Abstract
Consider a finite list of items
We show that, when the (limiting) request distribution has a heavy tail (e.g., generalized Zipf's law),
When the request distribution has a light tail
We experimentally demonstrate that the derived asymptotic formulas yield accurate results for lists of finite sizes. This should be contrasted with the exponential computational complexity of Burville and Kingman's exact expression for finite lists. The results also imply that the fault probability of LRU caching is asymptotically at most a factor
Citation
Predrag R. Jelenković. "Asymptotic approximation of the move-to-front search cost distribution and least-recently used caching fault probabilities." Ann. Appl. Probab. 9 (2) 430 - 464, May 1999. https://doi.org/10.1214/aoap/1029962750
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