A tiled storage array provides reduction in access latency for frequently-accessed values by re-organizing to always move a requested value to a front-most storage element of array. The previous occupant of the front-most location is moved backward according to a systolic pulse, and the new occupant is moved forward according to the systolic pulse, preserving the uniqueness of the stored values within the array, and providing for multiple in-flight access requests within the array. The placement heuristic that moves the values according to the systolic pulse can be implemented by control logic within identical tiles, so that the placement heuristic moves the values according to the position of the tiles within the array. The movement of the values can be performed via only next-neighbor connections of adjacent tiles within the array.