Critical sizing of LRU caches with dependent requests

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 popularity distribution, is asymptotically insensitive to the correlation in the request process. However, since the previous result is asymptotic, it remains unclear how small the cache size can become while still retaining the preceding insensitivity property. In this paper, assuming that requests are generated by a nearly completely decomposable Markov-modulated process, we characterize the critical cache size below which the dependency of requests dominates the cache performance. This critical cache size is small relative to the dynamics of the modulating process, and in fact is sublinear with respect to the sojourn times of the modulated chain that determines the dependence structure.

[1]  Robert E. Tarjan,et al.  Self-adjusting binary search trees , 1985, JACM.

[2]  Jon Louis Bentley,et al.  Amortized analyses of self-organizing sequential search heuristics , 1985, CACM.

[3]  Philippe Flajolet,et al.  Birthday Paradox, Coupon Collectors, Caching Algorithms and Self-Organizing Search , 1992, Discret. Appl. Math..

[4]  C. Klüppelberg,et al.  Large claims approximations for risk processes in a Markovian environment , 1994 .

[5]  James Allen Fill,et al.  On the distribution of search cost for the move-to-front rule , 1996, Random Struct. Algorithms.

[6]  Virgílio A. F. Almeida,et al.  Characterizing reference locality in the WWW , 1996, Fourth International Conference on Parallel and Distributed Information Systems.

[7]  James Allen Fill,et al.  An exact formula for the move-to-front rule for self-organizing lists , 1996 .

[8]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[9]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[10]  A. Lazar,et al.  Subexponential asymptotics of a Markov-modulated random walk with queueing applications , 1998, Journal of Applied Probability.

[11]  Li Fan,et al.  Web caching and Zipf-like distributions: evidence and implications , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[12]  P. Jelenkovic.  Asymptotic approximation of the move-to-front search cost distribution and least-recently used caching fault probabilities , 1999 .

[13]  Neal E. Young,et al.  On-Line Paging Against Adversarially Biased Random Inputs , 2000, J. Algorithms.

[14]  Predrag R. Jelenkovic,et al.  Asymptotic insensitivity of least-recently-used caching to statistical dependency , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[15]  Predrag R. Jelenkovic,et al.  Optimizing LRU Caching for Variable Document Sizes , 2004, Combinatorics, Probability and Computing.

[16]  Predrag R. Jelenkovic,et al.  Least-recently-used caching with dependent requests , 2004, Theor. Comput. Sci..