent and identically distributed, general expressions of miss probabilities for a single Random cache are provided as well as exact results for specific popularity distributions. Moreover, for any Zipf popularity distribution with exponent α > 1, we obtain asymptotic equivalents for the miss probability in the case of large cache size. We extend the analysis to networks of Random caches, when the topology is either a line or a homogeneous tree. In that case, approximations for miss probabilities across the network are derived by assuming that miss events at any node occur independently in time; the obtained results are compared to the same network using the Least-Recently-Used discipline, already addressed in the literature. We further analyze the case of a mixed tandem cache network where the two nodes employ either Random or Least-Recently-Used policies. In all scenarios, asymptotic formulas and approximations are extensively compared to simulations and shown to perform very well. Finally, our results enable us to propose recommendations for cache replacement disciplines in a network dedicated to content distribution. These results also hold for a cache using the First-In-First-Out policy.

Analyzing Replacement Policies in List-Based Caches with Non-Uniform Access Costs

“…Having determined the asymptotics of h(x, y), we can now use the Euler-Maclaurin formula [34] to rewrite (13) in terms of the variables m and n. For an arbitrary function f (x), the formula may be written as…”

Transient and Steady-state Regime of a Family of List-based Cache Replacement Algorithms

“…Considerable efforts have also been made to develop approximation methods to analyze networks of caches [23,11,26,14,25,5]. Some of these methods are iterative in nature and require the repeated solution of isolated caches, e.g., [26].…”

“…The proof of Theorem 7 is based on the construction of an iterative scheme z t+1 = G(z t ) that converges to the unique fixed point given by Equation (14). This iteration provides an efficient method to compute the fixed-point, as it converges exponentially fast to the fixed point and each iteration takes O(nh) time, that is, is linear in the number of items times the number of lists.…”

“…Further, these results are of little practical use due to the curse of dimensionality (except for FIFO and RANDOM). As such many approximation methods have been proposed for single caches [9,8,13,25,5] as well as for networks of caches [23,11,26,14,25,5]. While these approximations have often been shown to result in highly accurate predictions for the miss probability (under the IRM model), their theoretical support is most often rather limited.…”

Hybrid system analysis and design for scale-out storage environments

“…[178] measures the cache hit/miss ratio and response time under different settings to evaluate their multilevel caching system. [179] calculates the caching miss ratio to evaluate the Nanyang Technological University Singapore network cache performance by their analytical model. [180] proposes to use prefetch precision, pre-fetch coverage and pre-fetch pollution to evaluate the system performance under different pre-fetching policies, and select the best suitable prefetching policy.…”