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 LRU and MRU caching nodes , and numerically compare with a simple "Incremental Rank Progress" (CLIMB) and random eviction/replacement methods under a Zipf popularity distribution. The range of cache hit probabilities is smaller under MRU and larger under IRP compared to LRU.