Abstract
Belady’s algorithm defines a strategy for updating cache content in order to achieve the optimum hit rate, based on full information being available about future requests. In this work, we design a Markov state model to analyze and evaluate the hit rate of clairvoyant optimum caching.
We start deriving a new steady state solution for a cache that can store only a single object when requests are independent with arbitrary distribution. Results in literature are restricted to uniform request and we have to transfer them from paging systems to web caches, which refer to slightly different preconditions.
When we follow each specified state transition of the Markov process per request, this leads to an alternative implementation of Belady’s algorithm. Therefore the Markov approach can also be applied as an alternative to Belady’s algorithm for evaluating optimum caching based on request traces, in simulations and other use cases, e.g. for code optimization. Remarkably, the Markov process decides about optimum caching hits per request based on cache content, based on knowledge only of the past without look-ahead.
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Acknowledgements
This work has received funding from the European Union’s Horizon 2020 research and innovation programme in the EU SSICLOPS project <www.ssiclops.eu> under grant agreement No. 644866. This work reflects only the author’s views and the European Commission is not responsible for any use that may be made of the information it contains. The author would like to thank the anonymous reviewer, whose detailed report allowed to improve and correct several parts of this work.
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Hasslinger, G. (2018). Markov Analysis of Optimum Caching as an Equivalent Alternative to Belady’s Algorithm Without Look-Ahead. In: German, R., Hielscher, KS., Krieger, U. (eds) Measurement, Modelling and Evaluation of Computing Systems. MMB 2018. Lecture Notes in Computer Science(), vol 10740. Springer, Cham. https://doi.org/10.1007/978-3-319-74947-1_3
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DOI: https://doi.org/10.1007/978-3-319-74947-1_3
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