Analysis of cache memory strategies for some image processing applications

Neural networks and image processing algorithms typically use very large amounts of data and usually this data is processed iteratively. Hence, the issue of cache memories for enhancing the processing speed is important. A particularly important model that fits these applications is the simple loop model. Here, the exact solution for the cache memory simple loop model under random replacement is given using an urn model and the theory of Markov chains. The probability distribution is obtained as a quotient of Stirling Numbers of the Second Kind. It is also shown that asymptotically the number of elements in the urns follows a Truncated at Zero Poisson Distribution