Cover a line segment randomly with smaller line segments

Question

Covering a circle randomly with arcs has been well studied in the past (Geometric Probability - Solomon).

But the problem when the circle is changed to a line segment doesn't seem to have been studied before.

I'd like to know if there's any work out there who already obtained the probability distribution of the number and the length of the connected line segments that you get when randomly covering a line segment with another set of shorter segments, which may all be of equal length or have some kind of distribution.

Thanks!

Answer 1

This problem can actually be solved using the exact same method as Chapter 4 of Solomon's geometric probability by using the inclusion-exclusion principle in a similar fashion. A brief outline is available here (although it may contain small errors).

Answer 2

Are you referring to the Parking Problem? See e.g. http://mathworld.wolfram.com/RenyisParkingConstants.html

Answer 3

(Stunning downvote, probably due to the OP, who seems to like their own answers best.)

Invariance principle for the coverage rate of genomic physical mappings might interest you, if only for its list of references. (Caveat: I am the author.)