Markov Paging

Abstract

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This paper considers the problem of paging under the assumption that the sequence of pages accessed is generated by a Markov chain. We use this model to study the fault-rate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithm that achieves optimal fault-rate on any Markov chain. Next, we address the problem of devising a paging strategy with low fault-rate for a given Markov chain. We show that a number of intuitive approaches fail. Our main result is a polynomial-time procedure that, on any Markov chain, will give a paging algorithm with fault-rate at most a constant times optimal. Our techniques show also that some algorithms that do poorly in practice fail in the Markov setting, despite known (good) performance guarantees when the requests are generated independently from a probability distribution.