A tile for use in a tiled storage array provides re-organization of values within the tile array without requiring sophisticated global control. The tiles operate to move a requested value to a front-most storage element of the tile array according to a global systolic clock. The previous occupant of the front-most location is moved or swapped backward according to the systolic clock, and the new occupant is moved forward according to the systolic clock, according to the operation of the tiles, while providing for multiple in-flight access requests within the tile array. The placement heuristic that moves the values is determined according to the position of the tiles within the array and the behavior of the tiles. The movement of the values can be performed via only next-neighbor connections of adjacent tiles within the tile array.