It was recently proved in [12] 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 preceding result is asymptotic, it remains unclear how small the cache size can become while still retaining this insensitivity property. In this paper, assuming requests come from a nearly completely decomposable Markov-modulated process, we characterize the critical cache size below which the dependency of requests dominates the cache performance. It appears surprising that the critical cache size is very small, and in fact it is sub-linear to the sojourn times of the modulated chain that determines the dependency structure.
By: Predrag Jelenkovic; Ana Radovanovic; Mark S. Squillante
Published in: RC23779 in 2005
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