Properties of the miss ratio for a 2-level storage model with LRU or FIFO replacement strategy and independent references

The behavior of a two-level storage system operating with the least recently used (LRU) or the first-in, first-out (FIFO) replacement strategy, where accesses to the main storage are described by the independent reference model (IRM), is discussed. Let the size of main storage be m. It is proved 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 function (1-miss ratio)/m is nonincreasing in m under FIFO, and the miss ratio is a Schur-convex function of the reference probabilities under FIFO