Probabilistic aspects of caching are considered. The caching serves to keep popular contents inside a memory unit called 'cache' to be able to access them quickly. Using extreme value theory we propose a caching strategy called Cluster Caching Rule driven by content popularity that may change in time.
A non-Poisson request arrival process is used when requests are statistically correlated. The idea of the new approach is to locate in cache only contents whose popularity exceeds a sufficiently large threshold. Due to dependence and possible heavy-tailed distribution of inter-requests and inter-arrival times of documents, the popularity process builds clusters of exceedances. The cluster and inter-cluster sizes are geometrically distributed as derived in Markovich (2014). We use it to calculate means of the cache utilization and occupancy.
We escape assumptions like a constant size of content and a Poisson request process that are typical in the literature.
