Properties of the Miss Ratio for a 2-Level Storage Model with LRU or FIFO Replacement Strategy and Independent References

We consider the behavior of a 2-level storage system operating with the LRU or the FIFO replacement strategy where accesses to the main storage are described by the independent reference model (IRM). Let the size of main storage be m. We prove that the miss ratio (i.e. the steady-state probability that the item currently required is not in main storage) exhibits the following properties: The miss ratio is a convex function of m under LRU, The following function of the miss ratio, (1 ? miss ratio)=m, is non-increasing in m under FIFO, The miss ratio is a Schur-convex function of the reference probabilities under FIFO. Last, we disprove some results claimed earlier in the literature.