Birthday Paradox, Coupon Collectors, Caching Algorithms and Self-Organizing Search
@article{Flajolet1992BirthdayPC,
title={Birthday Paradox, Coupon Collectors, Caching Algorithms and Self-Organizing Search},
author={Philippe Flajolet and Dani{\`e}le Gardy and Lo{\"y}s Thimonier},
journal={Discret. Appl. Math.},
year={1992},
volume={39},
pages={207-229}
}426 Citations
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Mathematics
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It was recently proved by Jelenković and Radovanović (2004) that the least-recently-used (LRU) caching policy, in the presence of semi-Markov-modulated requests that have a generalized Zipf's law…
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Computer Science, Mathematics
The surprising insensitivity of LRU caching performance demonstrates its robustness to changes in document popularity, and the derived asymptotic result and simulation experiments are in excellent agreement, even for relatively small cache sizes.
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Mathematics
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A very simple asymptotic relation is derived between the expectation of the waiting time for a partial collection in the CCP, and the Miss rate of a LRU cache.
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Computer Science, Mathematics
This paper considers the class f* of stochastic matrices P such that move-to-front is optimal among on-line rules, with respect to the stationary search cost, and produces explicitly a large subclass of f*.
Least-recently-used caching with dependent requests
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Computer Science, Mathematics
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Mathematics, Computer Science
It is shown that, when the (limiting) request distribution has a heavy tail (e.g., generalized Zipf ’s law), PR = n ∼ c/nα as n→ ∞, α > 1, then the limiting stationary search cost distribution, or the least-recently used (LRU) caching fault probability, satisfies the law.
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An analysis of the sequence of expected communication costs is enabled by reducing their computation to that of three-dimensional arrays of certain probabilities, for which a recursion formula and an asymptotic expansion can be given.
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Computer Science
2021 19th International Symposium on Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt)
This paper derives a simple yet accurate approximation for the LRU content-wise hitrates under Zipf-distributed requests, in the regime of a large content population, and justifies the accuracy of these approximations by showing analytically that the characteristic time concentrates sharply around its mean.
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