A method of providing access to a plurality of values within a storage device implementing a single level of a cache memory hierarchy wherein the storage device comprises multiple storage tiles having an ordered arrangement in a plurality of electrical pathways interconnecting the multiple storage tiles from a front-most one of the multiple storage tiles to a back-most one of the multiple storage tiles, the method_comprising: storing the plurality of values in the multiple storage tiles that provide storage for the single level of the cache memory hierarchy, wherein the storing stores the plurality of values in unique corresponding ones of the multiple storage tiles; characterized by in response to an access request implicating one of the plurality of values not being already present in the front-most one of the multiple storage tiles, moving the requested value to the front-most one of the multiple storage tiles from another one of the multiple storage tiles in which the one of the plurality of values is present according to a systolic pulse and a placement heuristic that maintains the uniqueness of the values within the multiple storage tiles; moving a displaced value from the front-most storage tile backwards along one of said plurality of electrical pathways toward the back-most storage tile according to the systolic pulse, wherein multiple move-to-front operations for accessing multiple values are simultaneously maintained in-progress among the multiple storage tiles; and pushing-back values of said plurality of values by swapping the values among neighboring ones of the multiple storage tiles until one of the storage tiles having an empty storage location is reached or if the values are already stored in the back-most one of the multiple storage tiles swapping the values out into a backing store coupled to the back-most one of the multiple storage tiles. storing the plurality of values in the multiple storage tiles that provide storage for the single level of the cache memory hierarchy, wherein the storing stores the plurality of values in unique corresponding ones of the multiple storage tiles; characterized by in response to an access request implicating one of the plurality of values not being already present in the front-most one of the multiple storage tiles, moving the requested value to the front-most one of the multiple storage tiles from another one of the multiple storage tiles in which the one of the plurality of values is present according to a systolic pulse and a placement heuristic that maintains the uniqueness of the values within the multiple storage tiles; moving a displaced value from the front-most storage tile backwards along one of said plurality of electrical pathways toward the back-most storage tile according to the systolic pulse, wherein multiple move-to-front operations for accessing multiple values are simultaneously maintained in-progress among the multiple storage tiles; and pushing-back values of said plurality of values by swapping the values among neighboring ones of the multiple storage tiles until one of the storage tiles having an empty storage location is reached or if the values are already stored in the back-most one of the multiple storage tiles swapping the values out into a backing store coupled to the back-most one of the multiple storage tiles.