The effect of whitespace and aspect ratio on wirelength and timing

Whitespaces (empty space) are inserted in layouts in order to increase the routing resources of the chip. Have you ever studied the impact of whitespace (and aspect ratio) on timing and wirelength, by say increasing the whitespace from 0% to 100% and evaluate the impact on both wirelength and timing. Can you predict how this will look like? For a 300 mm wafer, can you parameterize the relationship between the number of dies produced, timing, die aspect ratio, wirelength and whitespace?