A simple analysis of the LRU buffer policy and its relationship to buffer warm-up transient

A simple analysis for the transient buffer hit probability for a system starting with an empty buffer is presented. The independent reference model (IRM) is used for buffer accesses. It is shown that the expected buffer hit probability when the buffer becomes full is virtually identical to the steady state buffer hit probability when the replacement policy is least recently used (LRU). The method is generalized to estimate the transient behavior of the LRU policy starting with a non-empty buffer. It is shown that this method can be used to estimate the effect of a load surge on the buffer hit probability. It is also shown that after a short load surge, it can take much longer than the surge duration for the buffer hit probability to return to its steady state value