A Fluid Limit for Cache Algorithms with General Request Processes

Osogami, Takayuki

doi:10.1109/infcom.2009.5062242

“…We thank Naoto Miyoshi for his helpful comments on technical aspects of the paper and Shannon Jacobs for his English rewriting on an earlier version of the paper. A five-page extended abstract of a preliminary version of the paper appears in [17].…”

Section: Acknowledgementsmentioning

confidence: 99%

A fluid limit for a cache algorithm with general request processes

Osogami

¹

2010

Advances in Applied Probability

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We introduce a formal limit, which we refer to as a fluid limit, of scaled stochastic models for a cache managed with the least-recently-used algorithm when requests are issued according to general stochastic point processes. We define our fluid limit as a superposition of dependent replications of the original system with smaller item sizes when the number of replications approaches ∞. We derive the average probability that a requested item is not in a cache (average miss probability) in the fluid limit. We show that, when requests follow inhomogeneous Poisson processes, the average miss probability in the fluid limit closely approximates that in the original system. Also, we compare the asymptotic characteristics, as the cache size approaches ∞, of the average miss probability in the fluid limit to those in the original system.

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Performance evaluation of the random replacement policy for networks of caches

Gallo¹,

Kauffmann

²

,

Muscariello

³

et al. 2014

Performance Evaluation

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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.

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Performance evaluation of the random replacement policy for networks of caches

Gallo

¹

,

Kauffmann

²

,

Muscariello

³

et al. 2012

Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE Joint International Conference on Measurement and Modeling of Computer Syste

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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.

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A Fluid Limit for Cache Algorithms with General Request Processes

Cited by 3 publications

References 16 publications

A fluid limit for a cache algorithm with general request processes

A fluid limit for a cache algorithm with general request processes

Performance evaluation of the random replacement policy for networks of caches

Performance evaluation of the random replacement policy for networks of caches

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