Expected performance of the shelf heuristic for 2-dimensional packing

The shelf heuristic is an on-line algorithm to pack oriented rectangles into an open-ended bin of unbounded height. The heuristic uses space effectively by partitioning the bin into 'shelves' into which rectangles of nearly equal heights are packed. We analyze the expected performance of the shelf heuristic when the dimensions of the rectangles are identically and independently distributed according to a uniform distribution on (0, 1]. In addition, we discuss how to choose the shelf sizes to optimize expected performance.