Transient and Steady-state Regime of a Family of List-based Cache Replacement Algorithms

In this paper we study the performance of a family of cache replacement algorithms. The cache is decomposed into lists. Items enter the cache via the first list. An item enters the cache via the first list and jumps to the next list whenever a hit on it occurs. The classical policies FIFO, RANDOM, CLIMB and its hybrids are obtained as special cases. We present explicit expressions for the cache content distribution and miss probability under the IRM model. We develop an algorithm with a time complexity that is polynomial in the cache size and linear in the number of items to compute the exact miss probability. We introduce lower and upper bounds on the latter that can be computed in a time that is linear in the cache size times the number of items.