Before revision:  We obtain a novel closed-form stationary invariant distribution for  LRU and MRU caching nodes , and numerically compare with a simple "Incremental Rank Progress" caching mechanism where cache hits result in slower progress through the ranks than LRU.
After revision:  We obtain a novel closed-form stationary invariant distribution for Markov model of a generalization of LRU and MRU caching nodes , and numerically compare with a simple "Incremental Rank Progress" caching mechanism where cache hits result in slower progress through the ranks than LRU.